Laser Basics - U.S. Particle Accelerator School · Laser applications for accelerators Laser Basics Yuelin Li Accelerator Systems Division Argonne National Laboratory [email protected]

Laser applications for accelerators

Laser Basics

Yuelin LiAccelerator Systems DivisionArgonne National [email protected]

USPAS 2008 Summer Session, Annapolis, June 23-27, 2008

2USPAS, 2008

ContentLaser and accelerator historyMap of laser application in acceleratorsLaser basics– Rate equations– Laser configurations– Gaussian beam optics and ABCD law– Laser cavity and laser modes

Laser configurations– Mode-lokcing and q-switch– MOPA – CPA and dispersion

Laser materials Other lasers– Semiconductor lasers– Fiber lasers

Frequency conversion and short wavelength lasers

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Lasers and accelerators at birth

Ancient: Let there be light…………………..1917, theory of stimulated

radiation by Einstein1960, flash-lamp pumped

ruby, Dr. Mainman1964, Nobel Prize, Towne,

Basov, and Prokhorov

Ancient: a cave man’s bow……………….1929, Cyclotron, Lawrence1939, Nobel Prize, Lawrence

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Today’s lasers and acceleratorsAiming for higher energy/intensity and better control

APS, ANL

(Panofsky, http://www.slac.stanford.edu/pubs/beamline) (http://www.eecs.umich.edu/CUOS)

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Newest developments

Accelerator-generated lasers: a free-electron laser

Laser as an accelerator: a compact accelerator

Geddes et. al., Phys Plasmas 12, 056709 (2005)

Laser plasma bubble

Laser

Gas jet

Electron beam

-0.4 0.0 0.4268

266

264

τ (ps)

FEL FROG trace

S.P.D. Mangles et al. Nature 431, 535 (2004); C.G.R. Geddes et al. Nature 431, 538 (2004); J. Faure et al. Nature 431, 541 (2004)

Credit: Becker et al, LMU

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A map for laser applications in accelerators

Beam generation

Beam Characterizationmonitoring

BeamProcessing treatment

Radiation/particle source generation

• Laser/accelerator synchronization• Laser pulse shaping• Plasma wake wave accelerator

• Laser beam cooling/heating• Laser modulation

• Laser beam scattering• Electroptical sampling • Inverse free-electron laser

• Laser beam scattering• Laser beam timing • Laser modulation

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Laser configurations– Mode-locking and Q-switch– MOPA – CPA and dispersion



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Laser

Light Amplification by Stimulated Emission of Radiation

Excited medium

If a medium has many excited molecules, one photon can become many.

This is the essence of the laser. The factor by which an input beam is amplified by a medium is called the gain and is represented by G.

Credit: R. Trebino

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Rate equations for a two-level system

Rate equations for the densities of the two states:

21 2 2( )dN BI N N AN

dt= − −

12 1 2( )dN BI N N AN

dt= − +

22 2d N BI N ANdtΔ

= − Δ +

Absorption Stimulated emission Spontaneous emission

1 2N N NΔ ≡ −1 2N N N≡ +

If the total number of molecules is N:

2 1 2 1 22 ( ) ( )N N N N NN N

= + − −= −Δ

2d N BI N AN A NdtΔ

= − Δ + − Δ⇒

⇒

2

1

N2

N1

LaserPump

Pump intensity

Credit: R. Trebino

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Why inversion is impossible in a two-level system

0 2BI N AN A N= − Δ + − Δ

1 / sat

NNI I

Δ =+

/ 2satI A B=

In steady-state:

( 2 )A BI N AN⇒ + Δ =

where:

ΔN is always positive, no matter how high I is!

It’s impossible to achieve an inversion in a two-level system!

⇒

2d N BI N AN A NdtΔ

= − Δ + − Δ

/( 2 )N AN A BI⇒Δ = +

/(1 2 / )N N BI A⇒Δ = +

Isat is the saturation intensity.

2

1

N2

N1

Laser

Credit: R. Trebino

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A 3-level system

Assume we pump to a state 3 that rapidly decays to level 2.

21 2

dN BIN ANdt

= −

11 2

dN BIN ANdt

= − +

1 22 2d N BIN ANdtΔ

= − +

Absorption

Spontaneous emission

1 2N N NΔ ≡ −1 2N N N≡ +

The total number of molecules is N:

22N N N= −Δ

d N BIN BI N AN A NdtΔ

= − − Δ + − Δ⇒

Fast decay

Laser TransitionRate: A

PumpTransition

Rate: BI

1

23

Level 3 decays fast and so is zero.

