Wavelength-locked parametric master oscillator power ...549344/FULLTEXT01.pdf · power ampliﬁer for high-energy generation ... power OPOs is the need to use large aperture crystals

Wavelength-locked parametric master oscillator

power amplifier for high-energy generation

at 2 µm

TOMISLAV REŠETAR

Master of Science Thesis

Laser Physics

Department of Applied Physics

School of Engineering Sciences

Royal Institute of Technology

Stockholm, Sweden 2012

ii

TRITA-FYS 2012:69ISSN 0280-316XISRN KTH/FYS/--12:69--SE

iii

Abstract

Development of high energy lasers emitting in the mid-infrared wavelengthregion (2-8 µm) is mainly driven by the potential applications in laser surgery,remote spectroscopy and defence. Free electron lasers can offer beams thatmeet the requirements for such applications, however, they are used mostly inexperimental research because of their size, complexity and cost. A promisingway to fully meet the desired requirements is by nonlinearly converting lightfrom 1 µm, where reliable light sources are available, to longer wavelengths.

In this master’s thesis project, a parametric master oscillator power ampli-fier (MOPA) was built and characterized. The MOPA consisted of two mainstages: the optical parametric oscillator stage (OPO) and the optical paramet-ric amplification stage (OPA). The focus of the experimental work was put onthe construction and characterization of the OPO since its output was used asa seed for the OPA, and, therefore, was playing a crucial role in the overallMOPA performance.

The OPO was utilizing a temperature-controlled large aperture (5x3 mm)periodically polled KTiOPO4 (PPKTP) crystal designed to operate at degen-eracy, converting the input beam at 1064 nm wavelength to the output beam at2128 nm wavelength. A volume Bragg grating (VBG) was used as an outputcoupler, ensuring a spectrally narrow output. The VBG was temperature-controlled, providing a possibility to operate the OPO both at and near degen-eracy. When operating near degeneracy, the conversion efficiency of 37 % andthe output power of 1.3 W was reached, offering the beam quality described bythe M2 value of 8 in horizontal and 10 in vertical direction. The 2 µm pulseswere measured to be 5 ns long and the spectral width FWHM of 0.46 nm (30GHz) was obtained. It was shown that operating at degeneracy resulted inlower efficiency, increased output power instability and further degraded thebeam quality.

The OPA stage consisted of two temperature-controlled large aperture (5x5mm) Rb-doped PPKTP crystals. The conversion efficiency of the OPA wasobserved to increase with both higher pumping powers and higher seedingpowers (saturating at 1 W of seed power). The maximum measured overallMOPA efficiency was 28.4 % while providing the maximum output power of3.75 W. The results suggested that the MOPA efficiency would further improvewith increasing the OPA pumping power. The MOPA beam quality was shownto be a major issue of such setup, having the M2 value of 14 in horizontal and29 in vertical direction. The MOPA spectral properties, as well as the outputpower stability were completely inherited from the OPO output.

iv

Acknowledgements

First and foremost, Nicky Thilmann, I would like to express my gratitude for yoursupervision. Thank you for teaching me how to get round numerous practical prob-lems in the lab, from cleaning mirrors onwards. I am also very thankful for yourhelp in clearing the theoretical concepts in my head and helping me interpret theexperimental results. Most importantly, thank you for believing that everythingwill eventually fit in its place when I myself had troubles to do so.

Prof. Pasiskevicius, I am most grateful for allowing me to work on this project,your supervision and sharing your knowledge and understanding. I am also trulythankful for your generous support and help regarding my future aspirations.

Hoon Yang and Charlotte Liljestrand, I would like to state my sincere thankfulnessfor your company, late night conversations and the support during my periodic ex-istential crises.

Gustav Lindgren, Finn Klemming Eklöf and Ashraf Mohamedelhassan, thank youfor sharing the office with me and for all the big and small talks during my stay.

Prof. Fredrik Laurell, thank you for letting me inside the Laser Physics corridor inthe first place and, together with Lars-Gunnar Andersson occasionally expressinginterest in the progress of my work.

Carlota Canalias, Andrius Zukauskas and Gustav Strömqvist, thank you for pro-viding the crystals used in this project and, also, Markus Henriksson, thank you forproviding the VBGs and their temperature-controlled holder.

Outside KTH, people that played a major role in my education and to whom I havean opportunity to express my thankfulness so rarely: Prof. Adrijan Barić, MirtaDagmar Muhić, Marijana Srebrenović, Nenad Cvijanović and Zvjezdana Zrinski.Thank you.

People having a permanent special place in my heart: Mihael Bošnjak, Tanja Grilec,Matija Koščica, Davor Kristijan, Vedran Lastovčić, Nereo Markulić, Lana Novoseland Marijan Stupar. A proper thank you for you would require a thesis on its own.

Mama, Tata, Seka, nothing would be possible without your selfless support throughthe years, I am infinitely grateful for that.

Finally, liefste Stephanie, thank you, and see you in a month!

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The objective of this work . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

I Theoretical background 5

2 Concepts from the laser theory 7

2.1 Basic laser operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Gaussian beam and the ABCD law . . . . . . . . . . . . . . . . . . . 8

2.2.1 Gaussian beam and its parameters . . . . . . . . . . . . . . . 8

2.2.2 Propagation of a Gaussian beam through an optical systemdescribed by an ABCD matrix . . . . . . . . . . . . . . . . . 11

2.2.3 Higher order modes of a Gaussian beam . . . . . . . . . . . . 11

2.3 Optical cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Longitudinal mode spacing . . . . . . . . . . . . . . . . . . . 12

2.3.2 Finite aperture cavities and the resonator Fresnel number . . 13

2.4 Spectral control of lasers . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.1 Volume Bragg gratings . . . . . . . . . . . . . . . . . . . . . . 14

2.5 The knife-edge beam spot size measurement . . . . . . . . . . . . . . 16

2.5.1 The M2 estimation . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Nonlinear optics 19

3.1 Nonlinear optical response of materials . . . . . . . . . . . . . . . . . 19

3.1.1 Origins of nonlinearity . . . . . . . . . . . . . . . . . . . . . . 19

3.1.2 Second order nonlinear processes . . . . . . . . . . . . . . . . 20

3.1.3 Energy and momentum conservation . . . . . . . . . . . . . . 21

3.1.4 Quasi phase matching . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Optical parametric processes . . . . . . . . . . . . . . . . . . . . . . 24

3.2.1 Optical parametric oscillation . . . . . . . . . . . . . . . . . . 26

3.2.2 Optical parametric amplification . . . . . . . . . . . . . . . . 27

v

vi CONTENTS

II Experiments 29

4 Pump laser characterization 314.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Output power measurements . . . . . . . . . . . . . . . . . . . . . . 31

4.2.1 Laser output power range . . . . . . . . . . . . . . . . . . . . 314.2.2 Output power stability . . . . . . . . . . . . . . . . . . . . . . 334.2.3 Beam polarization measurement . . . . . . . . . . . . . . . . 33

4.3 Spectrum measurement . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Beam quality investigation . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4.1 Beam spot size measurements and M2 estimation . . . . . . . 364.4.2 Beam profile visualization using a pyroelectric array camera . 37

5 OPO characterization 395.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.2 Spectrum measurement . . . . . . . . . . . . . . . . . . . . . . . . . 405.3 Power measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3.1 Output power and conversion efficiency . . . . . . . . . . . . 425.3.2 Output power stability . . . . . . . . . . . . . . . . . . . . . . 45

5.4 Pulse shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.5 M2 measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6 MOPA characterization 516.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2 OPA investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.2.1 OPA with one crystal vs. two crystals . . . . . . . . . . . . . 526.2.2 OPA conversion efficiency and pump depletion . . . . . . . . 53

6.3 MOPA power measurements . . . . . . . . . . . . . . . . . . . . . . . 556.3.1 Overall conversion efficiency . . . . . . . . . . . . . . . . . . . 566.3.2 Output power stability . . . . . . . . . . . . . . . . . . . . . . 56

6.4 Spectrum measurements . . . . . . . . . . . . . . . . . . . . . . . . . 576.5 Beam quality, M2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7 Discussion and outlook 617.1 Discussion and summary . . . . . . . . . . . . . . . . . . . . . . . . . 617.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Bibliography 65

List of abbreviations and symbols

The following abbreviations and symbols for physical quantities are used through-out the thesis.

AR anti reflectiveBPM birefringent phase matchingDFG difference frequency generationFWHM full width at half maximumHR highly reflectiveHWP half wave plateMOPA master oscillator power amplifierOPA optical parametric amplification/-erOPG optical parametric generationOPO optical parametric oscillation/-orPPKTP periodically polled KTiOPO4 nonlinear crystalQPM quasi phase matchingSFG sum frequency generationSHG second harmonic generationTFP thin film polarizerZGP ZnGeP2 nonlinear crystal

c = λν speed of light in vacuumE energyE electric fieldε0 permittivity of vacuumI = |E|2ε0cn/2 intensityK = 2π/Λ grating vectork = 2πn/λ wavenumberλ vacuum wavelengthΛ spatial periodn refractive indexν frequencyω = 2πν angular frequencyP powerP polarization densityR (power) reflectivityr = xx + yy + zz spatial coordinateT temperature

vii

Chapter 1

Introduction

1.1 Background

There are several main applications motivating the development of reliable mid-infrared1 laser sources. It has been shown that considerable improvement in tissueablation for purposes of corneal surgery can be achieved by using optical parametricoscillators in the 2.94 µm water absorption wavelength region in comparison to thepresently used techniques [1]. Also, experiments using free-electron lasers showedthat laser light in the 6.1 - 6.45 µm wavelength region produces minimal collateraldamage in some neural and ocular tissues [2, 3] and, therefore, considerable efforthas been done to develop laser sources for the purpose of minimally invasive surgery[4, 5]. Another motivation to develop compact and reliable laser sources in the mid-infrared wavelength region are the military defence requirements against homingmissiles [6]. An increasingly important application of such lasers could also be inremote spectroscopy for improving climate models since the molecules of gassessuch as methane, carbon dioxide and water vapour have absorption bands in themid-infrared region [7].

The requirements for such lasers are various and dependant on the particular ap-plication, however, generally, one usually requires good beam quality, high efficiencyand mechanical robustness (especially for remote applications), high enough pulseenergies and good spectral properties. In most cases, the mentioned requirementsare conflicting and very difficult to achieve. A promising approach for reachingthe mid-infrared wavelength region is by using nonlinear conversion of 1 µm lightsupplied by highly reliable and well developed Nd:YAG Q-switched lasers. By us-ing optical parametric oscillators (OPOs) with quasi phase matching (QPM), onecan, in theory, achieve any desired wavelength as long as a nonlinear crystal doesnot absorb it. Recent development on large aperture and high quality periodicallypolled KTiOPO4 (PPKTP) crystals made it possible to operate at high pulse ener-gies and achieve high conversion efficiencies [8]. The problem with KTP, however, isthat it starts to absorb wavelengths longer than 3 µm. For that reason, a cascaded

1For the purpose of this thesis defined as the wavelength region between 2 and 8 µm.

1

2 CHAPTER 1. INTRODUCTION

nonlinear conversion scheme can be applied to reach mid-infrared wavelengths. Wellperforming cascaded nonlinear conversion was show in [9] and [10] by using a PP-KTP OPO to reach 2 µm and another OPO, using a ZnGeP2 (ZGP) crystal toreach longer wavelengths.

Figure 1.1. Cascaded scheme for reaching mid-infrared wavelengths using a PPKTPOPO as a pumping source for the ZGP OPO.

The spectrum of the first OPO has to be narrower than the gain bandwidth of ofthe second one to achieve efficient pumping. OPOs with dielectric mirrors generallyproduce a broad output spectrum and, therefore, a line narrowing technique needsto be employed. One way to do so is by using a Fabry-Perot etalon, however, usingvolume Bragg gratings (VBGs) for that purpose results in both higher efficiency andsuperior spectral characteristics. An extensive research on using VBGs as outputcouplers in OPOs is presented in [11].

The final aspect discussed here is the beam quality. The problem with highpower OPOs is the need to use large aperture crystals which results in high res-onator Fresnel number cavities and, consequentially, poor beam quality. To possiblycircumvent this problem and extend the output power range beyond the OPO lim-its, another scheme for pumping the final conversion stage can be utilized. The ideais to use an OPO at lower powers and amplify its output in an additional stageutilizing optical parametric amplification (OPA). Such scheme is called the para-metric master oscillator power amplifier (MOPA) and is schematically presented inthe figure below.

