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Physical Optics

Lecture 8: Laser

2019-12-12

Michael Kempe

Physical Optics: Content

2

K = Kempe G = Gross

No Date Subject Ref Detailed Content

1 17.10. Wave optics GComplex fields, wave equation, k-vectors, interference, light propagation,

interferometry

2 24.10. Diffraction GSlit, grating, diffraction integral, diffraction in optical systems, point spread

function, aberrations

3 07.11. Fourier optics GPlane wave expansion, resolution, image formation, transfer function,

phase imaging

4 14.11.Quality criteria and

resolutionK

Geometric and wave optical critera, Rayleigh and Marechal criteria, Strehl

ratio, lateral and axial point resolution, two-point resolution, contrast

5 21.11. Photon optics KEnergy, momentum, time-energy uncertainty, photon statistics,

fluorescence, Jablonski diagram, lifetime, quantum yield, FRET

6 28.11. Coherence KTemporal and spatial coherence, Young setup, propagation of coherence,

speckle, OCT-principle

7 05.12. Polarization GIntroduction, Jones formalism, Fresnel formulas, birefringence,

components

8 12.12. Laser KAtomic transitions, principle, resonators, modes, laser types, Q-switch,

pulses, power

9 19.12. Nonlinear optics KBasics of nonlinear optics, optical susceptibility, 2nd and 3rd order effects,

CARS microscopy, 2 photon imaging

10 09.01. PSF engineering KApodization, superresolution, extended depth of focus, particle trapping,

confocal PSF

12 16.01. Gaussian beams G Basic description, propagation through optical systems, aberrations

13 23.01. Generalized beams GLaguerre-Gaussian beams, phase singularities, Bessel beams, Airy

beams, applications in superresolution microscopy

11 30.01. Scattering KIntroduction, surface scattering in systems, volume scattering models,

calculation schemes, tissue models, Mie Scattering

14 05.02. Miscellaneous G Coatings, diffractive optics, fibers

3

Content

• Gain and loss, population inversion

• Laser resonators

• Laser emission

• Pulsed lasers

• Laser types:

• Gas lasers

• Solid-state lasers

• Semiconductor lasers

• Laser safety

4

Laser = Light Amplification by Stimulated Emission of Radiation

• Typically spectrally narrow beam of light

• Spatially coherent

• First demonstrated in microwave regime – Maser (Townes, 1954)

• Laser in VIS shown in Ruby at 694 nm (Maiman, 1960)

Requirements:

1. Gain medium (inversion), G

2. Feedback by resonator, G ≥ L (losses in resonator)

Laser Sources

G

R=100% R<100%

L ≤ G

5

energy conservation:

spontaneous emission stimulated emissionabsorption

atomic energy level differences typically lie in the optical region

Photon-Matter Interactions

𝑃𝑠𝑝 =𝑐

𝑉𝜎 𝜈𝑃𝑎𝑏𝑠 = 𝑛

𝑐

𝑉𝜎(𝜈) 𝑃𝑠𝑡 = 𝑛

𝑐

𝑉𝜎(𝜈)

Probability densities:

𝜎(𝜈): transition cross section

absorbing one photon

from a mode with n photons

emitting one photon

into a mode

emitting one photon

in a mode with n photons

𝑛𝑐

𝑉= 𝜙(𝜈) for monochromatic wave

6

spontaneous emission stimulated emissionabsorption

Photon Flux Changes

∆𝜙 = 𝑃𝑠𝑡𝑁2 − 𝑃𝑎𝑏𝑠𝑁1 ∆𝑧Change of flux density

∆𝜙 = 𝜙𝜎𝑁2 − 𝜙𝜎𝑁1 ∆𝑧

∆𝜙 = 𝜙𝜎 𝑁2 − 𝑁1 ∆𝑧

𝜙(𝑧) = 𝜙0𝑒𝜎 𝑁2−𝑁1 ∆𝑧 𝑁2 < 𝑁1 loss of photons

𝑁2 > 𝑁1 gain of photonsI(𝑧) = 𝐼0𝑒𝜎 𝑁2−𝑁1 ∆𝑧

𝑃 ∙ 𝑁 =1

𝑠∙1

𝑚3

7

Population of Energy Levels

for N2= N1

At room temperature:

For photons of wavelength

0.5µm

𝑘𝑇 = 1.38 ∙ 10−23𝐽

𝐾∙ 293𝐾

≈ 4 ∙ 10−21𝐽

𝑁2𝑁1

= 𝑒−100 ≈ 10−44

8

3-level syste

m4-level syste

m

Ref. M. Kaschke

Population inversion

9

Stationary Laser Oscillator

Setup

Intensity inside the resonator

Ref.: M. Kaschke

)()( zz

HV

Pump

source

Laser Material

mirror

(R = 100%)

coupling mirror

(R < 100%)

Laser beamL

Z = 0 Z = L

10

𝐿 = 𝑞𝜆

2

Standing wave (stationary):

• Intensity is reproduced after roundtrip

• Knots at the mirror surface

Resonator Modes

𝜆 =2𝐿

𝑞=𝑐

𝜈𝜈 = 𝑞

𝑐

2𝐿

𝑞 = 1,2…𝑛

q=1

q=2

11

Laser Resonator Types

Ref: B. Böhme

Principle:

- feedback of the radiation field

- reproduction of the wave for one

round trip

- loss compensated by gain

- eigenmode solutions of the field

Description:

- length L

- radii of curvature R1 , R2

Definition of stability parameter

g1, g2

Internal ABCD matrix for

one round trip

w2w

RR

L

1

1

0w

2

gL

Rg

L

R1

1

2

2

1 1 ,

12422

212

2212121

22

gggggggL

Lgg

DC

BAM

oo

oo

o

Stable Gaussian Resonators

Stability of a Gaussian Resonator

14

Laser Emission

𝛾 𝜈 =𝛾0 𝜈

1 +𝜙𝜙𝑠

= 𝑁𝑡ℎσ(𝜈)

• Laser condition: gain = losses

• The initial small-signal gain 𝛾0is reduced due to saturation

and fixed (“clamped”) at a value

𝛾 = 𝛼𝑟

• The emitted flux is therefore

𝜙 = 𝜙𝑠𝛾0(𝜈)

𝛼𝑟− 1 Source: Saleh/Teich

𝛾0 = 𝑁0𝜎(𝜈) ∝ 𝑃𝑖𝑛

2ln( ) 2 0i thT R N L 𝛾 = 𝜎 𝜈 𝑁

Ti internal transmission

R reflectivity of the mirrors R = R1R2

Nth threshold inversion

L length of the gain medium

Pin: pump powerFor 3- and 4-level systems

15

Laser Output Power

Laser intensity inside the resonator

If the laser reaches the threshold, the inversion is constant

The additional power above threshold increases the intensity in the resonator

The output intensity grows linear with the slope efficiency hslope

Ref.: M. Kaschke

Pth pump power Pin

I, N

Nth

N

I

for 𝑃𝑖𝑛 > 𝑃𝑡ℎ𝐼 = 𝜂𝑠𝑙𝑜𝑝𝑒(𝑃𝑖𝑛−𝑃𝑡ℎ)

𝑁𝑡ℎ =𝛼𝑟𝜎(𝜈)

𝜙 = 𝜙𝑠𝛾0(𝜈)

𝛼𝑟− 1

16

Laser Output Power Optimization

Optimization of the reflectivity

according to gain/loss

Rigrod diagram

Curve of optimal reflectivities

for different pump powers

Ref.: M. Kaschke

laser power PCW

0,5 0,6 0,7 0,8 0,9 1,0

100

80

60

40

20

optimal

outcoupling

casedifferent pump

power levels

17

Laser Emission: Homogenous Broadening

• In a homogenously broadened

medium all modes interact with

the same transition

The gain clamping leads to an

emission of a single mode, if the

modes don’t occupy different

spatial regions of the gain medium

Source: Saleh/Teich

18

Laser Emission: Inhomogenous Broadening

• In an inhomogenously broadened medium the gain comes from different

transitions

• The gain clamping leads to spectral hole burning all modes within the

spectrum for which 𝛾0 > 𝛼𝑟 can oscillate

Source: Saleh/Teich

19

Types of Lasers

Continuous wave (cw)