12N N N= + Δ

Credit: R. Trebino

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Population inversion, 3 level system

1 /1 /

sat

sat

I IN NI I

−Δ =

+/satI A B=

In steady-state:

( ) ( )A BI N A BI N⇒ + Δ = −

where:

Now if I > Isat, ΔN is negative!

⇒

( ) /( )N N A BI A BI⇒Δ = − +

Isat is the saturation intensity.

d N BIN BI N AN A NdtΔ

= − − Δ + − Δ

0 BIN BI N AN A N= − − Δ + − Δ

Fast decay

Laser TransitionRate: A

PumpTransition

Rate: BI

1

23

Gain: Ng Δ−∝ σ Credit: R. Trebino

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Rate equations for a four-level system

Now assume the lower laser level 1 also rapidly decays to a ground level 0.

20 2

dN BIN ANdt

= −

1 0,N ≈

22 2( )dN BI N N AN

dt= − −

2N NΔ ≈ −

Laser Transition

Pump Transition

Fast decay

Fast decay

1

2

3

0As before:

Because0 2N N N≡ +

The total number of molecules is N :

0 2N N N= −d N BIN BI N A N

dtΔ

− = + Δ + Δ

At steady state: 0 BIN BI N A N= + Δ + Δ Credit: R. Trebino

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Population inversion in a four-level system (cont’d)

0 BIN BI N A N= + Δ + Δ

/1 /

sat

sat

I IN NI I

Δ = −+

/satI A B=where:Isat is the saturation intensity.

Now, ΔN is negative—always!

Laser Transition

Pump Transition

Fast decay

Fast decay

1

2

3

0

⇒

( / ) /(1 / )N BIN A BI AΔ = − +⇒

/( )N BIN A BIΔ = − +⇒

( )A BI N BIN+ Δ = −⇒

Credit: R. Trebino

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How to build a laser

R = 100% R < 100%

I0 I1

I2I3 Laser medium

I

• Laser medium• Depends on wavelength, pulse duration, power

• Pump it: ASE• Multimode in time and space

• Add resonator: laser oscillation• Mode selection

Credit: R. Trebino

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The historic ruby laser

Invented in 1960 by Ted Maimanat Hughes Research Labs, it was the first laser.

Ruby is a three-level system, so you have to hit it hard.

Credit: R. Trebino

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Helmholtz Equation: Gaussian beam optics

)(

2

2

2

22

),,(),,,(

0),,,(

tzki zezyxAtzyxE

tzyxEtc

n

ω−=

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∇

02 2

222

2

2

2

2

2

2

=+∂∂

+−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+∂∂ A

cnA

zkiAkA

zxx zzω

Wave equation

Paraxial condition

λπω 2, 2

222

2

2

nc

nkAz

Az z ==

∂∂

<<∂∂

Paraxial Helmholtz equation

022

2

2

2

=∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂ A

zkiA

yx z

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Gaussian beam optics

022

2

2

2

=∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂ A

zkiA

yx z

yxykxki

yx

ykxkiyx

dkdkezkkazyxA

dxdyezyxAzkka

yx

yx

)(2

)(

),,(4

1),,(

),,(),,(

+

+−

∫∫

∫∫=→

=

π

Fourier transform

Thus ( )

zkkk

i

yxyx

z

yx

yxykxki

zyx

z

yx

yx

ekkazkka

akkk

iaz

dkdkeaz

kiakk

20

22

)(222

22

)0,,(),,(

2

024

1

+−

+

=→

+−=

∂∂

→

=⎥⎦⎤

⎢⎣⎡

∂∂

+−−∫∫π

Paraxial Helmholtz equation

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.)0,,(20

2

20

22

00wr

wyx

eAeAyxA−

+−

==

20

22

20

22

40

20

)(0)0,,(

wkk

yxykxkiw

yx

yx

yx

yx

eAw

dkdkeeAkka+

−

+−+

−

=

= ∫∫

π

Fourier transform

Thus

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++−

+−+

−

+−

=

=

=

0

2220

2220

22

22

14

020

240

20

20 )0,,(),,(

zzikkw

zkkk

iwkk

zkkk

i

yxyx

yx

z

yxyx

z

yx

eAw

eeAw

ekkazkka

π

π

Let

λπ

20

20

0 2wwkz z ==Rayleigh length (diffraction length)