Figure 1.2. Basic MOPA schematic representation.

1.2 The objective of this work

The purpose of this thesis is to build an experimental MOPA setup for light conver-sion from 1064 nm to 2128 nm wavelength and optimize its properties in terms ofconversion efficiency, beam quality and spectrum. Since many of the MOPA outputbeam characteristics directly depend on the OPO output, the OPO performance

1.3. OUTLINE OF THE THESIS 3

is to be thoroughly investigated and optimized. The OPO is supposed to bewavelength-locked by a VBG for spectral narrowing. Also, the possibility of tuningthe OPO output wavelength to operate at degeneracy by VBG temperature controlis to be explored. Special attention should be given to the output beam qualitybehaviour as the MOPA should ultimately serve as a pump source for another con-version stage.

1.3 Outline of the thesis

The thesis is divided into two parts. Part I discusses key theoretical concepts usedin this thesis and Part II presents the the results of the experiments performed inthe laboratory. A brief outline by chapters is given below.

Chapter 2 discusses some of the basic theoretical concepts from the theory of lasers:generation of laser light, Gaussian beams, the M2 value, optical cavities and spec-tral control of lasers.

In chapter 3, some of the the principles of nonlinear optics relevant to this workare presented: nonlinear interaction between light and matter and second ordernonlinear processes. The focus is put on optical parametric oscillation and opticalparametric amplification, essential to MOPA operation.

Chapter 4 briefly presents the characterization of the pump laser used in this thesisto serve as a starting point for the design of the OPO and the MOPA and, later on,evaluation of their performance.

Chapter 5 presents the investigation of the OPO performance in terms of the con-version efficiency, spectral tuning, stability, pulse shapes and beam quality.

In Chapter 6, firstly, the OPA performance is presented alone and then, finally, theoverall MOPA output beam properties are discussed.

Chapter 7 summarises and discusses the outcomes of the experimental investigationand offers an outlook on further research.

Part I

Theoretical background

5

Chapter 2

Concepts from the laser theory

This chapter gives a short overview of some of the basic concepts from the lasertheory relevant to this work. The reason for this lies in the fact that OPOs generallyhave many similarities with lasers1 and, therefore, the theoretical concepts presentedin this chapter are later on used to discuss the experimental results.

2.1 Basic laser operation

Generally, a laser can be seen as an optical oscillator [12]. In order for an opticalelectromagnetic wave to oscillate in a certain system, two main conditions haveto be met: firstly, the system has to have a positive feedback, i.e. the wave hasto interfere constructively with itself and, secondly, the system has to amplify thewave in order to compensate for the losses. Practically, such a system is realised byputting a gain (amplifying) medium inside an optical cavity as schematically shownin Figure 2.1.

Figure 2.1. Basic laser operation.

1A major difference between the two lies in the fact that an OPO does not store energy in thegain medium and, also, nonlinear processes are relatively fast (order of fs) [11].

7

8 CHAPTER 2. CONCEPTS FROM THE LASER THEORY

In the simplest case, the origin of losses in a system can be divided into twomain categories: internal losses in the cavity (i.e. due to scattering or absorption)and mirror losses. Normally, one of the mirrors is designed to transmit a certainportion of the generated light as the laser output and is therefore called the outputcoupler. Amplification of light waves, on the other hand, is possible due to theprocess of stimulated emission taking place in the gain medium. A crucial conditionfor stimulated emission to dominate over stimulated absorption is the populationinversion, that is when more atoms/molecules are in the excited state than in thelower state. Since that condition is normally not satisfied for laser media at roomtemperature, energy needs to be delivered to the system. This process is usuallyreferred to as pumping. Already from this simple picture one of the fundamentalproperties of lasers can be concluded: by gradually increasing the pumping powerthere exists a certain point where the system gain overcomes the losses and thispoint is called the laser threshold. Figure 2.2 shows an example of a three-level gainmedium and the most relevant processes for laser operation: stimulated emissionand stimulated absorption (pumping). Additionally, two more processes are worthmentioning here: spontaneous emission and nonradiative decay to indicate that alaser can never be perfectly monochromatic nor perfectly efficient.

Figure 2.2. Three-level pumping scheme and the following processes: a-stimulatedabsorption, b-fast (nonradiative) decay, c-nonradiative decay d-spontaneous emissionand e-stimulated emission.

2.2 Gaussian beam and the ABCD law

A certain percentage of photons generated in the laser gain medium exit the laserthrough the output coupler in the form of a laser beam. This section presentsmathematical tools which are useful for predicting the behaviour of laser beamswhen propagating through linear media, namely the Gaussian beam and the ABCDlaw.

2.2.1 Gaussian beam and its parameters

In the field of optics, a particularly interesting outcome of Maxwell’s equations isthe paraxial approximation of Helmholtz’s equation as it assumes a slow variation

2.2. GAUSSIAN BEAM AND THE ABCD LAW 9

of the spatial distribution of the electric field in the direction of propagation. Inthat case, the complex amplitude of the electric field can be written as E(r) =A(r)e−ikz where A(r) is the complex envelope of the electric field modulating aplane wave given by the exponential term. For many applications the magnitudeof the complex envelope2 of a laser beam can be approximated with a Gaussiandistribution. Moreover, a common way of expressing the beam quality is done bycomparing the profile of a given beam with a Gaussian profile as the ideal case. Theevolution of the complex envelope of a Gaussian beam along the propagation axisz can be written as following [12]:

A(r) =A0

Q(z)· exp

(

−ik · x2 + y2

2Q(z)

)

, (2.1)

where A0 is a constant and Q represents the complex Gaussian beam parameter:

1

Q(z)=

1

R(z)− i

(

λM2

πW 2(z)

)

. (2.2)

At a certain position z1 on the propagation axis R(z1) represents the radius ofcurvature of the wavefront and W (z1) represents the beam spot size which is thedistance from the point (0, 0, z1) in the x − y plane where the field amplitude dropsby 1/e or, equivalently, intensity drops by 1/e2. A very important parameter isintroduced in the above equation, that is the M2. In the case of a Gaussian beamprofile M2 = 1 and its value increases as the beam profile deviates further from aGaussian. Figure 2.3 represents the comparison of the beam profile with M2 = 2with respect to the ideal case with M2 = 1.

Electric field amplitude

0

0.2

0.4

0.6

0.8

1

x [mm]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

M2=1

M2=2

W(x,z1)

W(x,z1)Am/e

Am/e

Am

Am

Figure 2.3. Transverse electric field distribution of a Gaussian beam with M2 = 1and M2 = 2.

2The radial intensity distribution is proportional to the square of the magnitude of the complexenvelope of the electric wave and is often referred to as the beam profile. For a Gaussian complexenvelope the intensity also has a Gaussian shape.


Assuming R = ∞ at z = 0, the spot size has a minimum value and is denotedas W0. The beam profile can be expressed as following:

A(r) =A0

izR· W0

W (z)exp

[

−(

x2 + y2

W (z)2

)]

exp

[

−ik ·(

x2 + y2

2R(z)

)]

exp (iφ(z)) , (2.3)

with W (z), R(z) and φ(z) given by the following expressions:

W 2(z) = W 20

[

1 +

(

z

zR

)2]

(2.4)

R(z) = z

[

1 +

(

z

zR

)2]

(2.5)

φ(z) = tan−1(

z

zR

)

. (2.6)

The parameter zR is called the Rayleigh range and is defined as follows:

zR =πW 2

0

M2λ. (2.7)

The Rayleigh range is the distance from the beam waist position at which the thebeam spot size (radius) increases by

√2 or, in other words, the spot area doubles.

Finally, the definition of the divergence angle is given by:

θd =M2λ

πW0. (2.8)

From the above equations it can be concluded that, essentially, the M2 value ismultiplying λ in all expressions since it originates from the defining equation of theGaussian beam parameter [13] (equation 2.2). The above mentioned parametersare illustrated in the following figure for the case of a Gaussian beam with M2 = 1and M2 = 2.

Figure 2.4. Free-space propagation of a Gaussian beam with M2 = 1 and M2 = 2.

2.2. GAUSSIAN BEAM AND THE ABCD LAW 11

2.2.2 Propagation of a Gaussian beam through an optical system

described by an ABCD matrix

Within the paraxial approximation, optical components (lenses, mirrors, propagat-ing media etc.) can be described by the so called ABCD matrices. An ABCDmatrix is a 2x2 matrix which linearly transforms two variables from the input tothe output of an optical component. The main advantage of using such matriceslies in the fact that it is easy to cascade them and, in the end, describe the wholeoptical system with just one ABCD matrix which relates the output to the input.In the ray approximation of light, the two variables are the angle and the position ofthe ray at the input/output. As seen from the previous subsection, the behaviourof a Gaussian beam is completely described by only one parameter: Q. Since itis a complex number it contains independent information in both the real and theimaginary part from which the values of the variables R and W can be calculated.Therefore, it is possible to describe the propagation of a Gaussian beam through anarbitrary linear optical system by an ABCD matrix. The following transformationrelates the Qout to Qin via values A, B, C and D:

1

Qout=

C + (D/Qin)

A + (B/Qin). (2.9)

In this thesis ABCD matrices were used to predict the behaviour of the pumplaser beam when propagating through a system of two to three lenses forming atelescope, used for reducing the beam spot size.

2.2.3 Higher order modes of a Gaussian beam

The profile of a Gaussian beam does not necessarily have to be a bell-shaped Gaus-sian function with only one maximum. There are other solutions for the radial fielddistribution of a beam with the same Q parameter. Those solutions are called higherorder modes and one possible way of describing them is by Hermite polynomials[14]. Equation 2.3 can thus be rearranged as follows:

Amn(r) =A0

izRHm

( √2x

W (z)

)

Hn

( √2y

W (z)

)

W0

W (z)exp

[

−(

x2 + y2

W (z)2

)]

·

·exp

[

−ik ·(

x2 + y2

2R(z)

)]

exp [i(m + n + 1)φ(z)] .

(2.10)

Since Hermitian polynomial of the lowest order H0 equals 1, it can be observedthat, for the indices m = 0 and n = 0, the complex envelope turns into a Gaussiandistribution. This case is usually referred to as the fundamental mode, or the TEM00

mode. The abbreviation TEM stands for Transverse Electric and Magnetic whichmeans that, within the paraxial approximation, the vectors of electric and magneticfields are both perpendicular to each other and to the direction of propagation z.


The beam profiles of some low order Hermite-Gaussian modes are plotted in figure2.5 below.

Figure 2.5. Radial intensity distributions of some low order Hermite-Gaussianmodes.

It can be seen that the lowest order mode has the smallest spot size and is theonly one having the maximum in the centre of the beam. The presence of higherorder modes is usually undesirable and the beam is said to have lower beam quality.The appearance of higher order transversal modes in optical oscillators is discussedin section 2.3.2.

2.3 Optical cavities

2.3.1 Longitudinal mode spacing

By trapping a travelling electromagnetic wave between two mirrors a standing wavecan be formed. For a fixed mirror distance (cavity length), formation of standingwaves is possible only at some discrete frequency values νn for which the waveinterferes with itself constructively. This condition can be written as:

νn = nc

2L, n = 1, 2... (2.11)

where L stands for the cavity length and n is an integer number describingdifferent longitudinal modes. The frequency spacing between the two consecutivemodes is then: ∆ν = c/2L, therefore, the mode spacing in terms of wavelength canbe expressed as following3: ∆λ = λ1λ2/2L. Since in most practical cases λ1,2 ≫ ∆λ,a useful approximation can be formulated:

∆λ ≈ λ2/2L = λ2∆ν/c, (2.12)

where the value of λ is taken in the proximity of λ1 and λ2. In application,it is often required that the laser should operate at a single longitudinal mode,

3Strictly speaking, that is valid only in the absence of dispersion, when ∆λ/λ0 = ∆ν/ν0, whereλ0 = (λ1 + λ2)/2 and ν0 = (ν1 + ν2)/2.

2.4. SPECTRAL CONTROL OF LASERS 13

this requirement becomes increasingly difficult with longer cavity lengths since themode spacing is in that case narrower. Cavity mode selection is further discussedin section 2.4.