Dt = 0.05 ...1 s

Pulsed (pw)

Dt = 10-6 s = 1 ms

Q-switched pulse

Dt = 10-9 s = 1 ns

Mode locked pulses

Dt = 10-15 s = 1 fs

Quasi cw, pulsed with high frequency

(kHz-MHz)

Ref.: M. Kaschke

time

power

timeDt

powerarea corresponds

to pulse energy

power

time

average

power

20

Q-Switch

Time dependencies for cw and pulsed pumping

a) continuous wave b) pulsed mode

pump

intensity

loss

inversion

laser

pulse

Ref.: M. Kaschke

21

Mode Coupling

Axial mode frequencies given by round

trip time in resonator of length L

All modes inside the gain profile are coupled/synchronized:

mode locking

Fabry-Perot resonator:

typical Dn = 100 Mhz...2 GHz

Ref.: M. Kaschke

axial modes

resonator

gain

gain

profile

threshold

frequency n

Dn

laser

lines

n0

L

cqq

D

21,n

22

Laser with Mode Coupling

Fixed phase relation between modes

Full interference of amplitudes

qq 1

field E

power P

average power P

1st wave Eq

3rd wave Eq+2

2nd wave Eq+1

4th wave Eq+3

coherent

superposition

Ref.: M. Kaschke

Laser Source Data

Laser type

Typical

power /

energy

Operation

mode

Pulse

length

Beam

diameter

in mm

Divergence

2

in mrad

efficiency

h in %

Excimer, ArF 193 nm 30 W / 1 J pulse 20 ns6x20 –

20x302 – 6 0.2

Nitrogen-gas

laser337 nm

0.5 W / 10

mJpulse 10 ns

2x3 –-

6x301–3x7 0.1

Argon-ion

laser

455 –

529 nm0.5 – 20 W cw 0.7 –- 2 0.4–1.5 0.1

HeNe-gas laser 632.8 nm0.1 – 50

mWcw 0.5 – 2 0.5 – 1.7 0.1

HF-chemical

Laser

2.6 – 3.3

mm5 kW / 4 kJ cw or pulse 20 ns 2 – 40 1 – 15 10

CO2 – gas laser 10.6 mm 1 kW / 1kJ cw or pulse50 –

150 ns3 – 4 1 – 2 15 – 30

Ruby – solid

state laser694 nm 10 J pulse 0.5 ms 1.5 – 25 0.2 – 10 0.5

Nd:YAG-solid

state laser,

flash bulb

1.064 mm 1 kW pulse0.1 – 20

ns0.75 – 6 2 – 18 0.5

Nd:YAG-solid

state laser,

diode-pumped

1.064 mm 2 W cw 0.75 - 6 2 – 18 5

Semiconductor

laser

0.4 – 30

mm0.1-10 W cw or pulse

0.1 – 1

ms

0.001–

0.5200 x 600 30

Ga

s la

se

rS

olid

Sta

te la

se

rLD

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

25

Flashlamp Pumped Solid State Laser

Typical setup of a flash lamp pumped solid state Nd:YAG laser resonator

Ref.: M. Kaschke

Laser rod Flow tube

flash lamppump chamber flash lamp

HR mirroroutcoupling

mirror

Laser beam water cooling

26

Diode Pumped Solid State Lasers

Longitudinal pumping geometry

Usually good mode quality due to coaxial gain distribution

Ref.: M. Kaschke

pump diode

laserNd:YAG rod

laser

beam

resonator mirrorpump

optical

system

AR @ 809 nm

HR @ 1064 nm

27

Diode Pumped Solid State Lasers

good mode quality due to coaxial gain distribution enables efficient intra-cavity frequency

conversion

Second harmonic generation (SHG) in nonlinear crystals with phase matching

pump diode

laserNd:YAG rod

laser

beam

resonator mirrorpump

optical

system

AR @ 809 nm

HR @ 1064 nm / 532nmHR @ 1064 nm

SHG

28

Disc Laser

Extrem aspect ratio of the laser rod:

- very thin disc (< 1mm)

- large diameter

Advantage:

- no thermal lensing high power laser e.g. for material

- effective cooling from front side processing applications

Complicated pump geometry, skew incident beams

Ref.: M. Kaschke

29

Fiber Laser

Ref: B. Böhme

outer cladding

inner cladding

core Double clad structure for efficient pumping

Typical structure of edge-emitting

semiconductor laser

Astigmatic beam radiation:

1. fast axis perpendicular to junction

2. slow axis parallel to junction

Semiconductor Laser

metal contact

metal contact

insulatorp-region

heterojunction

n-region

substrate

light

x

y

x

y

x

y

z

Q

perpendicular

parallel

Model of beam profiles:

- Gaussian in fast axis

- Gaussian with Lorentzian envelope

in slow axis

oyoy R

yi

w

y

yo eEyE

22

)(

oxR

xi

x

xxo e

xw

wExE

2

22

0

2

0|| )(

Semiconductor Laser Materials

Material Color Wavelength in nm Spectral Fwhm in nm Luminence in cd/m2

InGaAsP NIR 1300 50-150

GaAs:Si NIR 940

GaAs:Zn NIR 900 40

GaAlAs NIR 880 30-60

GaP:Zn,N dark red 700

GaP red 690 90

GaAlAs red 660

GaAs6P4 red 660 40 2570

GaAs0.35P0.65:N orange 630

InGaAlP orange 618 20 2 107

GaAsP0.4 amber 610

SiC yellow 590 120 137

GaP green 560 40 1030

InGaAlN green 520 35 107

GaN blue 490

InGaN blue 450-460 25 3 106

InGaN blue 400-430 20 3 104

SiC deep blue 470

Semiconductor Laser

Typical laser with housing

Continuous transition from

incoherent LED below threshold

to coherent laser above threshold

Ref: M. Kaschke

monitoring PIN photodiode

Window

Heat sinkLaser chip

Case

Laser beam

1

0I threshold

LED Regime

Laser Regime

P(W)

I(A)

V = 2-3 Volt

Usual semiconductor lasers:

edge emitter, small elliptical emitter surface

astigmatic beam form

VCSEL-Laser:

Emission perpendicular to pn-junction

area typical D < 10 mm

Good beam quality, monomode

Power scaling by area size possible

VCSEL-Laser

n-layer

p-layer

LED

VCSEL

semiconductor

laser

edge emitter

34

Optically pumped VCSEL-Laser

• Optically pumped semiconductor laser (OPSL) combine high beam quality with

wavelength flexibility at low to high cw power

• Wavelengths: 700-1200 nm and 350-600 nm with intracavity frequency

doubling

Optional: SHG

Source: Coherent Inc.

35

Tunable Semiconductor Lasers

• Semiconductor laser with external cavity (Littrow configuration: grating with

MEMS scanner; semiconductor optical amplifier - SOA)

• Wavelengths: several bands with 1500-1620 nm, 1250-1400 nm and 1000-

1100 nm most common)

• Tuning speed: 1 kHz-150 kHz

Source: Exalos AG

36

Laser Safety

• Due to its spatial coherence, even

a low-power laser can achieve

high intensities at the retina

• For comparison: sun at earth

surface: 1000 W/m², focused at

retina ~ 0.1 Mio W/m² (2mm pupil)

• Different wavelength penetrate

differently deep in the eye

potential damage occurs at

different parts of the eye

• For the retina VIS-NIR light is

particularly dangerous

37

Laser Safety Considerations

Ma

xim

um

allo

we

d c

wp

ow

er

[mW

]

Wavelength [nm]

Class 3B

Class 3R

Class 2

Class 1

Class Eye Safety Skin Safety

1 Safe under normal conditions

2 Safe if exposure is less than 0.25s Safe

3R Direct exposure dangerous, indirect exposure safe Safe

3B Indirect exposure safe in distance > 13 cm Skin damage possible

Appoximate values since limits are

usually given in J/cm² or W/cm² !