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( )

( ) ( )

ηη

π

ππ

π

izRyxik

zwyxi

zzi

zwyx

zzi

zwyx

zzi

zizwyx

yxykxkikk

zizw

yxykxkiz

zikkw

yxykxki

yx

eezwwAe

zwwA

eezz

Aeziz

A

dkdkeeAw

dkdkeeAw

dkdkezkkazyxA

yxyx

yxyx

yx

−++

−−⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−−

++

−

+++

−

+⎟⎟⎠

⎞⎜⎜⎝

⎛++−

+

==

+=

+=

=

=

=

−

∫∫

∫∫

∫∫

)(2)(001

)(00

1)(

tan

20

20)/1(

0

0

)(4/1

0

20

)(1

40

202

)(2

22

2

22

02

22

02

22

0

1

020

22

222

00

0

2220

)()(

/1/1

41

41

),,(4

1),,(

0

12

20

2/1

20

2

0 tan1)(1)(zz

zzzzR

zzwzw −=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+= η

Inverse Fourier transform

Beam radius

0

1tan

20

2

020

20

/11

1/1

1/1

1

zzi

ezz

zzi

zzziz−−

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

+

Wave front radius of curvature

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Gaussian optics: summary

.2

,2

,

,1)(

,)(

exp)(

),(

0

0

20

0

2

00

2

20

0

zb

w

wz

zzwzw

zwr

zwwEzrE

=Θ

=

=

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

πλλπ

w0: beam waistz0: Rayleigh rangeb: confocal parameter

• Gaussian distribution is the solution of paraxial Helmholtz equation• TM00 mode

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Beam propagation: ABCD matrices

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛θθr

DCBAr

''

For a thin lens

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=⎟⎟⎠

⎞⎜⎜⎝

⎛1/101

fDCBA

For free space (drift space)

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛10

1 dDCBA

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Cavity: Optical resonators

Credit: W. Koechner: Solid State Laser engineering, Credit: Wekipedia

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Stability of laser resonators

.1

,1

,2110

22

11

21

RLg

RLg

RL

RL

−=

−=

<⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−<

Credit: W. Koechner: Solid State Laser engineering, Credit: Wekipedia

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High order modes

K

xxxHxxHxxH

xH

128)(24)(

2)(1)(

33

22

1

0

−=

−=

==

⎥⎦

⎤⎢⎣

⎡++−

+−+

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

)()1()(2)(

2

20

0

22

2

22

)(2

)(2

)(),,(

zmnzRyxki

zwyx

mn eezwyH

zwxH

zwwEzyxE

η

Hermite polynomials

The M2 factor

0

2

2 wM

πλθ =

Θ=

M2=1=diffraction limited; M2 >1, M2 times diffractions limited

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High order modes

Hermite-Gaussian modesIntensity profile

Guided modes in fibersField

Encyclopedia of Laser Physics and Technologyhttp://www.rp-photonics.com/higher_order_modes.html

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A cavity and laser oscillator

Resonant condition for cavity: L=nλ

Energetic electrons in a glow discharge collide with and excite He atoms, which then collide with and transfer the excitation to Ne atoms, an ideal 4-level system.

Credit: R. Trebino

Credit: Cundiff, UCB

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Laser configurations– Mode-locking and Q-switch– MOPA – CPA and dispersion



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Mode locking: what

Credit: Cundiff, UCB

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Mode locking: how

Introduce amplitude or phase modulation/control

Active mode locking• Acousto-optic modulator, drive with RF

Passive mode locking • Saturable absorption• Nonlinear lensing + aperture• Nonlinear polarization rotation + polarizer

Mode locking: result

Shorter pulse, high intensity, larger bandwidthSingle modeAccurate timing at round trip time

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Ti: Sapphire oscillator: an example

Femtolasers: Fusion(28”x12”x3”)

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Q-switch

LTQ πν 2

=

Q factor of a resonator

T: round trip time; ν: optical frequency; I: fraction power loss per round trip

Q switch: reducing the loss

Active: accousto-optical, electro-optical, and mechanicalPassive: saturable absorbers

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Compressing,Shaping,

Conversion,diagnosing

filteringstretching, shaping,filtering

A MOPA systemMaster Oscillator – Power Amplifier

An oscillator usually does not have enough energy, thus needs amplificationA MOPA is expected to carry over the characteristics of an OSCPulse duration is limited at 10 ps due to damage

Master Oscillator Pre-amp Power amp Post

processing

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A MOPA example: Flash drive laser

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Chirped pulse amplification

To be able to amplify a short pulse.

