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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 !
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