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Physical Optics
Lecture 8: Laser
2017-05-24
Beate Boehme
Most slides from Herbert Gross
Physical Optics: Content2
No Date Subject Ref Detailed Content
1 05.04. Wave optics G Complex fields, wave equation, k-vectors, interference, light propagation, interferometry
2 12.04. Diffraction B Slit, grating, diffraction integral, diffraction in optical systems, point spread function, aberrations
3 19.04. Fourier optics B Plane wave expansion, resolution, image formation, transfer function, phase imaging
4 26.04. Quality criteria and resolution B Rayleigh and Marechal criteria, Strehl ratio, coherence effects, two-point
resolution, criteria, contrast, axial resolution, CTF
5 03.05. Polarization G Introduction, Jones formalism, Fresnel formulas, birefringence, components
6 10.05. Photon optics D Energy, momentum, time-energy uncertainty, photon statistics, fluorescence, Jablonski diagram, lifetime, quantum yield, FRET
7 17.05. Coherence G Temporal and spatial coherence, Young setup, propagation of coherence, speckle, OCT-principle
8 24.05. Laser B Atomic transitions, principle, resonators, modes, laser types, Q-switch, pulses, power
9 31.05. Gaussian beams D Basic description, propagation through optical systems, aberrations
10 07.06. Generalized beams D Laguerre-Gaussian beams, phase singularities, Bessel beams, Airy beams, applications in superresolution microscopy
11 14.06. PSF engineering G Apodization, superresolution, extended depth of focus, particle trapping, confocal PSF
12 21.06. Nonlinear optics D Basics of nonlinear optics, optical susceptibility, 2nd and 3rd order effects, CARS microscopy, 2 photon imaging
13 28.06. Scattering G Introduction, surface scattering in systems, volume scattering models, calculation schemes, tissue models, Mie Scattering
14 05.07. Miscellaneous G Coatings, diffractive optics, fibers
D = Dienerowitz B = Böhme G = Gross
3
Content
- Spontaneous and Stimulated Emission
- Laser Amplifiers and Feedback
- Resonator optic
- Laser types
Laser
- Quality of laser beams
- Introduction
- Summary
4
Laser
Light Amplification by Stimulated Emission of Radiation difffraction-limited beams with high intensity well defined, in general narrow spectral width - monochromatic Spatial (lateral) and temporal (axial) coherence
Components Amplifier active medium: emission of photons by atoms or molecules
stimulated emission of photonssolids (crystals: ruby 1960, semiconductors, fibers, … ) gases (HeNe, CO2), fluids (dye lasers), gain saturation
Power supply creation of an inverse occupation of energy levels at minimum 3-energy levels with relaxation time optic or electric energy
Resonator positive feedback of selected frequencies
Steady-state: gain = resonator loss4
Laser – safety of radiation
laser warning sign: DIN EN ISO 7010 Laser classes: DIN EN 60825-1 (2007)
DIN VDE 0837 class 1: the accessible laser radiation is safeclass 2: it’s a VIS laser (400-700nm)
an exposure less than 0,25s is safe for the eye (in discussion) class 3B: the radiation is dangerous for the eye, sometimes for skin
diffuse scattered light is safe class 4: danger for eye, tissue
and with scattered light
Visible laser: eye lid closure Invisible laser no lid closure,
often class 3B Classification depends on wavelength,