Oscillator Stretcher Amplifier Regen/multipass + power Compressor

shaping

fs- ps ps - ns fs - ps

ps- ns

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A CPA example

S. Backus et al, Rev. Sci. Instrum. 69, 1207 (1998).

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How to stretch/compress a pulse: adding second order phase

A transform-limited Gaussian pulse in the time and frequency domain

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛Δ

−=⇔⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=

2

0

2

0 21exp)(

21exp)(

ωωω

τEEtEtE


Add a second order phase, which is to ‘chirp’ a pulse

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛Δ

−=′ 22

0 21exp)( ω

ωωω iaEE

What is the new pulse form in the time domain? How does the frequency change as function of time? (Home work)

40USPAS, 2008

Stretcher and compressor


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Stretcher and compressor


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Dispersions


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Laser materials

What we care– Lasing mechanism: four-level systems is always preferred– Lasing wavelength: tunable is better– Lasing bandwidth: bigger is better but not always– Pump requirement: visible preferred– Gain lifetime: longer is better– Damage threshold: higher is better– Saturation flux: higher is better– Heat conductivity: as high as possible– Thermal stability: as small as possible– Form: solid is always preferred

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Laser materials

Host + active ions Host

– Crystalline solids (Sapphire, Garnets, Fluoride, Aluminate, etc.)• Difficult to grow to large size• Narrow line width thus lower lasing threshold, and narrow absorption

band • Good thermal conductivity

– Glass (property varies by make, and processing)• Easy to make in large size and large quantities• No well defined bonding field thus larger line width and higher lasing

threshold, large absorption band• Lower thermal conductivity thus severe thermal birefringence and

thermal lensing, lower duty cycleActive ions

– Rare earth ions: No. 58-71, most importantly, Nd3+, Er3+…– Transition metals: Ti3+, Cr3+,

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Laser material: Ti: Saaphire (Al2O3:Ti3+)

• Giving shortest pulse so far• Wonderful tunability• Good thermal properties• Short gain lifetime (has to be

pumped by a ns-pulsed green laser)

47USPAS, 2008

Laser material (Nd:YAG)

• High saturation flux• Narrow bandwidth (0.15 nm), thus

long pulse (>10 ps), high gain• Good thermal properties• Long gain lifetime (diode pump)

Absorption spectrum

Fluorescent spectrum

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Laser material: (Nd:Glass)

• High saturation flux• large bandwidth (20 nm), thus short

pulse (<1 ps),• Poor thermal• Long gain lifetime (diode pump)• Only for big lasers now (PW or MJ)

Absorption spectrum

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Laser Material: Nd:YLF

• High saturation flux• Narrow bandwidth (0.15 nm), thus

long pulse (>10 ps), high gain• Good thermal properties• Long gain lifetime (diode pump)• Difficult to handle

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Laser materials: summary

-0.57.3dn/dT (10-6/°C)

1.51.551.81.76n

10107.5Thermal expansion coef(10-6/°C)

0.060.00840.140.5Thermal conductivity( w cm-1 K-1)

.434.5 0.60.9Saturation flux(J/cm2)

1.80.46.53Emission cross section (10-19

cm2)

1220.15220 Line width (nm)

1047,105310541064780 Peak wavelength (nm)

4853302303.2Fluorescence life time (μs)

Nd:YLFLiY1.0-xNdxF4

Nd:Glass (Kigre Q-88)

Y3Al5O12:Nd

Nd:YAGY3.0-xNdxAL5O12

Ti:SaAl2O3:Ti

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Semiconductor laser: laser diode

Credit: http://www.olympusmicro.com/

• Convert current into light, can be tuned by junction temperature• Used mostly for pumping other lasers, also CD and DVD players• VCSELs and VECSELs (virtical cavity surface emission

lasers and virtical exteranl cavity surface emission lasers)• Also for seeding pulse fiber lasers (next page)

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Mode-locked semiconductor lasers:(using V)

• Can achieve sub picosecond pulse duration• 500 mW power• Widely tunable• Very high rep rate, up to 100 GHz

Opt. Express 16, 5770 (2008)

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Pump for lasersFlash lamps: – Converts electrical power to light– Cheap, low pumping efficiency, and poor

stability. – Still opted for situations when high energy

capacity is the key (NIF), suitable for ruby laser, Nd:Glass, Nd:YAG, Nd:YLF, etc.