2.3.2 Finite aperture cavities and the resonator Fresnel number

By assuming a laser beam with a Gaussian profile inside a cavity, it is obvious thatthe cavity mirrors need to be infinitely large in order to confine the complete beam.Since, in reality, the mirrors are always limited in size, a certain portion of energy islost from the system. For the discussion about the effects caused by the finite-sizemirrors in optical resonators, a parameter called the resonator Fresnel number isintroduced and defined as follows [15]:

Nf =a2

Lλ, (2.13)

where L stands for the cavity length and a is the mirror radius assuming thatthe mirror is circular. It is instructive to express the resonator Fresnel number fora confocal resonator in terms of the mirror size and the spot size on the mirrorsurface: Nf = a2/πWm. Expressed in that way, it can be seen that the resonatorFresnel number is a measure of the finite mirror size losses: the larger the number,the lower the losses. On the contrary, however, one would want relatively smallNf values so that only the TEM00 mode is excited in the cavity and all highertransversal modes are below the laser threshold. In high energy optical parametricoscillators, it is necessary to use large resonator Fresnel number cavities becauseone needs to use large aperture nonlinear crystals to operate below crystal damageintensity. Consequentially, higher order modes start to be excited in the cavitywhich degrades OPO output beam quality and results in a broad output spectrum.

2.4 Spectral control of lasers

In section 2.1. it has already been mentioned that, in general, a laser can never beperfectly monochromatic or, in other words, the laser output always shows a certainband of frequencies. As seen from the previous section, that is also true for opticalparametric oscillators, however, physical mechanisms responsible for line broadeningare different4. A frequently used measure for the spectral width of laser light is theFull Width at Half Maximum (FWHM) value. FWHM is especially convenient forcomparing the experimental results since they usually do not strictly follow a certainanalytical distribution. On the other hand, it is sometimes useful to fit the measureddata with either a Gaussian or Lorentzian distribution if the data approximatelyresembles an analytical function. The table below gives a useful transformationbetween the width parameters of Gaussian and Lorentzian distributions and theircorresponding FWHMs.

4The properties of nonlinear interaction of light and matter is further discussed in chapter 3.


Distribution Analytical expression FWHM

Gaussian f(x) = 1σ

√2π

exp[

− (x−x0)2

2σ2

]

2√

2 ln 2σ

Lorentzian f(x) = 1π

[

γ(x−x0)2+γ2

]

2γ

Table 2.1. Analytical expressions for FWHMs of Gaussian and Lorentzian distribu-tions.

2.4.1 Volume Bragg gratings

For many applications (e.g. spectroscopy, interferometry, telecommunications, etc.)the spectrum of the laser light is required to be as narrow as possible. In some casesthe bandwidth of the gain medium is narrow enough to select only one cavity modeand suppress the others. On the other hand, if the mode spacing is narrow andthe gain medium bandwidth is broad, other ways of cavity mode selection have tobe employed. One of the possible techniques for mode selection (frequency locking)is using volume Bragg gratings (VBGs). A VBG is a piece of bulk glass (usuallysilicate) with the refractive index periodically modulated in one direction. Theglasses used to produce VBGs are referred to as photo-thermo-refractive glassesbecause one can change their refractive index by UV light exposure. The periodicrefractive index modulation is achieved by projecting an interference pattern fromthe UV laser on the glass. Afterwards the glass is typically heated to around 520◦C for a few hours [11], which results in a permanent change in the refractiveindex inside the glass. As an example, a VBG with a sinusoidal refractive indexmodulation along the z direction is considered: n(z) = n0 + n1 sin (Kz), where n0

stands for the average refractive index in the glass, n1 for the modulation strengthand K = 2π/Λ for the wave vector with a period Λ. For further analysis, figure 2.6represents a schematic setup for the reflection of a plane wave incident on a VBG.

Figure 2.6. Reflection of a plane wave from a volume Bragg grating.

It can be seen from the previous figure that every modulation period reflects a

2.4. SPECTRAL CONTROL OF LASERS 15

certain portion of the incident power. In reality, the refractive index modulation isvery weak (the order of 10−4) so there are usually a few thousands of modulationperiods inside a VBG to obtain the desired reflection. It can also be noticed that theplane of the refractive index modulation is not parallel to the VBG front surface,the reason for this is avoiding the front surface power reflection contributing to Pr

since that reflection is broadband.

The three most important properties of a volume Bragg grating are its cen-tral wavelength λB , spectral bandwidth ∆λ and peak reflection Rp. An analyticaltreatment of these properties is given in [16]. The expression for the total powerreflectivity is:

R(δ) =κ2 sinh2 (

√κ2 − δ2d)

κ2 cosh2 (√

κ2 − δ2d) − δ2, (2.14)

where δ is the phase mismatch from the Bragg condition (kR = kin − K + 2δ)given by: δ = π/Λ − 2πn0 cos θ/λ, where θ is the angle shown in the Figure 2.6. κis the coupling strength given by: κ = πn1/λ cos(θ) and d is the VBG length. Thepeak reflectivity of a VBG is simply found by setting the phase mismatch in theequation 2.14 to zero:

Rp = R(0) = tanh2(κd). (2.15)

It can be seen that the peak reflectivity can be increased by either increasingthe coupling strength κ (e.g. by higher refractive index modulation n1) or by usinglonger VBGs. The center of the reflectivity curve is also called the Bragg wavelengthand is given by:

λB = 2n0Λ cos θ0. (2.16)

The modulation period Λ therefore plays a crucial role in VBG design and man-ufacturing since it directly influences the center wavelength. Obtaining a FWHMspectral bandwidth from the equation 2.14 requires numerical calculation, however,a useful expression for the wavelength distance between the first zeros from the leftand the right side of the Bragg wavelength can be written as:

∆λ = λB

√

n21

n20 cos4 θ0

+4Λ2

d2. (2.17)

∆λ is also referred to as the zero-to-zero bandwidth of a volume Bragg grating.It can be concluded that narrow band VBGs can be achieved by increasing theirlength d and by weakly modulating the refractive index (n1). As an example, figure2.7 represents the VBG power reflectivity curve compared with the mode spacingof a 2 cm long cavity with mode spacing of δλ ≈ 0.11 nm. The VBG parameters


are chosen to achieve the peak power reflectivity Rp = 50 % and λB = 2128 nm.The zero-to-zero bandwidth of such a VBG is5: ∆λ ≈ 1.57 nm.

Pow

er ref

lect

ivity, ca

vity m

odes

0

0.1

0.2

0.3

0.4

0.5

0.6

Wavelength [nm]

2125 2126 2127 2128 2129 2130 2131

Cavity modes

VBG reflectivity

Figure 2.7. Cavity supported modes (L = 2 cm) in comparison with the VBGpower reflectivity curve (n0 = 1, n1 = 2 · 10−4, d = 3 mm, θ = 0o and λB = 2128nm). The bandwidth of the cavity modes is not considered in this figure.

2.5 The knife-edge beam spot size measurement

Knowing the beam spot size of a laser beam is often of great importance whendesigning an experiment or investigating the beam quality. There are many tech-niques for measuring the beam spot size, however, they differ in precision as well aspractical convenience [17]. One of the most often used techniques is the so calledknife-edge technique. A typical measurement setup is illustrated in figure 2.8 below.

Figure 2.8. Schematic representation of the knife-edge beam spot size measurementsetup.

As seen from the presented figure, an object with a sharp edge (i.e. a bladeof a razor/knife) is placed in the beam before the power meter and can be moved

5The parameter values approximately describe the setup used in the experimental part of thisthesis.

2.5. THE KNIFE-EDGE BEAM SPOT SIZE MEASUREMENT 17

perpendicularly to the beam propagation direction. For obtaining the beam spotsize, the blade is firstly placed to block 16 % of total beam power and then movedfurther to block 84 % of the total beam power. For Gaussian beams, the distancebetween those two points corresponds to the beam spot size6. A brief mathematicaljustification of the technique is presented below [11].

A Gaussian distribution of the beam intensity in the x-y plane (perpendicularto the direction of propagation z) at an arbitrary point z1 can be written as:

I(x, y, z1) = I0 exp

[

−2

(

x2

w2x

+y2

w2y

)]

(2.18)

where wx and wy are the beam spot sizes in x and y direction7. The total powercan therefore be written as:

Ptot = I0

∫ ∞

−∞exp

(

−2x2

w2x

)

dx

∫ ∞

−∞exp

(

−2y2

w2y

)

dy = I0π

2wxwy. (2.19)

If measuring the spot size in x direction, the blade is positioned at some x0:

P(x0)

Ptot=

1

Ptot

∫ x0

−∞

∫ ∞

−∞I(x, y) dx dy =

1

wx

√

2

π

∫ x0

−∞exp

(

−2x2

w2x

)

dx. (2.20)

The integral above does not have an analytical solution, however, it can besolved by using the standard error function: erf(u) ≡ 2/

√π∫ u

0 exp(−x2)dx:

P(x0)

Ptot=

1

2

[

1 + erf(√

2x0

wx)

]

. (2.21)

By inserting x01 = wx/2 and x02 = −wx/2 into the above equation, one obtainsP(x01)/Ptot = 0.84 and P(x02)/Ptot = 0.16. The spot size is therefore symply:wx = w01 − w02.

2.5.1 The M2 estimation

By using the same setup as shown in figure 2.8, it is possible to estimate the M2

value of a laser beam. In that case, the blade is mounted on a translation stage sothat the beam spot size can be measured on different positions along the z direction.The data is then fitted by an analytical expression describing the Gaussian beamspot size along the propagation direction:

6In theory, by measuring the total power and the remaining powers after the blade at any twopositions would be sufficient for obtaining the beam spot size. Often the 90 % - 10 % standard isused in practise [17].

7Such description is valid only for beams having a nearly elliptical/circular beam profile.


W (z) = W0

[

1 +

(

M2 λ(z − z0)

πW 20

)2]1/2

, (2.22)

which is a slightly modified version of the equation 2.4. Parameter z0 is addedto describe the relative beam waist position. In the fitting process, one can chooseto let all three parameters (W0, M2 and z0) variable if the beam waist position andthe spot size are not known, otherwise, the only free parameter is the M2. By usingequations 2.7 and 2.8 the Rayleigh range (zR) and the divergence angle (θd) of thebeam can be calculated.

In practise, the beam spot sizes are measured around the focus (within theRayleigh range) and in the far field (a few Rayleigh ranges away from the focus).The M2 estimation is better if the beam waist and its position are measured asprecise as possible, therefore, more measurements are done around the beam waistwhile just a few points in the far field are usually sufficient.

Chapter 3

Nonlinear optics

3.1 Nonlinear optical response of materials

3.1.1 Origins of nonlinearity

Electromagnetic radiation, when passing through a dielectric material exerts forceson electrons and ions which results in their oscillation. This interaction can bedescribed by the input electric field vector E and the resulting polarization densityvector P in the material. Generally, if we expand the relationship between thosetwo vectors in a Taylor series and assume that the first three terms represent asufficiently good approximation, the following expression can be written:

P ≈ ε0(χ(1)E + χ(2)E2 + χ(3)E3) (3.1)

Where χ(n) stands for the susceptibility value of n-th order. For low light inten-sities, the forces exerted on charges are small in comparison with the interatomic orcrystalline fields inside the medium and the relationship between P and E is linear,i.e. higher order terms in the above equation are negligible [12]. Linear processes,such as light refraction and linear absorption can both be described by only using

χ(1) via the refractive index: n =√

Re[

χ(1)]

+ 1 and the absorption coefficient1:

α = Im[

χ(1)]

ω/(nc) [11]. Historically, nonlinear effects could normally not be ob-

served before the development of lasers since the intensity of the sunlight or thelight generated by lamps is usually not high enough.

Equation 3.1 does not provide a complete picture needed to understand nonlineareffects of interest in this thesis. For instance, third order nonlinearities are presentin all dielectric media (even air or water) while second order nonlinearities are onlypresent in non-centrosymmetrical materials [6]. That suggests that the materialsusceptibility cannot be described only by a scalar value, rather it has to be treated

1It should be noted that these expressions are valid only away from absorption resonance pointsand that χ(1) is a frequency-dependant value which gives rise to light dispersion.

19

20 CHAPTER 3. NONLINEAR OPTICS

as a tensor. Generally, that allows that a wave polarized in one direction can excitea polarization density vector in another direction. This is shown in the followingsubsection with the mathematical treatment of the second order nonlinear processes.