cw or pulsed exposure type and time, divergence
5
19
https://wikimedia.org: Von Danh - Eigenes Werk, CC BYSA 3.0
Example: MZB for collimated cw laser
6
Laser
Spontaneous and Stimulated Emission
Laser amplification
7
Spontaneous and stimulated emission
Excitation of an atom to a higher energylevel
Energy of the photon and wavelength
Ref.: M. Kaschke
Photon
E1
E2
21 EEhc
photon
21 EEhEPhoton
> 90nm
Photon
sp
Absorption
Spontaneous emission
Stimulated emission
Deexcitation Statistical process with finite life time sp
2 Photonen1 Photon
Deexcitation stimulated by incoming photon
ZNa eII 112
0
ZNst eII 221
0
7
8
Thermodynamic Equilibrium and 2-Level-System
Equilibrium of population according to the Boltzmann distribution
Ref.: M. Kaschke
kTEE
eNN 12
1
2
Photon
N2
N1
Energy
population
E2
E1
E
absorptionspontaneousemission
stimulatedemission
If N2 > N1: inversiongain
Total gain factor over a length z
With a two-level system it is impossible to obtain an inversionof the population, because absorption and stimulated emission have equal probability
)()( 1212 NNg
zgeIIG 0
8
9
3-Level System
Three energy levels
Inversion is only possible for strongpumprates W
Non-radiative relaxation:life time 3
Laser level must have longer life time 2
At least 50% of the atoms must be in theupper level
Ref.: M. Kaschke
21
2 WNN
2 >> 3
pumprate
pump level
2
3
basic/ground level
LASER
fast non-radiativetransition
E2
E3
E1
W
9
10
4-Level System
Two fast non-radiative transitions
If the relations:
4 << 3 , 3 large , 2 small
are fulfilled:inversion of population is independent of thepump rate
Comfortable laser scheme
Ref.: M. Kaschke
2
3
2
3
NN
E2
E3
E1
E4
WLASER2
3
fast non-radiativetransition
fast non-radiativetransition
10
11
Stationary Laser Oscillator
Setup
Laser condition: Gain at active medium > Resonator losses
Cw-laser: gain = loss
Ref.: M. Kaschke
Pumpsource
Laser Material
mirror
(R = 100%)
coupling mirror
(R < 100%)
Laser beamL
Z = 0 Z = L
gain
loss
powerSteady-state condition
11
12
Axial Modes
The mirrors are phase surfaces
The standing wave inside the resonator must have knots at the mirrors
Every integer q gives one axial mode
2/qL
L
q / 2
mirror mirror
(q+1) / 2
q q+1q-1
c 2L
12
Spectral distribution of amplification 13
Freq.
Gain
Loss res
axial resonator modes
Spectral bandwidth B with gain res loss Finite number of axial modes M ~ B / inhomogeneously broadened medium:
independent processes multimode laser Homogeneously broadened medium:
gain saturation central modes compete with the peripheral. in ideal case one mode remains, but spatial hole burning
B
Laser spectrum
13
Pulsed Lasers: Methods 14
Cw-laser and external switch: peak power < cw power
Internal modulation: collection of energy:
Gain switching: pumping power Q-switching = loss switching: increasing resonator losses by modulated absorption: ns Cavity dumping: modification of mirror transmission
Mode-locking: multimode-modes are locked with their phases togetherperiodic pulse train with period T = 2L/c = time for single round trippulse width: fs, t = T / M = 1/ M
14
15
Q-Switch
Time dependencies for cw and pulsed mode
Ref.: M. Kaschke 15
16
Mode Locking
Fixed phase relation between modes Full interference of amplitudes Pulse corresponds to Fourier transformation sin (M)/sin()