Laser diodes: – converts electrical current into light– High efficiency, high stability especially in CW

mode. – Opted now for most off the shelf KHz system

and fiber lasers Pump lasers (Nd:YAG or Nd: YLF)– Both pumped by flash lamps and diodes– Normally for Ti: Sapphire system.

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Fiber lasers

Power progress in fiber laser sources

Teodoro et al, Laser Focus World, Nov. 2006

Peak Power over 1 MW

Average power over 2 kW

limited by available pump

Credit: David Richardson

56USPAS, 2008

Laser configuration: Fiber lasers

Can be a straight MOPA or a CPA Low threshold, high efficiency, high rep rate, high powerNo thermal problem, good stabilityRelatively large bandwidth for CPA fiber

Credit: David RichardsonJ. Limpert et al., 'High-power ultrafast fiber laser systems,' IEEE Xplore 12, 233 (2006).

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Fiber laser wavelength


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Fiber laser capabilities


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Fiber laser architecture


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A short pulse MOPA fiber laser example1 GHz, 20 ps, 321 W average and 13 kW peak power

Dupriez et al, http://www.ofcnfoec.org/materials/PDP3.pdf

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A CPA fiber laser example 73 MHz, 220 fs, 131 W average and 8.2 MW peak power

Roeser et al., Opt. Lett. 30, 2754 (2005)

J. Limpert et al., 'High-power ultrafast fiber laser systems,' IEEE Xplore 12, 233 (2006).

1 μm, 1 mJ, 1 ps, 50 kHz has been achieved, F. Roeser et al, Opt. Lett. 32, 3294 (2007)

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Maxwell equation in a medium

The induced polarization, P, contains the effect of the medium:

0 0 0

0

0

BE Et

E PB Bt t

μ ε μ

∂∇ ⋅ = ∇× = −

∂∂ ∂

∇ ⋅ = ∇× = +∂ ∂

rr r r r

r rr r r r

The induced polarization in Maxwell’s Equations yields another term in the wave equation:

As we’ve learned, this is the “Inhomogeneous Wave Equation.”The polarization is the driving term for a new solution to this equation.

2 2 2

02 2 2 2

1E E Px c t dt

μ∂ ∂ ∂− =

∂ ∂

Credit: R. Trebino

64USPAS, 2008

Maxwell equation in a nonlinear medium

Credit: R. Trebino

What are the effects of such nonlinear terms? Consider the second-order term:

2ω = 2nd harmonic!

Harmonic generation is one of many exotic effects that can arise!

(1)0ε χ⎡ ⎤= ⎣ ⎦c X

*

*2222

( ) ,

( )

exp( ) ex

2exp(2 ) exp(

p

2

(

)

)

E

E i t

i t E

E i t

i t

t

t E

ω ω

ω ω

∝

−∝

+ −

+ +

X

X

Since

(1) (2) 2 (3) 30 ...ε χ χ χ⎡ ⎤= + + +⎣ ⎦c X X X

Nonlinear optics is what happens when the polarization is the resultof higher-order (nonlinear!) terms in the field:

65USPAS, 2008

[ ] [ ][ ] [ ]

* *1 2 1

* *1 2 1 2 1 2 1 2

2 *

2

2 21 2

2 1 2

2

2

1 2

2 2

21 1 1

2

*1

2

2 exp (

exp(2 ) exp(

2 exp (

exp(2 ) exp( 2 )

) 2 exp

) 2 ex

2 )

(

p

( )

)

(

2

)

2

E i t E

E

E E i t E E i t

i t

E

E i t E E i t

E t

E E

i t E i t

ω ω

ω ω

ω ω ω

ω

ω

ω

ω

ω

+

+

∝

+

+

+ −

+ − +

+

+

−

+

+ −

− −

Sum and difference frequency generation

Suppose there are two different-color beams present:

*1 1 1 1

*2 2 2 2exp( ) e exp( ) exp( ) x (( )) pE i t E i t E i t E i tE t ω ω ωω + − −∝ + +

Note also that, when ωi is negative inside the exp, the E in front has a *.