3.1.2 Second order nonlinear processes

If we note waves polarized in x, y and z direction with i, j and k, respectively,and use ωα, ωβ and ωγ to note waves at different frequencies, the second orderpolarization component polarized in x direction and oscillating at the frequencyωα = ωβ + ωγ can be written as:

P(2)i (ωα) =

1

2ε0D

∑

jk

∑

βγ

χ(2)ijkEj(ωβ)Ek(ωγ). (3.2)

This expression represents the result of the interaction of wave pairs of the sameamplitude and frequencies ωβ and ωγ allowed by the susceptibility tensor compo-

nents χ(2)ijk. The constant D equals 1 if ωβ = ωγ and 2 otherwise. The susceptibility

tensor generally has 27 components, however, due to the crystal symmetries, manyinteractions are usually not allowed, setting the related tensor components to zero.

Furthermore, permutation symmetry (χ(2)ijk = χ

(2)ikj) is valid for the the interacting

fields E(ωβ) and E(ωγ) and, in case of all fields being far from material resonances,Kleinman symmetry holds [6]. The susceptibility tensor can then be described in amore simple manner by a 3 x 6 matrix d:

d =

d11 d12 d13 d14 d15 d16

d21 d22 d23 d24 d25 d26

d31 d32 d33 d34 d35 d36

(3.3)

where dil = 12χ

(2)ijk. l is obtained by the following substitution:

jk = 11 22 33 23 32 13 31 12 21l = 1 2 3 4 4 5 5 6 6

. (3.4)

Finally, the second-order polarization density vector component can be writtenas:

P(2)x (ωα)

P(2)y (ωα)

P(2)z (ωα)

= ε0Dd

Ex(ωβ)Ex(ωγ)Ey(ωβ)Ey(ωγ)Ez(ωβ)Ez(ωγ)

Ey(ωβ)Ez(ωγ) + Ez(ωβ)Ey(ωγ)Ex(ωβ)Ez(ωγ) + Ez(ωβ)Ex(ωγ)Ex(ωβ)Ey(ωγ) + Ey(ωβ)Ex(ωγ)

. (3.5)

For performing practical calculations, one would also need to take into accountthe fact that vectors P and E have different coordinate frames. For that reason,another tensor accounting for the coordinate system transformation would have tobe added into the above equation.

3.1. NONLINEAR OPTICAL RESPONSE OF MATERIALS 21

As an instructive example, one can imagine an interaction between the twoplane waves: Ex(ωβ) = A cos(ωβt) and Ez(ωγ) = A cos(ωγt) polarized in x and zdirections respectively and assume a material with d15 6= 0. By applying equation3.5, the resulting polarization density would be2:

P (2)x (ωα) = 2ε0d15A2 cos(ωβt) cos(ωγt). (3.6)

The induced polarization density inside the medium acts as a source for a newelectromagnetic wave at the same frequency (i.e. ωα). That wave can also interactwith the two existing waves (ωβ and ωγ) and this process is called three-wave mixing.From the simple example above, it can be seen that the newly created wave canexist at either the sum frequency (ωα = ωβ + ωγ) or at the difference frequency(ωα = ωγ − ωβ), the third case is when ωβ = ωγ and then the resulting waveappears at the double frequency ωα = 2ωβ,γ . These processes are usually addressedas sum frequency generation (SFG), difference frequency generation (DFG) andsecond harmonic generation (SHG), respectively.

Figure 3.1. Schematic representation of sum frequency generation, difference fre-quency generation and second harmonic generation processes.

3.1.3 Energy and momentum conservation

The previous subsection discussed nonlinear processes in terms of optical electro-magnetic waves of different frequencies. To continue with the discussion, it is moreinstructive to look at light from the particle point of view. In that case, for thethree wave mixing process, it can be said that it involves three photons of differentenergies: ~ωα, ~ωβ and ~ωγ . From this perspective it is clear that for any nonlinearprocess to occur, energy needs to be conserved. For instance, in the case of SFG,the photon of the highest energy (ωα) is seen as an output and the two photons of

2In reality, usually, if d15 6= 0 then d31 6= 0 and d15 = d31. In that case, the resulting polarizationdensity does not consist of the x component alone. Only the simplest case is considered here tointroduce the three wave mixing process.


lower energies (ωβ and ωγ) as an input of the process. Therefore, the conservationof energy can be written as:

~ωα = ~ωβ + ~ωγ . (3.7)

The same argument holds for photon momentum. If we denote the photonwavenumber with k = n(ω)2π/λ, the momentum conservation for SFG can bewritten as:

~kα = ~kβ + ~kγ . (3.8)

From the above expressions, it can be seen that, because of the material dis-persion (n(ωα) > n(ωβ,γ)) there exists a certain phase mismatch (∆k) between theinteracting waves. In the case of SFG, the phase mismatch can be written as:

∆k = 2π

(

n(ωα)

λα− n(ωβ)

λβ− n(ωγ)

λγ

)

. (3.9)

This situation is illustrated in a diagram below:

Figure 3.2. Diagram illustrating the phase mismatch in a dispersive nonlinearmedium.

In practise, a nonlinear process is taking place in a specifically chosen crystal andwaves are interacting (exchanging energy) while propagating along the distance L(the crystal length). It can therefore be concluded that, if there is a phase mismatchin the process, after a certain distance, the waves will become out of phase and theprocess will be reversed3. If we denote the intensities of the input waves with Iβ

and Iγ , the intensity of the output wave after the crystal can be written as [18]:

Iα =8dω2

αIβIγ

n(ωα)n(ωβ)n(ωγ)ε0c2L2sinc2

(

∆kL

2

)

, (3.10)

where the function sinc(x) ≡ sin(x)/x.

3The distance at which it occurs is: Lc = π/∆k, usually referred to as the coherence length.

3.1. NONLINEAR OPTICAL RESPONSE OF MATERIALS 23

sinc2(∆kL/2)

0

0.2

0.4

0.6

0.8

1

∆kL/2

-10 -5 0 5 10

Figure 3.3. Function sinc2(∆kL/2) vs. ∆kL/2.

As it can be seen from the figure above, if one wants to have an efficient conver-sion, ∆k needs to be zero, that condition is also referred to as the phase matching.As already mentioned, phase matching is normally not satisfied due to materialdispersion, however, there are ways to circumvent this problem. The two mostusual approaches are birefringent phase matching (BPM) and quasi phase match-ing (QPM).

BPM exploits the property of some crystals to have different refractive indexesfor waves polarized in different directions. In that case, the polarization of the waveof the highest frequency is oriented to experience the lowest refractive index. If thedifference in the refractive indexes is large enough to compensate for the materialdispersion, one can achieve phase matching. Usually, two cases of birefringent phasematching are distinguished: type I, when the two low frequency waves have the samepolarization and type II, when the low frequency waves are orthogonally polarized[19]. Since the QPM, rather than BPM, is of special interest for this thesis, it istreated separately in the following subsection.

3.1.4 Quasi phase matching

Even though many crystals have birefringent properties, it is often the case thatthe birefringence is not strong enough to ensure phase matching. Furthermore, ifone wants to exploit the d33 coefficient in the nonlinear process, it is not possibleto use BPM since d33 applies only for waves polarized in the same direction (seeequations 3.3 and 3.5). Yet another issue with BPM is the so called beam walk off4

which lowers the spatial overlap of the interacting waves. To avoid the mentioneddrawbacks of BPM, one can utilize quasi phase matching instead.

We can imagine, as an example, a nonlinear process that involves the d33 coeffi-cient. As already mentioned above, all three waves are then polarized in z direction

4The effect is present when angle tuning the birefringent crystal. In that case, the Poyntingvector S and the wavevector k of extraordinary waves point in different directions [18].


and, therefore, BPM is not possible. Since after one coherence length in the crys-tal, the nonlinear process is being reversed, one can think of a case where that isprevented by waves experiencing a nonlinear coefficient of −d33 instead. If the signof the nonlinear coefficient is changed at every coherence length periodically, theinteracting waves will never be out of phase and, therefore, the nonlinear processwill be sustained. This method is referred to as quasi phase matching.

Figure 3.4. Schematic representation of the periodically inverted domains in anonlinear crystal for QPM.

Mathematically, the periodic change along the axis x in the nonlinear coefficientsign can be described as following:

d(x) = d33sign [cos(2πx/Λ)] (3.11)

where Λ = 2Lc = 2π/∆k. That can be understood if we write d(x) in terms ofFourier series:

d(x) = d33

∞∑

m=−∞

Gm exp (ikmx) (3.12)

where Gm is the Fourier coefficient of the order m given by: Gm = (2/mπ) sin(mπ/2)and km is the magnitude of the grating vector of the order m given by: km = 2πm/Λ.Since the lowest order component of the Fourier series is the dominant one in de-scribing d(x), one uses the approximation ∆k ≈ k1 for the (quasi) phase matching.

3.2 Optical parametric processes

In addition to SFG, SHG and DFG introduced in the previous section, three moreprocesses are discussed: optical parametric amplification (OPA), optical parametricgeneration (OPG) and optical parametric oscillation (OPO). Parametric processesare usually discussed in terms of the pump (p), signal (s) and idler (i) waves, for thatpurpose the designations from the previous section are changed such that ωp = ωα,ωs = ωβ and ωi = ωγ . Their relative relation is defined as following: ωp > ωs > ωi,i.e. the wave of the highest energy is called the pump followed by the signal and

3.2. OPTICAL PARAMETRIC PROCESSES 25

the idler with lower energies. In a parametric process, the energy of the pump waveis transferred to the signal and the idler wave. The diagram below represents theenergy conservation in a parametric process.

Figure 3.5. Energy conservation diagram in parametric processes.

OPA is essentially a DFG process with a distinction in the relative intensitiesof the input and output waves. In DFG the intensities of both input waves are ofthe same order while in OPA the intensity of the pump wave is greater than theintensity of the signal wave [6]. The signal wave, also referred to as the seed is thenamplified by taking energy from the pump wave. The process is discussed further inthe separate subsection below. In OPG and OPO processes, there is only one inputwave, namely, the pump. The energy from the pump wave is transferred to thesignal and the idler wave which are amplified from the field noise fluctuations in themedium. OPO is actually an OPG process placed inside a resonator cavity in whicheither the signal, the idler or both waves oscillate5. The figure below schematicallysummarises the mentioned parametric processes.

Figure 3.6. Schematic representation of the three parametric processes: OPA, OPGand OPO.

5Therefore one distinguishes between the singly resonant oscillation (SRO) and the doublyresonant oscillation (DRO). In practise, DRO is usually more difficult to achieve then the SRO.


3.2.1 Optical parametric oscillation

As already mentioned, an OPO is made by placing a nonlinear crystal in a resonatorwhich provides feedback for (some of) the waves generated in the nonlinear process.Because of the cavity feedback, the OPO process is generally more efficient thanOPG. An example of an OPO where the signal wave is resonating in the cavity isschematically presented in the figure below.

Figure 3.7. Schematic representation of a singly resonant OPO.

The frequency of the signal and idler waves are determined by the phase match-ing condition. One can therefore imagine a case where the crystal is designed togenerate the signal and the idler with the same frequency. That condition is calleddegeneracy. An OPO designed to operate near degeneracy generally can not dis-criminate between the two waves, e.g. the cavity mirror is reflective for both thesignal and the idler. However, since the nonlinear processes are preserving the phaseinformation of the involved waves (there is a fixed phase relation between them),normally only one wave is favoured by the cavity. Especially when approaching thedegenerate point this can cause unstable operation since very small cavity lengthinstabilities can cause switching from the resonating signal to the resonating idlerand vice versa.

Similarly to lasers, OPOs also start operating above some threshold input energyvalue. To gain some insight on the threshold condition, an expression for the OPOthreshold energy is given below [20, 11]:

Eth =0.6τ(w2

p + w2s)

κL2

[

25l

τc+

1

2ln

2

R(1 − A)

]2

. (3.13)

Therefore, as a rule of a thumb, one can say that the threshold energy increaseswith: larger pulse length τ , larger signal and pump mode radius ws and wp, longercavity length l and larger cavity losses A. On the contrary, Eth decreases by usinglonger crystals (L) and increasing the mirror reflectivity R. The parameter κ isdefined as: κ = 8π2d2/(ε0cnpnsniλsλi).

Yet another advantage of the OPO process over OPG is its spectral properties.In OPG, the gain bandwidth of the generated output is dependant on the phasemismatch ∆k which is a direct consequence of the dispersive properties of the non-linear crystal. The more the crystal is dispersive, the narrower the bandwidth. Inthe case of an OPO, placing a crystal inside a cavity narrows the spectrum. For

3.2. OPTICAL PARAMETRIC PROCESSES 27

further line narrowing of the OPO output one can employ some spectral filters suchas volume Bragg gratings discussed in subsection 2.4.1. An example of the spec-tral narrowing of an OPO output by replacing the output mirror with a VBG ispresented in the figure below.