shorter pulses for high number of modesrepetition rate correspons to
qq 1
Ref.: M. Kaschke 16
17
Laser
Resonator optic
18
Laser resonators
Planar mirror resonator
Ring resonator
Fiber resonator
Spherical mirror resonator
18
19
Laser resonators – ray description
paraxial description with matrix formalism for rays:
′′
10 1
1 0 1
free space, distance L
lens / mirrorStable resonator: Conservation of rays after m periods:
Differential equation for ray parameters
Grating: extension of formalism possible
1 01 1 0
0 1
R1 R2
19
20
Laser resonators – ray description
g
-3 -2
1
-1
2
3
g1
-3
-2
1
-1
2 3
2
stable regimes
symmetric confocal
plane-plane
Symmetric concentric
Confocal-planar
Concave/convexStable resonator with real solution: Condition
0 < g1 g2 < 1
22
11 11
RLg
RLg
R1= R2=oo
R1= R2= L
R1= R2= L/2
Mirrors are phase surfaces
g1-g2 diagram of stability
yellow regions deliverstable operation
Good tolerances for
g1, g2 = 1/2
20
R
critical configuration in the center of the stability diagram, but sensitive One round trip creates the Fourier transform of the starting field:
due to mirror focal length is R/2 Especially good transverse mode selection Small mode volume stop with radius a at first mirror
beam radius @1: beam radius @2:
Fresnel numberresonator losses defined
Beam quality
Reproduction of the field for one round trip: TEM00 mode, gauss mode More general: the field inside the resonator is given by a set of eigensolutions
these are the modes of the resonatorThe transverse limitations of the field due to a stop governs the modesThe eigenvalues g determine the losses of the modes ()
aw 1
LaNF
2
a
Lw 2
FNM 2
Symmetric Confocal ResonatorR1= R2= - L
RR1 2
A BC D
En,m(x,y)
round tripstop
Hermite Gaussian Modes
n = 0 n = 1 n = 2 n = 3 n = 4 n = 5
m = 5
m = 4
m = 3
m = 2
m = 1
m = 0
22
22
Compare: Modes of a closed box with length L square Cross-section b
, , 2
circular symmetry Indices:
p: azimuthall: radial
p = 5p = 4p = 3p = 2
l = 5
p = 0 p = 1
l = 0
l = 1
l = 2
l = 3
l = 4
Laguerre Gaussian Modes
23
23
Keplerian telecope with pinhole in focal plane Higher modes with larger spatial extend are blocked:
only fundamental mode transmitted, beam clean up, mode filter for higher modes laser condition not fulfilled
Approximate size of pinhole diameter: 2 0.637Pinholein in
f fDw w
Beam Clean Up Filter
24
24
zwin
f
second lens ffirst lens f stop d
f wo
More general: Increase off losses for higher modes Diameter of active material Pinhole at minimum beam diameter
Small Fresnel number Long resonators High power lasers: instable resonators
LaNF
2
Laser types 25
Types of lasers:- Ar laser- CO2 laser- YAG laser- disc laser- fiber laser- semiconductor laser- Excimer laser
Beam quality of lasers
25
Type Power Mode Puls-length
Beam Dia. mm
Full Divergenz
mrad
efficiency %
Excimer, ArF 193 nm 30 W Puls 20 ns 6x20 - 20x30 2 - 6 0.5 Nitrogen gas 337 nm 0.5 W Puls 0.5-5 ns 2x3 - 6x30 1-3x7 0.1 Argonionen 505 nm 20 W cw 0.7 - 2 0.4-1.5 0.1 HeNe agas 632 nm 0.1 - 50 mW cw 0.5 - 2 0.5 - 1.7 0.1
HF-Chemical 2.7 - 3.3 m 150 W cw oder
Puls 1 s 2 - 40 1 - 15 10
CO2 – Gas 10.6 m 10 kW cw oder Puls 3 - 4 1 - 2 5 - 30
Rubin Solid State 694 nm Puls 0.5 ms 1.5 - 25 0.2 - 10 0.5
Semiconductor 0.4 - 30 m 100 mW cw oder
Puls 5 ps 200 x 600 25
Nd:YAG Solid State, with Flash lamp