2nd-harmonic gen

2nd-harmonic gen

Sum-freq gen

Diff-freq gen

dc rectification

So:

Credit: R. Trebino

66USPAS, 2008

Credit: R. Trebino

Conservation laws and phase matching

Unfortunately, may not correspond to a light wave at frequency ωsig!

Satisfying these two relations simultan-eously is called "phase-matching."

sigkr

1 2 3 4 5 sigω ω ω ω ω ω+ + − + =

1 2 3 4 5 sigk k k k k k+ + − + =r r r r r r

Energy must be conserved:

Momentum must also be conserved:

sigkr

ωsig

67USPAS, 2008

Phase matching and conversion efficiency

Small signal second harmonic conversion efficiency

2/30

30

200

222

22222

2

2222

46.58

,2

sin

2

2sin

nd

ncd

C

lLcILC

kL

kL

ILCI

effeff

c

λλεπ

πωωω

==

=

⎟⎠⎞

⎜⎝⎛ Δ

Δ

=

Δk=4π/λ1(n1-n2): difference in wave umberL: crystal lengthlc=π/Δk, coherence length (when phase is matched)deff: effective nonlinear coefficient, in m/V

Credit: W. Koechner: Solid State Laser engineering,

68USPAS, 2008

Conversion efficiency at small signal

The small signal conversion efficiency and effect of phase mismatch

clLcLC

2sin 222 πη =

Credit: W. Koechner: Solid State Laser engineering,

69USPAS, 2008

Quasi phase matching

Quasi-phase matching Achieve phase matching by modulating the spatial nonlinear property

Tune the interaction here

Encyclopedia of Laser Physics and Technologyhttp://www.rp-photonics.com

70USPAS, 2008

Quasi-phase matching: Periodically poling crystals

The most popular technique for generating quasi-phase-matched crystals is periodic poling of ferroelectric nonlinear crystal materials

Credit: www.raicol.com/products.asp

Wavelength Range: 400-4000 nmDimensions:

Thickness: up to 1 mm Width (typical): 2 mm Length: up to 30 mm

71USPAS, 2008

Pump depletion and signal saturation

Phase match, with pump depletion

,2

sintanh 2/122 ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

clLcCLIII π

ωωω

Consider frequency quadrupling– At low pump power, highly nonlinear

Consider frequency quadrupling– At high pump power, linear, desired

4224

22

ωωω

ωω

IIIII

∝∝⇒

∝

ωωω

ωω

IIIII

∝∝⇒

∝

24

2

linearsaturation

72USPAS, 2008

Frequency conversion: High order harmonics generation

Atoms as the nonlinear mediaEmission due to multiple photon absorption of electrons bounded to an atomCarry over the spatial coherence of the driving laserOf short pulse duration comparable or shorter than the drive laser up to attosecondsCurrently at ~10 nm.

H. Kaptyn et al., 'Harnessing Attosecond Science in the Quest for Coherent X-rays,' Science 317, 775 (2007).

73USPAS, 2008

High order harmonics generation: phase matching

Phase mismatching due to group velocity difference or continuous signal emission or group velocity mismatchCan be accomplished by modulating the interaction via modulated laser propagation or counter propagating beams

H. Kaptyn et al., 'Harnessing Attosecond Science in the Quest for Coherent X-rays,' Science 317, 775 (2007).

74USPAS, 2008

Short wavelength lasers

Plasma base soft-x-ray lasers– Still a traditional laser based on population inversion, but in hot dense

plasma to accommodate the high energy difference between atomic levels, wavelength from 1 nm to 100 nm.

– Can be pumped by laser, discharge, and bombs– Challenges: tunability and capability for shorter wavelengths,

stabilities– J. Hecht, “The history of X-ray lasers,” Optics & Photonics News 19,

26 (2008); Y. Wang et al., Nature Photonics 2, 94 (2008)

75USPAS, 2008

Short wavelength lasers

X-ray Free electron lasers: 0.1 nm, high brightness, high transverse coherence, etc. Design with cavity going onMany projects going on

Documents

Laser Basics - U.S. Particle Accelerator School · Laser applications for accelerators Laser Basics Yuelin Li Accelerator Systems Division Argonne National Laboratory [email protected]