Figure 3.8. Comparison of the OPO spectrum by using a dielectric mirror (gray)and a VBG (black) as an output coupler [21].

3.2.2 Optical parametric amplification

Apart from OPO, another way of improving the efficiency and the spectral proper-ties of an OPG process is the optical parametric amplification. However, OPA isviable only when one already has a (low power) light source of the desirable spec-tral properties. That input wave is called the seed and is coherently amplified bydepleting the pump energy. A brief analysis of the seed amplification is presentedbelow.

If we define the gain parameter Γ = κIp where Ip is the pump intensity and κis the same as defined in previous subsection, one can write an expression for theseed intensity at the output of the crystal (of length L) as follows [22]:

Is(L) = Is(0)

1 + (ΓL)2sinh2

[

√

(ΓL)2 − (∆kL/2)2]

(ΓL)2 − (∆kL/2)2

. (3.14)

The above expression is taking into account the phase mismatch ∆k and is validonly for week pump depletion. In the case of a phase mismatch (∆k 6= 0), thesignal exhibits the same behaviour illustrated in figure 3.3. On the other hand,in the phase matching case (∆k = 0), the expressions for the signal and the idlerintensities are [23]:

Is(L) = Is(0)cosh2(ΓL) (3.15)

Ii(L) =ωi

ωsIi(0)sinh2(ΓL), (3.16)


from which one can conclude that both the signal and the idler grow exponen-tially as a function of the crystal length. In reality, however, the pump energy isbeing depleted which directly lowers the gain coefficient which in the end limits theexponential amplification.

Part II

Experiments

29

Chapter 4

Pump laser characterization

4.1 Introduction

In this chapter the results of the pump laser characterization are presented. Thesemeasurements were done in order to investigate some basic properties of the pumplaser: output power, spectrum, beam quality and beam polarization. Knowledgegained through these measurements was used in the MOPA design later on andserved as a reference point to evaluate experimental results presented in chapters 5and 6.

The pump laser used in this thesis is the Innolas Spitlight DPSS, Q-switchedNd:YAG, lasing at 1064 nm wavelength. The repetition rate is 100 Hz and themaximum output power exceeds 20 W. The combination of relatively low repetitionrate and relatively high powers results in quite high pulse energies (over 200 mJ)which, together with short pulse lengths, makes this laser a good choice for per-forming experiments in nonlinear optics, suggesting a possibility of achieving highconversion efficiencies. The laser is seeded by an external fibre laser to operate atthe single frequency and produce pulses of 10 ns FWHM. Pumping of the laser isachieved by light emitting diodes which can be controlled in two separate stages:the oscillator and the amplifier stage.

4.2 Output power measurements

4.2.1 Laser output power range

Firstly, the pump laser output power range was investigated by gradually increasingthe input currents of the pumping diodes. Figure 4.1 represents the measurementof the oscillator output power range, while the amplifier was switched off.

31

32 CHAPTER 4. PUMP LASER CHARACTERIZATION

Output power [W]

0

2

4

6

8

10

Input current [A]

160 180 200 220 240 260 280 300

Oscillator output power

Linear fit

Figure 4.1. Oscillator output power vs. pump diodes input current and a linear fitto the measured data f(x) = 0.085x − 15.12.

It can be seen from the figure that the oscillator has the current threshold valueof approximately 178 A and the maximum output power of 8.55 W. A linear fit withthe slope of 85 mW/A describes the data fairly accurately. The next measurementwas performed to investigate the behaviour of the amplifying stage of the laser whilekeeping the oscillator output power at maximum. The graph below presents theoutput power behaviour when gradually increasing the amplifier pumping diodesinput current1.

Output power [W]

10

15

20

25

Input current [A]

-50 0 50 100 150 200 250 300 350 400

Amplifier output power

Linear fit

Figure 4.2. Laser output power vs. amplifier pump diodes input current and alinear fit to the measured data f(x) = 0.05x − 7.55.

The maximum output power value of 24.2 W was measured. It can also beobserved that the dependence is not entirely linear, however, a linear function with

1The software used to control the laser offers control over the amplifier pumping diodes in-put current in terms of the oscillator pumping diodes input current percentage. The pumping istherefore controlled by setting the percentage value from 1 % to 130 %.

4.2. OUTPUT POWER MEASUREMENTS 33

the slope value of 50 mW/A was fitted to the measured data as an approximation.It was decided that, for all further experiments, the laser is going to be operatedat the maximum output power. The amount of power needed for experiments willthen be controlled by beam separation using a thin film polarizer and a half waveplate as will be described in one of the following subsections.

4.2.2 Output power stability

The goal of the measurements presented in this subsection was to investigate thelonger term stability (during one hour) after switching the laser on to the maximumoutput power. Apart from the output power, the pulse FWHM was also measuredduring that period. The measurement results are presented in figure 4.3 below.

Laser output power [W]

18

19

20

21

22

23

24

25

Pulse FWHM [ns]

7

8

9

10

11

12

13

14

15

Time [min]

-10 0 10 20 30 40 50 60 70

Laser output power

Pulse FWHM

Figure 4.3. Maximum laser output power and pulse FWHM vs. time.

From the presented measurement, it was concluded that the laser should beleft to stabilize for at least one hour before performing the experiments. One ofthe reasons for the observed power changes might be the temperature stabilizationas the laser is heating up and the equilibrium state needs to be achieved in thelaser housing, the cooling system and the surroundings. It should also be notedthat, during that period, the beam changed its direction, causing alignment issues,however, that effect also seamed to stabilize after approximately 90 minutes. Apartfrom the long-term changes, a short investigation of the power fluctuations duringone minute was performed. The resulting RMS instability of 0.08 % was obtainedwhen the laser was already operating in the long term steady state.

4.2.3 Beam polarization measurement

As described in chapter 3, wave polarization in a nonlinear process plays an im-portant role in the phase matching and the conversion efficiency. It is thereforedesirable that the pump beam has a well defined polarization. In this subsection,the investigation of the beam polarization is presented.


The polarization selectivity was achieved by using a half wave plate and a thinfilm polarizer. The angle of polarization of a linearly polarized wave can be changedby propagating through a half wave plate as a consequence of its property to delayorthogonally polarized components by 180◦. Rotation of the half wave plate there-fore causes a change in the polarization angle of the output wave. For instance, byrotating the wave plate by 45◦, the polarization angle changes by 90◦. A thin filmpolarizer is a polarization selective component which, at a specific angle, transmitswaves polarized in one direction and reflects waves of different polarizations. In thefollowing experiment, the beam was propagated firstly through a half wave plateand then through a thin film polarizer. The transmitted power was measured whilerotating the wave plate from 0◦ to 45◦.

Transmitted power [W]

0

5

10

15

20

25

Half wave plate rotation angle [o]

0 10 20 30 40

Transmitted power

Figure 4.4. Power transmitted through a half wave plate and a thin film polarizervs. the half wave plate angle.

If the beam would be polarized in just one direction one would expect that, ata certain wave plate angle, all the power would be transmitted or reflected. As canbe seen from the figure above, the minimum value of 2.64 W was measured instead,suggesting that a (minor) part of the beam is polarized in another direction. Theundesired polarization contributed to roughly 11 % of total output power and thatpart was filtered out for all further experiments. The polarization filtering wasdone to prevent crystal damage since that part of the beam energy could possiblybe focused in the crystal while not contributing to the conversion process. Sincethe transmitted part of the beam then had a well defined polarization, the sametechnique was later on used for beam splitting, with the splitting ratio regulated bychanging the wave plate rotation angle.

4.3 Spectrum measurement

As already mentioned in the introduction part of this chapter, the pump laser issupposed to operate at a single resonator mode and, therefore, the spectrum was

4.3. SPECTRUM MEASUREMENT 35

expected to be very narrow. Two ways of measuring the pump spectrum wereavailable, firstly, the spectrum was measured using the ANDO AQ-6315A opticalspectrum analyzer (OSA) and, then, using the spectrometer (HORIBA Jobin YvoniHR550). The OSA offers a maximum resolution of 0.05 nm and the light is fibrecoupled to the device. The spectrometer offers higher resolution, however, themeasurement setup is more complex and precise beam alignment was required.Also, the lock-in amplifier was needed for enhancing the signal to noise ratio of thedetector output.

Figure 4.5. Schematic representation of the measurement setup using a spectrome-ter and a lock-in amplifier. Letters from a-e in brackets denote: a-entrance slit, e-exitslit, b,d-mirrors and c-diffraction grating.

The resolution of the spectrometer can be increased by decreasing the entranceand the exit slit size, this in turn decreases the amount of light arriving to the Sidetector which results in a bad signal to noise ratio. For the measurement presentedbelow the resolution was set to 0.014 nm (3.7 GHz) with the minimum slit size of0.01 mm and using a grating with 1200 grooves/mm.

Normalized amplitude

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Wavelength [nm]

1063.9 1064 1064.1 1064.2 1064.3 1064.4

OSA measurement

Spectrometer measurement

Figure 4.6. Pump spectrum measured with the spectrometer and the optical spec-trum analyzer.

It can be seen that the FWHM of the spectrum is comparable to the OSA reso-lution which makes the measurement fairly unreliable. The spectrometer, however,


offered about three times higher resolution and in that case the approximate spectralFWHM of 0.05 nm (13.2 GHz) was measured.

4.4 Beam quality investigation

In this thesis, the most important figures of merit for the beam quality are the M2

values. In a few cases, the beam quality was examined by recording the beam profileusing a pyroelectric array camera. Unfortunately, this technique was not availablethroughout the whole project period.

4.4.1 Beam spot size measurements and M2 estimation

Section 2.5 describes the beam spot size measurement with the knife-edge techniqueand explains the estimation of the M2 value. All beam spot size measurements inthis thesis are performed separately for horizontal and vertical direction. In thefollowing measurement, the pump laser beam was focused by a lens with the focallength f = 300 mm. The laser was operated on full power so the measurementsetup included some flat separation mirrors to lower the power of the measuredbeam. That was necessary because the light intensity in the focus can easily behigh enough to burn the blade.

Bea

m spot size

W [µm

]

0

500

1000

1500

2000

z [mm]

0 50 100 150 200 250 300 350 400

Measured data, horizontal

Theoretical fit, horizontal

Measured data, vertical

Theoretical fit, vertical

Figure 4.7. Measured spot sizes along the focused beam and theoretical fits to themeasured data for horizontal and vertical direction.

The above figure represents the measurement results as well as the theoreticalfits for both horizontal and vertical direction. The measurements seam to be infairly good agreement with the Gaussian beam propagation expression given byequation 2.22. The values estimated from the fitting process are presented in thefollowing table. Additionally, the divergence angle θd and the Rayleigh range zR

were also calculated.

4.4. BEAM QUALITY INVESTIGATION 37

M2 z0 [mm] W0 [µm] θd [◦] zR [mm]

Horizontal 1.89 151 85 0.86 11.3

Vertical 1.91 148 82.4 0.9 10.5

Table 4.1. Beam parameters estimated from the measured data for horizontal andvertical direction: M2 value, beam waist position z0, beam waist W0, divergenceangle θd and Rayleigh range zR.

It can be seen that the pump beam seamed to be slightly more divergent invertical direction and that the M2 value is higher than 1, suggesting that the beamprofile is not perfectly Gaussian. Also, a slight astigmatic behaviour can be noticedsince the beam waist position in horizontal and vertical direction differ by 3 mm.The following section further investigates the beam profile measurement using apyroelectric array camera.

4.4.2 Beam profile visualization using a pyroelectric array camera

A pyroelectric array camera enables beam profile visualization for beam intensitiesthat would by far damage an ordinary CCD detector, nevertheless, for performingthe measurement presented below, the beam needed to be significantly attenuated(below 100 mW) to safely perform the measurement. Since the beam polarizationwas filtered, both the useful and the undesired part of the beam were recorded. Thepixel data was exported so that the vertical and horizontal intensity distributionscould be plotted separately.

Rel

ativ

e in

ten

sity

-1e+04

0

1e+04

2e+04

3e+04

4e+04

Relative position

0 20 40 60 80 100 120

Vertical distribution

Horizontal distribution

Figure 4.8. Beam profile and intensity distributions for vertical and horizontaldirection in the filtered (useful) polarization.