1.064 m 1 kW Puls 5 ms -
10 ns 0.75 - 6 2 - 18 0.5
Nd:YAG Solid State with Diode-pumped
1.064 m 2 W cw 0.75 - 6 2 - 18
Dye fluid 400 - 950 nm 10 W cw oder
Puls 0.4 - 0.6 1 - 2 20
Laser types26
26
Gas laser with flow tube Brewster windows suppress reflected light Outcoupled radiation linear polarized
Gas Laser with Brewster Window
Brewsterangle
no reflected light
no reflected light
p
p
linearpolarised
Brewsterangle
4.00|| rr
27
27
28
Argon Laser
Energy scheme
Ref.: M. Kaschke
4p S2 0
4p P2 0
4p D2 0
4p D045/2
1/23/2
7/2
1/2
1/2
3/2
5/2
3/2
4s P21/2
3/2
35.6
35.7
35.5
35.3
35.4
33.0
32.972nm
Ar ground state+
0
5
10
15
20
25
30
35
E
Ar ground state
3.105
2.105
105
(eV)(cm )-1
0
514.5nm
488nm
= 267,4 .... 528,7 nm
10 ns1 ns
28
29
Argon Laser
Setup
Two elastic strikes are necessary for excitation1. ionization2. excitation of upper laser level
Efficiency low: < 0.1 %
Output power tyical: 10 W
Wavelengths: 488 nm or 514 nm
Ref.: M. Kaschke
HV
magnetic coilanode
silica/ceramic tubeBrewster's window
water cooling system
cathode output mirror
end mirror
laser beam
29
30
CO2 Laser
Ref.: M. Kaschke
0
500
1000
1500
2000
2500
3000
ground leveldN2 CO2
(000)
(001)
(100)
(010)
(020)
10.6 mm
0.1
0.2
0.3
0.4
(eV) -1(cm )
9.6 mm
0.0
transfer of vibration energyE = 0.002 eV,
E
t > 0.1s
30
Atoms in electrical ground level - Laser transitions correspond to rotations and vibrations Oscillations of the laser energies:
1. asymmetric stretching, upper level2. symmetrical stretching, lower level3. bending, lower level
Energy scheme: Additional gases:
N2: excitation by collisions of 2nd kindHe: de-excitation of lower levels
Infrared wavelength ranges High efficiency:
cw mode: 30% and 100 kW pulsed mode: 100 kJ
O C O
31
Nd:YAG Laser
Typical setup of a flash lamp pumped solid state Nd:YAG laser resonator
Ref.: M. Kaschke
Laser rod
pump chamber flash lamp
HR mirroroutcoupling
mirror
Laser beam water cooling
31
Typical pump cavity of solid stat lasers: coaxial rods a) elliptic reflector b) diffuse scattering
and oval shape
Quartz bodySilverreflector
ceramicreflector
scatteringmaterial
flash lamp
Flow‐tube
laser rod
32
Nd:YAG Laser
Energy scheme of anNd:YAG laser
Ref.: M. Kaschke
E
0
2
4
6
8
10
12
14
16
18
20
4F
4I
4I
4I
4I
3/2
15/2
13/2
11/2
9/2
730
nm
800
nm
1064
nm
1320
nm
1
2
(eV) (10 cm )3 -1
0
32
33
Diode Pumped Solid State Lasers
Transversal pumping geometry
Quality problems due to- astigmatism and coma by
broken symmetry- birefringence- thermal lensing
Ref.: M. Kaschke
100%mirror
outputcouplerTOC
laserrod
flash lamps
33
34
Diode Pumped Solid State Lasers
Longitudinal pumping geometry
Usually good mode quality due to coaxial gain distribution
Ref.: M. Kaschke 34
35
Disc Laser
Extrem aspect ratio of the laser rod:- very thin disc (< 1mm)- large diameter
Advantage:- no thermal lensing- effective cooling from front side
Complicated:Pump geomertry, skew incident beams
Ref.: M. Kaschke 35
36
Fiber Laser
Basic idea: fiber core with active medium propagation of pump and laser light mode confinement inside the fiber, defines beam qualitygood dissipation of heat
36
Si / Phosphat / Fluirid-Glas-fiber: losses < 3dB/km Core doped with rare earths Single mode for
V < 2,4 rcore ~ 6µm for VIS
Double-glad fibers for pump light Absorption and emission linewidth broadened to 15nm typ,
