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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