Ideally, one would expect that the pump beam has a Gaussian beam profile.It can be seen from figure 4.8 above that it is not quite the case for this pumpbeam. However, knowing the M2 value, that result was expected as discussed inthe previous subsection. The following figure presents the intensity distributions


and the beam profile visualization of the part of the beam that was filtered out bya thin film polarizer.

Rel

ativ

e in

ten

sity

-5e+04

-4e+04

-3e+04

-2e+04

-1e+04

0

1e+04

Relative position

0 20 40 60 80 100 120

Vertical distribution

Horizontal distribution

Figure 4.9. Beam profile and intensity distributions for vertical and horizontaldirection in the undesired polarization.

Chapter 5

OPO characterization

5.1 Introduction

After the pump laser characterization was completed, the setup for optical para-metric oscillation was built. This chapter presents the experimental results of theOPO characterization as an intermediate step before the investigation of the MOPAperformance. The motivation for investigating the OPO behaviour lies in the factthat the OPO 2 µm output would later serve as a seed in the OPA stage and, there-fore, many of the seed beam characteristics were expected to be transferred to thefinal 2 µm MOPA output. To discuss the OPO experimental setup in more detailits schematic representation is shown in the figure below.

Figure 5.1. Schematic representation of the OPO experimental setup.

The first two stages: filtering of the unwanted polarization and the beam separa-tion are discussed in the previous chapter. Since the beam spot size was measured tobe approximately 2 mm in both horizontal and vertical direction, the telescope stagewas built to lower the beam spot size. That was necessary for the following reasons:

39

40 CHAPTER 5. OPO CHARACTERIZATION

firstly, the dimensions of the front facet of the PPKTP crystal were 5x3 mm so thebeam spot size had to be lowered below 1.5 mm to fit the crystal dimensions and,secondly, by increasing the pump beam intensity, the nonlinear conversion efficiencyincreases and the OPO threshold energy decreases. On the other hand, narrowingthe beam spot size too much could result in crystal damage. The telescope con-sisted of three lenses with f1 = 300 mm, f2 = 1000 mm (only horizontal direction1)and f3 = −190 mm. After the telescope, the beam spot size was measured to beapproximately 1.2 mm in both directions at the crystal position. The mirror used asthe OPO input coupler had both sides anti reflection (AR) coated at 1064 nm andthe back side coated for high reflection (HR) of the 2 µm beam. The VBG served asan output coupler with the peak reflectivity for the 2 µm beam of 50 %. The VBGfront facet was AR coated for 1064 nm and was tilted by approximately 11◦ withrespect to the refractive index modulation planes which made the alignment fairlydifficult. The PPKTP nonlinear crystal was 10 mm long and had a QPM period ofΛ = 38.8 µm, designed to operate at degeneracy. Both the VBG and the nonlinearcrystal were placed on the specifically designed holders that enabled temperaturecontrol.

It should be noted that, before building the actual OPO used in the MOPAsetup, an OPO with two flat dielectric mirrors was built to investigate the rela-tive efficiencies of different crystals that were available. Also, the 2 µm beam wasneeded to precisely investigate the angle at which the VBG had to be placed toachieve Bragg reflection. Once the angle was known, it was easier to align the VBG(replacing the dielectric mirror as an output coupler). Generally, the alignment ofa VBG in the OPO can be a demanding task since all the beams are outside thevisible spectral range, for that reason a He-Ne laser, emitting red light, was used asan alignment tool.

5.2 Spectrum measurement

Once the OPO was constructed, fine tuning and alignment was performed to achievethe highest possible conversion efficiency. That criteria was also used for choosingthe PPKTP crystal temperature of 58 ◦C. Even though the crystal was designed tooperate at degeneracy, since the VBG selected spectrum is much narrower than thePPKTP gain bandwidth and, also, not precisely known, the question was how farfrom the exact degenerate point the OPO was operating. The temperature controlof the VBG was therefore designed in hope to be able to tune the VBG Braggwavelength on and off degeneracy. That was examined by gradually changing theVBG temperature and measuring the spectrum.

There are two main issues with measuring such narrow bandwidth spectra at 2µm wavelength. Firstly, the resolution has to be high enough, and, secondly, the

1The cylindrical lens was used to better match the horizontal and vertical spot size since largerdivergence in the horizontal direction was observed.

5.2. SPECTRUM MEASUREMENT 41

detector has to be able to detect photons in that wavelength region. For both reasonsmeasuring the spectrum with the OSA was not an option, instead, the spectrometerwas used with a grating with 300 grooves/mm and a PbS detector cooled down to−40 ◦C. For the measurement presented below, the VBG temperature was changedfrom 15 ◦C to 70 ◦C and the OPO output spectrum was measured every 5 ◦C.For each temperature point the central wavelengths for both signal and idler wererecorded.

Wavelength [nm]

2126.5

2127

2127.5

2128

2128.5

2129

2129.5

2130

2130.5

VBG temperature [oC]

10 20 30 40 50 60 70 80

Signal data Linear fit to signal data

Idler data Linear fit to idler data

Merged peaks with FWHM as error bars

Figure 5.2. VBG Temperature tuning of the OPO signal and idler wavelength.

As can be seen from the figure above, VBG tuning to the degenerate point waspossible. The temperature tuning was ultimately limited by the Peltier element usedto heat the VBG since its maximum operating temperature is approximately 80 ◦C.One would expect that, if it was possible to further rise the VBG temperature, thesignal and idler peaks would start to move away from each other again. The tuningconstant was evaluated from the linear fitting: K ≈ 0.024 nm/◦C. After 55 ◦C,the signal and idler peaks started to merge and the FWHMs of the single peak arepresented instead. The degenerate point was observed to be at approximately 65 ◦Cwith the single peak of 0.46 nm (30 GHz) FWHM. Figure 5.3 shows the measuredspectrum for the three representative temperature points: 25 ◦C, 45 ◦C and 65 ◦C.


Normalized intensity

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Wavelength [nm]

2126.5 2127 2127.5 2128 2128.5 2129 2129.5 2130

T=25 oC

T=45 oC

T=65 oC

Figure 5.3. OPO output spectrum at the VBG temperatures of 25 ◦C, 45 ◦C and65 ◦C.

Apart from the VBG temperature tuning of the signal and idler wavelength,it was also observed that usually one spectral peak is of higher intensity then theother. The difference in the relative peak intensities of the signal and idler is aconsequence of the fact that only one wave is resonant in the OPO, whereas theother one is not reflected by the VBG. However, it should be noted that, because ofthe energy conservation in the nonlinear process, there is always an equal amountof signal and idler photons created.

5.3 Power measurements

Knowing the VBG temperature at which the OPO operates at degeneracy allowedfurther investigation of the OPO performance and comparison between the degener-ate and non-degenerate state. This section discusses the OPO output power and itsstability, as well as the OPO performance in terms of energy conversion efficiency. Inall further experiments, the term off degeneracy assumes the VBG operating at theroom temperature T = 25 ◦C and the term on degeneracy, as mentioned, assumesT = 65 ◦C. It should also be stated that the term OPO output power assumes thepower of the 2 µm beam, i.e. the total power of the signal and the idler together. Inpractise, the 2 µm beam was separated from the pump beam by two flat separationmirrors that were transparent for the pump beam and 99.9 % reflective for the 2µm beam.

5.3.1 Output power and conversion efficiency

A common way to characterize an OPO in terms of energy conversion properties isdone by estimating its conversion efficiency and pump depletion. Even though themeasurements are performed by measuring average powers, results are commonly

5.3. POWER MEASUREMENTS 43

discussed in terms of pulse energies2. Energy conversion efficiency is therefore de-fined as:

η =Es + Ei

Ep, (5.1)

where Es and Ei are the sigal and idler pulse energies, respectively, and Ep is thepump pulse energy. Also, pump depletion is defined as follows:

ηp = 1 − Edp

kEp, (5.2)

where Edp stands for the depleted pump pulse energy and k is a coefficientrepresenting linear losses in the OPO. In an ideal case, the efficiency would beequal to pump depletion, however, there are always some losses due to nonlinearabsorption or other nonlinear processes. Nevertheless, big discrepancies between thepump depletion and the conversion efficiency can indicate an existence of another(efficient) nonlinear process such as backward back-conversion which is going to bediscussed later. The following figure describes the measurement setup.

Figure 5.4. Schematic representation of the OPO characterization setup. Measure-ment points represented with circles are denoted with letters a-d: a-pump power,b-combined signal and idler power, c-depleted pump power and d-backwards back-conversion power.

The measurements were taken by increasing the pump power from 0 to 3.6 Wand calculating the conversion efficiency and pump depletion for each measurementpoint. Higher pumping was not performed to prevent potential crystal damage.

2For the pulse repetition rate of 100 Hz a simple conversion is valid: 10 · P [W]= Epulse [mJ].


Efficiency, pump depletion

-0.1

0

0.1

0.2

0.3

0.4

0.5

Output pulse energy [mJ]

0

2

4

6

8

10

12

14

Pump pulse energy [mJ]

0 5 10 15 20 25 30 35 40

Efficiency

Pump depletion

Output pulse energy

Figure 5.5. OPO conversion efficiency, pump depletion and output pulse energy (offdegeneracy).

As can be seen from figure 5.5, the maximum OPO efficiency achieved was 37 %at the maximum pump pulse energy of 37 mJ. The maximum output pulse energymeasured was 13.3 mJ and the OPO threshold energy was observed to be below 3mJ. The linear losses were investigated below the OPO threshold energy and theyresulted in the factor k = 0.69 (equation 5.2), i.e. around 30 % of pump power islinearly lost in the OPO. A part of those linear losses came from the imperfect ARcoatings of the VBG and the PPKTP crystal.

The measurement was repeated with tuning the VBG temperature to operateat degeneracy. The results are presented in the following figure.


0

0.1

0.2

0.3

0.4

0.5

0.6


0

2

4

6

8

10

12


0 5 10 15 20 25 30 35 40

Efficiency

Pump depletion

Output pulse energy

Backward back-conversion efficiency

Figure 5.6. OPO conversion efficiency, backward back-conversion efficiency, pumpdepletion and output pulse energy (on degeneracy).

As can be seen from the presented measurement, the OPO behaviour on degen-eracy is fairly different from the off degenerate case. To start with, the maximumefficiency was observed to be 31 % and the maximum output pulse energy 11.2 mJ,which is more than 15 % worse than in the first case. Secondly, there was a big

5.3. POWER MEASUREMENTS 45

discrepancy observed between the conversion efficiency and the depleted pump. Forthat reason, it was investigated whether the 2 µm beam was being converted backto 1 µm propagating backwards, a process called backwards back-conversion. Thatwas done by simply using a glass plate as shown in figure 5.4 and measuring thepower at point d. The measured backwards back-converted power was accountingfor around 10 % of the pump power. The linear losses were additionally investi-gated by misaligning the OPO at every point and measuring the the power at thepoint c which showed good agreement with the below-threshold estimation. Apartfrom being less efficient, the OPO operating on degeneracy was observed to be lessstable, i.e. the output power fluctuations were noticeable. The following subsectionis briefly going to discuss this phenomenon.


It was already explained in subsection 3.2.1 from the theoretical point of view thatan OPO is expected to be less stable at degeneracy because the small changes inthe resonating condition can cause switching from resonating signal to resonatingidler and vice versa. To investigate the OPO output power stability, the VBGtemperature was gradually changed from 25 ◦C to 70 ◦C and the OPO outputpower was measured during one minute for each point. The following figure presentshow the output power mean value and RMS instability changed with the VBGtemperature.

Output power RMS instability [%]

0

0.5

1

1.5

2

2.5

Average output power [W]

0.8

0.85

0.9

0.95

1

1.05


20 30 40 50 60 70

Output power RMS instability

Average output power

Figure 5.7. OPO average output power and RMS instability vs. VBG temperature.

It can be seen from the figure above that the OPO stability, when reachingdegeneracy, behaves as expected: RMS instability rises from below 1 % to 2 %at degeneracy, also the mean output power decreases as already observed in theprevious subsection.