caused by interaction with glass
Diode pump laser
20..50m fiber Dope nm
Er 3400
Nd 1340
Yb 975
Tm 800
Pr 635
Er 546
Tm 4552
=2
37
Fiber Laser
Interesting wavelength ranges forfiber lasers
Ref.: O. Okhotnikov 37
Fiber laser38
Double glad fibers Coupling for pump light increased reduced tolerance sensitivity
Increase of pump light absorption byKidney bending
refractive index
n (laser core)n (pump core)
n (gladding)Gladding
Pump core DM <~ 400µm
Laser core DM <~ 5µm
Thünnermann et all: TopApplPhys78(2000),
39
Fiber Laser
Increase of pump light absorption byBending or Broken symmetry
Max 100W cw Limited by nonlinear effects
PCF = photonic crystal fibers Microstructures (holes) simulate
reduced n, n ~ 10e-4 Single modefor For
Max 2000W
Ref.: Thünnermann / O. Okhotnikov 39
V = 2
41
Fiber Laser
Example for active q-switched fiber laserAcousto-optical modulator: 1. diffraction order coupled back
Typical setup of a semiconductor laser
Astigmatic beam radiation:1. fast axis perpendicular to junction2. slow axis parallel to junction
Semiconductor Laser
metal contact
metal contact
insulatorp-regionheterojunctionn-region
substrate
light
x
y
x
y
x
y
z
Q
perpendicular
parallel
42
42
Typical spectral widths:IR greater than deep blue
Spectral position depends on material
Semiconductor Diodes: Spectra
43
43
Material Color Wavelengthin nm
SpectralFWHM nm
InGaAsP NIR 1500 ‐ 1300 50‐150GaAs:Si NIR 940GaAs:Zn NIR 900 40GaAlAs NIR 880 30‐60GaP:Zn,N dark red 700GaP red 690 90GaAlAs red 660GaAs6P4 red 660 40GaAs0.35P0.65:N orange 630InGaAlP orange 618 20GaAsP0.4 amber 610SiC yellow 590 120GaP green 560 40InGaAlN green 520 35GaN blue 490InGaN blue 450‐460 25InGaN blue 400‐430 20SiC deep blue 470
Semiconductor Laser
Typical laser with housing
Continuous transition fromincoherent LED below thresholdto coherent laser above threshold
Ref: M. Kaschke
monitoring PIN photodiode
WindowHeat sink Laser chip
Case
Laser beam
44
44
Usual semiconductor lasers: edge emitter, small elliptical emiter surface astigmatic beam formVCSEL-Laser: Emission perpendicular to pn-junction area typical D < 10 m Good beam quality, monomod Power scaling by area size possible
VCSEL-Laser
n-layerp-layer
LED
VCSEL
semiconductorlaser
edge emitter
n-layerP-layer
Demonstrated powers
Ref.: O. Okhotnikov
45
45
Excimerlaser : Types and System Data
Excimer Spectral range
Wavelength[nm]
Lifetime[ ns]
Capture cross-section [ 10-16 cm2]
Pulse width[ ns]
Divergence angle [ mrad]
XeF 351 12 - 19 5.0XeCl 308 11 4.5XeBr 282 12 2.2KrF UV 248 6.5 – 9 2.5 25 6.6 / 2.6ArF DUV 193 4.2 2.9 15 7.4 / 3.2
12 11.0 / 4.8F2 DUV 157 9 13.0 / 6.0Ar2 DUV 126 9 13.0 / 6.0
near field far field
193nm
157nm
46
46
Typical setup gas tube with Brewster windows rectangular aperture outcoupling mirror Line narrowing elements:
Etalon
Grating, Also asoutcoupler tube
reflector
gratingoutcoupler
in -1st order
stop
reflector in 1st order
Typical Setup andSpectral Narrowing in Excimer Laser
tubeetalon
outcouplingmirrorreflector stop
47
47
Prism and grating:
Real example for Littrow setup
Typical Setup andSpectral Narrowing in Excimer Laser
48
48
Spectral line width of a 248 nm Excimer laser
Typical double line of the gain with distancxe 0.5 nm
Selected and narrowed by dispersive elements in the resonator
247.5