5.4 Pulse shapes

In this section a discussion on pulses involved in the OPO process is presented.As it was already mentioned, the pump laser pulses were around 10 ns long, thequestion was how long were the 2 µm pulses and what could be concluded from thedepleted pump pulse shapes. Measuring 2 µm pulses requires a detector that is ableto absorb in that wavelength region, moreover, its response has to be fast enough tomeasure on nanosecond scale. Such a detector was not available for use during thetime of this project, however, a regular Si detector diode was fortunately shown tobe able to detect 2 µm pulses. That was, however, only possible at very high lightintensities, suggesting that some sort of low efficient nonlinear process was startingto take place in the detector. Since the Si detector is sensitive to wavelengths shorterthan 1.2 µm it was crucial to filter all other potential spectral components from themeasured beam. For that purpose, a long-pass filter was placed in the measuredbeam to block all light with wavelengths shorter than 1.7 µm when necessary. Themeasurement presented in figure 5.8 compares four types of pulses that were ofinterest: input pump pulse, depleted pump pulse, pump pulse attenuated only bylinear losses and, finally, the 2 µm pulse. All except the input pump pulse can becompared temporally since they were measured at approximately the same distancefrom the OPO and an external time reference was employed3. It should also benoted that the pulses were normalized in such a way that the area under the inputpump pulse is 1 and the area of every other pulse is scaled with respect to the pulseenergy.

Normalized amplitude

0

0.02

0.04

0.06

0.08

0.1

Time [ns]

10 20 30 40 50

Input pump

Input pump - linear losses

Depleated pump

Output pulse

Figure 5.8. OPO pulse shapes normalized to pump input pulse energy.

It can be seen that the OPO output pulse is, firstly, shorter than the pump pulse(5 ns FWHM) and, secondly, delayed with respect to the depleted pump. That canbe understood by the fact that the intensity at the leading and the trailing edge ofthe pump pulse is not above the OPO threshold intensity. Therefore, the nonlinear

3The oscilloscope was triggered by the laser trigger signal.

5.5. M2 MEASUREMENTS 47

process does not take place during that time, causing the 2 µm pulse to appear laterand end sooner than the depleted pump pulse which is suggesting that lowering theOPO threshold intensity may directly improve the conversion efficiency since thelarger portion of the pump pulse is available for energy conversion.

5.5 M 2 measurements

This section discusses the OPO performance in terms of the output beam quality.The M2 measurements were performed for three different cases: OPO pumpedwith low and high power off degeneracy and OPO pumped with high power ondegeneracy. The terms low and high refer to 1.5 W of pump power and 3 W ofpump power, respectively4. From the theoretical perspective, it was expected thatthe beam quality would decrease (e.g. M2 value would increase) with both highpumping, and operating at degeneracy. As discussed in section 2.3.2 about theresonator Fresnel number, with high pump energies, higher-order modes becomepresent in the resonator. Also, another effect that contributes to lower beam qualityat high pump energies is the multiple conversion from 1 µm to 2 µm and vice versa.The purpose of the investigation presented below was to gain understanding of howstrong these effects in this particular OPO design were, especially because of thehigh spectral selectivity of the VBG and its possible repercussions on the beamquality. The result of the first of the three mentioned measurements are presentedin figure 5.9 below and summarized in table 5.1. It should be noted that all thefollowing M2 measurements were performed by using the same lens with f = 300mm as used for the pump characterization, allowing direct comparison of the beamwaist values W0 at the focus for all the measured beams.

Bea

m spot size

W [µm

]

0

500

1000

1500

2000

2500

3000

3500

z [mm]

100 150 200 250 300 350 400 450 500





Figure 5.9. Measured spot sizes along the focused 2 µm beam and theoreticalfits to the measured data for horizontal and vertical direction. OPO off degeneracy,Ppump = 1.5 W.

4The pumping power was limited to 3 W in this case as a precautionary measure because minorPPKTP crystal coating damage was observed.


M2 z0 [mm] W0 [µm] θd [◦] zR [mm]

Horizontal 6.9 297 302 1.79 19.4

Vertical 10.0 296 392 1.98 22.6

Table 5.1. Beam parameters estimated from the measured data for horizontal andvertical direction: M2 value, beam waist position z0, beam waist W0, divergenceangle θd and Rayleigh range zR. OPO off degeneracy, Ppump = 1.5 W.

From the presented values, it can be noticed that, already for this pumpingpower, the beam seamed to be quite more divergent in comparison with the pumpbeam. The obtained result is suggesting that some of the higher order modes werealready excited inside the cavity at this pumping power. If compared with 0.3 W ofthe threshold pump power, 1.5 W can be seen as operating many times above thethreshold power and, in that light, the obtained results can be seen as less surprising.Unfortunately, performing the M2 measurement with lower OPO pumping powerswas too difficult since the OPO output energy was severely fluctuating making itimpossible to accurately estimate the beam spot sizes using the knife-edge technique.In the same manner as above, the following figure with the associated table representthe measurement results when the OPO pumping power was set to 3 W.

Bea

m spot size

W [µm

]

0

500

1000

1500

2000

2500

3000

z [mm]

100 150 200 250 300 350 400 450 500





Figure 5.10. Measured spot sizes along the focused 2 µm beam and theoreticalfits to the measured data for horizontal and vertical direction. OPO off degeneracy,Ppump = 3 W.

M2 z0 [mm] W0 [µm] θd [◦] zR [mm]

Horizontal 7.8 302 336 1.81 21.3

Vertical 9.9 296 293 1.96 23.0

Table 5.2. Beam parameters estimated from the measured data for horizontal andvertical direction: M2 value, beam waist position z0, beam waist W0, divergenceangle θd and Rayleigh range zR. OPO off degeneracy, Ppump = 3 W.

5.5. M2 MEASUREMENTS 49

Except for the slight increase in the beam divergence in horizontal directionand slight astigmatic behaviour, there seamed to be no severe change in the beamquality when pumping the OPO with higher powers. The presented results thereforecontribute to the assumption that the higher order modes and/or cascading effectsbecome present already at lower pumping powers. As presented in section 5.3, theOPO is significantly more efficient at 3 W pumping power than at 1.5 W so that waschosen as the operating point for performing further measurements as a compromisebetween the power stability, conversion efficiency and the beam quality. For the finalmeasurement presented below, the VBG temperature was tuned to operate the OPOat degeneracy. Since the power fluctuations increase in that case, the measurementpoints were expected to be in somewhat worse agreement with the theoretical fittingfunctions, resulting in the less accurate M2 estimation.

Bea

m spot size

W [µm

]

0

500

1000

1500

2000

2500

3000

z [mm]

100 150 200 250 300 350 400





Figure 5.11. Measured spot sizes along the focused 2 µm beam and theoreticalfits to the measured data for horizontal and vertical direction. OPO on degeneracy,Ppump = 3 W.

M2 z0 [mm] W0 [µm] θd [◦] zR [mm]

Horizontal 8.9 241 396 1.75 26.0

Vertical 12.0 235 475 1.96 27.8

Table 5.3. Beam parameters estimated from the measured data for horizontal andvertical direction: M2 value, beam waist position z0, beam waist W0, divergenceangle θd and Rayleigh range zR. OPO on degeneracy, Ppump = 3 W.

From the presented results, it can be seen that the beam quality seams to de-teriorate when the OPO is operated at degeneracy, however, the effect is not thatsevere in comparison with the effects related to higher pumping powers.

Chapter 6

MOPA characterization

6.1 Introduction

Once the OPO characterization was done, the amplifying stage was built to completethe MOPA experimental setup. Its schematic representation is shown in figure 6.1.

Figure 6.1. Schematic representation of the MOPA experimental setup.

As can be seen, the pump beam was separated in two beams: one for the OPOand the other one for the OPA stage. Another separation stage was built in theOPA beam so that the OPO and OPA pump powers could be controlled separately.Yet another half wave plate was placed in the beam to have precise control overthe beam polarization angle. Also, a telescope made with two lenses (f4 = 300 mm

51

52 CHAPTER 6. MOPA CHARACTERIZATION

and f5 = −200 mm) was built to increase the conversion efficiency of the OPA1. Onthe other hand, the seed beam from the OPO was just separated from the depletedpump with two separation mirrors as previously presented in subsection 5.3.1. TheOPA consisted of two large aperture (5x5 mm) Rb:PPKTP crystals [8] placed oneafter another on a temperature controlled copper holder. Each crystal was 10 mmlong and had the same QPM period as the crystal used in the OPO (Λ = 38.8 µm).Also, the crystals were heated to 58 ◦C as in the OPO case. After the alignmentwas done to ensure good overlap between the pump and the seed beam, fine tunigwas performed once the OPA was started, to ensure maximum conversion efficiency.

6.2 OPA investigation

Before evaluating the overall MOPA performance in terms of output power, spec-trum and beam quality, a short discussion on the OPA performance is presented.The following figure schematically illustrates the OPA characterization setup andmeasurement points.

Figure 6.2. Schematic representation of the OPA characterization setup with thefollowing measurement points: a-input pump power, b-seed power, c-depleted pumppower and d-output power.

6.2.1 OPA with one crystal vs. two crystals

The first OPA experiment was performed with only one crystal placed on the holderand the OPO being pumped with pulse energies of 10 mJ, seeding the OPA with1.6 mJ pulses. The OPA pump pulse energies were then changed gradually from 0to 120 mJ, while measuring the OPA output. At maximum pumping, the outputpower of nearly 1 W was measured. Since the pump depletion was in that case lessthan 10 %, it was decided that the second crystal would be placed on the holder,doubling the total length of the nonlinear medium. The same experiment was thenperformed with two crystals. The comparison between the two mentioned cases ispresented in the following figure.

1Lowering the beam spot size in the OPA case, apart from increasing the light intensity in thecrystal, also increased the overlap between the pump and the seed beam.

6.2. OPA INVESTIGATION 53


0

5

10

15

20

25


0 20 40 60 80 100 120

One crystal

Two crystals

Figure 6.3. Comparison of OPA output pulse energies when using one or twocrystals.

In the case of two crystals being placed in the holder, the maximum OPA outputpower of 2.4 W was measured, depleting the pump by approximately 20 %. Becauseof such significant improvement in performance, both crystals were used in all thefollowing experiments. It should also be noted that, as predicted by the theoreticaldiscussion in subsection 3.2.2, with increasing the pump power linearly, the outputpower grows exponentially for low pump depletion condition.

6.2.2 OPA conversion efficiency and pump depletion

Unlike the OPO, the OPA process requires 2 input beams and, moreover, the outputbeam consists of both the seed photons and the photons converted from the pump.For those reasons there are more ways of defining the conversion efficiency. In thisthesis, the OPA conversion efficiency is defined as follows:

η =Eout − pEseed

Epump, (6.1)

where Eout is measured at the point d in figure 6.2, Epump at the point a andEseed at the point b. The factor p is accounting for linear losses of the seed occuringbetween the points b and d. For amplifiers in general, one also usually defines theamplifier gain. In this thesis, the amplifier gain is denoted as γ and is defined asfollows:

γ =Eout − pEseed

Eseed. (6.2)

The linear seed losses were investigated separately yielding the value of p = 0.64.The pump depletion is defined in the same manner as for the OPO, with the linearpump losses of 20 %, resulting in the value of k = 0.8. Figure 6.4 represents thebehaviour of the OPA when changing the pump pulse energy from 0 to 120 mJwhile seeded with Eseed = 1.6 mJ.



-0.05

0

0.05

0.1

0.15

0.2

0.25


0

5

10

15

20

25


-20 0 20 40 60 80 100 120 140

Efficiency

Pump depletion

Output pulse energy

Figure 6.4. OPA conversion efficiency, pump depletion and output pulse energy(Eseed = 1.6 mJ).

It can be seen from the presented figure that the efficiency linearly increases withincreasing the pump pulse energy, which can be understood by the fact that thenonlinear process is more efficient at higher intensities. At maximum pumping, theefficiency of η = 18.5 % was measured. The OPA output pulse energy was alreadypresented in figure 6.3, with the maximum value of Eout = 24 mJ. The measurementpresented in the following figure was performed in the same manner with the onlydifference in the seed pulse energy which was increased to Eseed = 10 mJ.


-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35


5

10

15

20

25

30

35

40


0 20 40 60 80 100

Efficiency

Pump depletion

Output pulse energy

Figure 6.5. OPA conversion efficiency, pump depletion and output pulse energy(Eseed = 10 mJ).

From the presented measurements, it was concluded that, not only the efficiencyincreases with higher pumping, it also increases with higher seed pulse energies. Themaximum pump pulse energy in the presented measurement was limited to 100 mJsince the rest of the available energy was delivered to the OPO. The maximum effi-ciency measured was 28 %, with the maximum output pulse energies of Eout = 37.5mJ. It should be noted that the only limit in the conversion efficiency in this

6.3. MOPA POWER MEASUREMENTS 55

measurement was the available total power delivered by the pump laser since theefficiency seamed as if it would continue to grow with increased pumping2. Sincesuch strong improvement in the conversion efficiency was observed when seedingwas increased, another measurement was performed to further investigate that be-haviour.

To investigate the dependence of the conversion efficiency on the seed pulseenergy, the OPO was increasingly pumped to produce seed pulse energies from 1 to10 mJ while the pump pulse energy was kept constant to Epump = 50 mJ.


0.05

0.1

0.15

0.2

0.25

0.3

Am

plifier

gai

n

1

1.5

2

2.5

3

3.5

4

4.5

Seed pulse energy [mJ]

2 4 6 8 10

Efficiency

Pump depletion

Amplifier gain

Figure 6.6. OPA conversion efficiency dependence on the seed pulse energy.

As already concluded from the previous measurements, the conversion efficiencyincreases with higher seed pulse energies, however, it can be seen from the pre-sented measurement that this effect is getting weaker as the seed pulse energies areincreased. This behaviour was expected since, with increasing efficiency, the pumpenergy is being more depleted which lowers the pump intensity in the crystal and,in turn, lowers the efficiency. It can be concluded that seeding the OPA with pulseenergies above 10 mJ does not have a further significant impact on the conversionefficiency.

6.3 MOPA power measurements

From this section, the results are discussed in terms of the overall MOPA perfor-mance, rather than the OPA stage alone. Since most of the properties in terms ofthe conversion efficiency were already presented in the previous section, this section

2The pump laser performance in terms of the maximum pump power severely decreased duringthe months of performing experiments. The maximum output power was around 14 W at the timewhen these measurements were performed. The laser was later on repaired, however, there wasunfortunately no time to repeat the measurements with higher pumping powers.


is just briefly discussing the overall MOPA conversion efficiency and output powerstability.

6.3.1 Overall conversion efficiency

Firstly, as in the case of OPA, the MOPA conversion efficiency needs to be defined:

η =Eout

EP OP O + EP OP A, (6.3)

where EP OP O is the OPO pump pulse energy, EP OP A is the OPA pump pulseenergy and Eout is the total 2 µm output pulse energy. Figure 6.7 represents theMOPA conversion efficiency when gradually changing the OPA pump pulse energiesto 100 mJ while keeping the OPO pump energy constant to 34 mJ.

Efficiency

0.23

0.24

0.25

0.26

0.27

0.28

0.29

OPA pump pulse energy [mJ]

0 20 40 60 80 100

Efficiency

Figure 6.7. MOPA overall conversion efficiency vs. OPA pump pulse energy withconstant OPO pumping EP OP O = 34 mJ.

It can be concluded from the figure above that the MOPA obviously extendsthe output power range when compared to the OPO. However, as expected, themaximum overall efficiency of the MOPA was lower than the OPO alone. It canalso be noticed that there is a point of minimal efficiency which can be explainedby the fact that the OPA efficiency is comparable to the OPO efficiency only athigher pumping powers and, therefore, at low pumping powers, the OPA stage onlydegrades the overall efficiency. The maximum overall MOPA efficiency η = 28.4was measured. Nevertheless, it can be concluded that, if one would pump the OPAwith even higher powers, the overall MOPA efficiency would continue to increaseup to a certain point of saturation.


The measurements presented in this subsection were performed to investigate towhat degree the MOPA output power inherits the properties of the seed beam in

6.4. SPECTRUM MEASUREMENTS 57

terms of power stability. The following measurement was performed in the samemanner as explained in subsection 5.3.2 for the case of the OPO, gradually tuningthe VBG to degeneracy and pumping the OPO with 3 W. The OPA stage waspumped with 5 W.

Output power RMS instability [%]

0

0.5

1

1.5

2

2.5

3

Average output power [W]

1.6

1.65

1.7

1.75

1.8

1.85

1.9


20 30 40 50 60 70

Output power RMS instability

Average output power

Figure 6.8. MOPA output power RMS instability and average vs. VBG tempera-ture.

Similar behaviour as presented in the figure 5.7 is observed for both the averagepower and the RMS instability showing that the seed power instability is directlytransferred to the MOPA output.

6.4 Spectrum measurements

The MOPA output spectrum was measured using the same technique as in the OPOcase. The spectrum was also taken for several VBG temperatures, tuning the OPOto degeneracy. As in the previously presented measurement, the OPO was pumpedwith 3 W and the OPA with 5 W. The output power was further attenuated by30 % and 50 % separation mirrors and aligned into the spectrometer. MeasuredMOPA output spectra for the VBG temperatures of 25 ◦C, 45 ◦C and 65 ◦C arepresented in figure 6.9.


Normalized intensity

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Wavelength [nm]

2127 2128 2129 2130 2131

T=25 oC

T=45 oC

T=65 oC

Figure 6.9. MOPA output spectrum at VBG temperatures set to 25 ◦C, 45 ◦C and65 ◦C.

If compared to the figure 5.3, it can be concluded that the MOPA almost com-pletely inherits the OPO spectral properties.

6.5 Beam quality, M 2

The final measurement was performed to evaluate the MOPA output beam quality.The M2 measurement was performed with high OPO pumping (3 W) operating offdegeneracy. The OPA stage was again pumped with 5 W and the output power wasattenuated in a similar manner as for the spectrum measurement. The followingfigure represents the measured spot sizes and table 6.1 summarizes the obtainedbeam parameters.

Bea

m spot size

W [µm

]

500

1000

1500

2000

2500

3000

z [mm]

50 100 150 200 250 300 350





Figure 6.10. Measured spot sizes along the focused MOPA output beam and theo-retical fits to the measured data for horizontal and vertical direction.

6.5. BEAM QUALITY, M2 59

M2 z0 [mm] W0 [µm] θd [◦] zR [mm]

Horizontal 14.3 204 589 1.88 35.8

Vertical 29.4 182 873 2.61 38.3

Table 6.1. MOPA output beam parameters estimated from the measured data forhorizontal and vertical direction: M2 value, beam waist position z0, beam waist W0,divergence angle θd and Rayleigh range zR.

Unfortunately, from the above presented measurement, it can be concluded thatthe MOPA output beam spatial characteristics are not only inherited from the OPObut also seriously degraded. Firstly, strong astigmatic behaviour can be noticed withthe focus offset of 22 mm between horizontal and vertical direction, and, secondly,a significant increase in the M2 value for the vertical direction was observed. Thisdegradation in the beam quality is assumed to be a consequence of the fact thatboth signal and idler are present in the amplifier and, moreover, they are both phaserelated to the OPA pump since the same pump source is used for the OPO and theOPA. For these reasons, the nonlinear conversion and the phase matching in theOPA is not precisely defined. Unfortunately, that seams to be a fundamental designissue of this MOPA setup and further investigation on the beam quality was out ofthe scope of this project.

Chapter 7

Discussion and outlook

7.1 Discussion and summary

The final outcome of this thesis was the design and characterization of a parametricmaster oscillator power amplifier. This section will shortly summarise the mostimportant results of the experimental work.

The pump laser used in this work was a Q-switched diode pumped solid stateNd:YAG laser operating at 100 Hz repetition rate. Firstly, the pump laser propertieswere characterized to serve as a starting point for further MOPA design. It wasmeasured that the pump laser offered 21 W of power in vertical polarization with10 ns long pulses and the RMS power instability of 0.08 %. The beam quality wasdescribed in terms of the M2 value that was shown to be approximately 1.9 in bothvertical and horizontal direction. Also, the spectrum FWHM of 0.05 nm (13 GHz)was measured1.

The emphasis of the experimental investigation was put on the design and char-acterization of the OPO since its behaviour was expected to highly influence theoverall MOPA performance. The OPO was built using a large aperture (5x3 mm)10 mm long PPKTP crystal designed to operate at degeneracy. A planar dielectricmirror was used as an input coupler and a VBG as an output coupler for spectralnarrowing. Temperature control of the crystal and the VBG was employed whichallowed both near-degenerate and degenerate OPO operation and, therefore, oper-ating in both modes was further investigated. Operating near degeneracy resulted inthe maximum OPO conversion efficiency of 37 % and the maximum output powerof 1.3 W while pumping with maximum pumping power of 3.6 W. RMS outputpower instability of < 1 % was measured and the beam quality described with theM2 value of 8 in horizontal and 10 in vertical direction was obtained. On the otherhand, operating at degeneracy offered lower performance in all mentioned aspects:lower conversion efficiency (31 %), lower output power (1.1 W), higher RMS in-stability (2 %) and lower beam quality (horizontal M2 = 9, vertical M2 = 12).

1It should be noted that spectrum measurements performed in this project were close to theresolution limits of the measurement equipment used.

61

62 CHAPTER 7. DISCUSSION AND OUTLOOK

Additionally, the 2 µm pulses were measured to be 5 ns long and the OPO outputspectral FWHM of approximately 0.46 nm (30 GHz) was obtained.

In theory, one could expect higher OPO efficiencies since the calculated OPOefficiency for Gaussian beams is around 70 % [24]. However, high linear losses (30%), partially due to imperfect crystal and VBG coatings, and excitement of higherorder transversal cavity modes, contribute to lower efficiency. OPO efficiencies of24 % and 42 % were reported in similar systems [25, 9], however, at lower pulseenergies and lower repetition rates. OPO spectral properties were similar to thementioned systems, where it was shown that a VBG lowers the spectrum FWHMby two orders of magnitude compared to using a flat mirror as an output coupler.The obtained OPO output beam quality can be seen as already fairly degradedwhich can be accounted to operating many times above the OPO threshold and,consequentially, excitement of higher order transversal modes in the cavity.

The OPA stage consisted of two temperature controlled large aperture (5x5 mm)10 mm long Rb:PPKTP crystals. The OPO 2 µm output beam was used as a seedin the OPA process, whereas the pump beam was provided by the same laser asfor the OPO. The OPA conversion efficiency showed large dependence on the seedpower: at low seeding (160 mW), maximum efficiency of 18 % was measured and,at high seeding (1 W), the maximum efficiency of 28 % was achieved, resultingin the maximum output power of 3.7 W. Seeding with more than 1 W showed nosignificant improvement in the conversion efficiency.

Finally, the overall MOPA performance was evaluated. As expected, many ofthe output beam properites were directly inherited from the OPO, particularly thespectral properties and output power stability. The overall conversion efficiencywas shown to be 28.4 % with the mentioned output power of 3.7 W. At the timeof measurement, full power range of the pump laser was not available, however, themeasurements suggested that both the output power and the conversion efficiencycould be increased with higher OPA pumping. Similar system reported in [26]showed higher efficiency (43 %), however, lower total output power (2.6 W). Thebeam quality investigated for high seeded (1 W) OPA pumped with 5 W resulted inthe M2 value of 14 in horizontal and 29 in vertical direction. Unfortunately, that ispointed out as a major drawback of such a design and requires further investigationand improvement.

7.2 Future work

There are three major properties of the presented MOPA setup that could be mostbeneficial to improve: the overall conversion efficiency, the beam quality and theoutput power stability (especially when operating at degeneracy).

In terms of the conversion efficiency, it seams that the OPA stage offers mostspace for improvement. Firstly, using longer crystals might improve the OPA per-formance since it was already shown that the usage of two crystals provides superiorperformance over using only one. That approach, however, has its limits because

7.2. FUTURE WORK 63

the gain would eventually saturate and the efficiency wouldn’t further increase af-ter a certain crystal length. Another approach for increasing the efficiency couldbe utilizing a double-pass OPA setup by reflecting both the 2 µm output and thedepleted pump to pass once more through the crystals in the opposite direction.That approach, on the other hand, could be difficult to achieve since the beam spotsize is comparable to the crystal dimensions and, therefore, separation of the outputbeam could represent a technical issue. Apart from the OPA stage, the OPO wasshown to have fairly large linear losses (30 %). Since those linear losses are partiallydue to imperfect crystal and VBG coatings, improving them would potentially offerhigher OPO efficiency.

As already mentioned, a major drawback of the presented MOPA design isthe beam quality. Improvement of the OPA beam quality degradation could bepossible by seeding the OPA with only signal or idler, resulting in a better definedamplification process. That could be possible by using another spectral filteringstage, possibly a VBG.

Finally, the shortcomings of the degenerate OPO operation (lower conversionefficiency, higher power instability, lower beam quality) could possibly be circum-vented by utilizing an active cavity stabilization. Another approach could be theuse of a ring OPO cavity and, therefore, avoiding the formation of standing waves.Ring cavities, on the other hand, are usually longer and are more difficult to align.

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