intensity
wavelength
248.5 249.5248.0 249.0
gain2 nm
usual laser line0.3 nm
narrowed laser line
0.003 nm
Excimerlaser: Spectral Line Shape
49
49
Excimer Lasers: Spatial-Temporal Profile of Pulses
3.6 mm
8.0 mm
1.1 mrad2.8 mrad
51
51
dydxyxE
dydxyxExx
mm
2
2
),(
),(
ddE
ddEmm
2
2
),(
),(
o
xxxx k
kvu
Quality of Laser Beams: Moments
Conventional criteria of imaging systems are nor useful for laser beams:1. significant apodization2. no imaging application3. status of coherence may be complicated
Description of the complex fields by moments of second order:1. spatial moments of intensity profile
second moments describes beam widththird moment describes asymmetry
2. angular moment of the direction distributionsecond moment describes the divergence
Alternative descriptions of impuls:1. angle ux2. spatial frequency x3. transverse wavenumer kx
Mixed moments: description of twist effects
52
52
2222xxxxx wwM
M wx ox x2
Quality of Laser Beams: M2
Characterizing beam qualityM2
Special case: definition in waist plane
Properties of M2:1. Gaussian beam TEM00: M2 = 1
Smallest possible value2. Paraxial optical systems: M2 remains constant for propagation3. Real beams: M2 > 1 describes the decrease in quality and focussability
relative to a gaussian beam
Reasons for degradation of beam quality:1. intensity profile2. phase perturbation3. finite degree of coherence
Incoherent mixture of modes: additive composition of M2
General beams: components and mixed terms 4442
21
xyyx MMMM
53
53
Hermite-Gauß modes
Laguerre-Gaußmodes
Incoherent mixture of modesrelative contributions gnm
Gauß-Schell-Beam
Gauß-Schell-Beam with Twist
12 mnM
122 mpM
n
nm mngM 12
22 1
c
o
LwM
2
2
222
21
c
o
c
o
Lw
LwM
Beam Quality of Special Profiles
54
54
Beam quality of high-power lasers:space bandwidth product Lw
Typical M2 grows with power
Beam Quality of Lasers
55
55
Laser Source Properties
Criterion Types ExamplesBehavior in time pulsed systems solid state laser, excimer laser
continuous wave laser HeNe-laserSpectral width, coherence
single mode HeNe-lasermultiple mode YAG-solid state laser with high power,
fiber laser, Ti:Sa-laserSpectral position UV excimer laser
VIS Argon-ion-laser, HeNe-laserIR CO2-laser
Beam quality Fundamental mode HeNe-lasermultiple modes YAG-solid state laser with high power,
excimer laserBeam shape high NA semiconductor laser
low NA HeNe-laser, CO2-lasersmall diameter HeNe-laserlarge diameter CO2-laserring structures CO2 -laser with unstable resonatorelliptical excimer laser, semiconductor laser astigmatic semiconductor laserasymmetric CO2 - waveguide laser
Power range signal laser HeNe-laserpower laser CO2-laser
56
56
Spectral bandwidth very narrowquasi monochromatic
Coherence very highin case of monomode beam perfectideal for interferometric applicationscreates speckle
Power density very highin multimodes sometimes hotspots in the profileheating of componentsdamage of coatings possible
Stability low due to non-linear systema change of laser power may cause changes of beam modes
Beam profile characteristic gaussian shapesbeam quality criteria hard to defineaperture not clearly defined
Space-bandwidth productvery lowfor monomodes diffraction limited
Properties of Laser Light and Consequences
57
57
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