physical optics - friedrich-schiller-universität jena...physical optics: content 2 no date subject...
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www.iap.uni-jena.de
Physical Optics
Lecture 8: Laser
2018-05-30
Michael Kempe
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Physical Optics: Content
2
No Date Subject Ref Detailed Content
1 11.04. Wave optics GComplex fields, wave equation, k-vectors, interference, light propagation,
interferometry
2 18.04. Diffraction GSlit, grating, diffraction integral, diffraction in optical systems, point spread
function, aberrations
3 25.04. Fourier optics GPlane wave expansion, resolution, image formation, transfer function,
phase imaging
4 02.05.Quality criteria and
resolutionG
Rayleigh and Marechal criteria, Strehl ratio, coherence effects, two-point
resolution, criteria, contrast, axial resolution, CTF
5 09.05. Photon optics KEnergy, momentum, time-energy uncertainty, photon statistics,
fluorescence, Jablonski diagram, lifetime, quantum yield, FRET
6 16.05. Coherence KTemporal and spatial coherence, Young setup, propagation of coherence,
speckle, OCT-principle
7 23.05. Polarization GIntroduction, Jones formalism, Fresnel formulas, birefringence,
components
8 30.05. Laser KAtomic transitions, principle, resonators, modes, laser types, Q-switch,
pulses, power
9 06.06. Nonlinear optics KBasics of nonlinear optics, optical susceptibility, 2nd and 3rd order effects,
CARS microscopy, 2 photon imaging
10 13.06. PSF engineering GApodization, superresolution, extended depth of focus, particle trapping,
confocal PSF
11 20.06. Scattering LIntroduction, surface scattering in systems, volume scattering models,
calculation schemes, tissue models, Mie Scattering
12 27.06. Gaussian beams G Basic description, propagation through optical systems, aberrations
13 04.07. Generalized beams GLaguerre-Gaussian beams, phase singularities, Bessel beams, Airy
beams, applications in superresolution microscopy
14 11.07. Miscellaneous G Coatings, diffractive optics, fibers
K = Kempe G = Gross L = Lu
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3
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
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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
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Population of Energy Levels
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6
3-level syste
m4-level syste
m
Ref. M. Kaschke
Population inversion
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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
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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
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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
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Laser Resonator Types
Ref: B. Böhme
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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
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Stability of a Gaussian Resonator
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Laser Emission
𝛾 𝜈 =𝛾0 𝜈
1 +𝜙𝜙𝑠
= Nσ(𝜈)
• Laser condition: gain = losses
• The initial small-signal gain 𝛾0is reduced due to saturation
and fixed (“clamped”) at a
value 𝛾 = 𝛼𝑟
per round-trip
• The emitted flux is therefore
𝜙 = 𝜙𝑠𝛾0(𝜈)
𝛼𝑟− 1
𝜙 = 𝜙0𝑒𝛾 𝜈 2𝐿
Source: Saleh/Teich
𝛾0 = 𝑁0𝜎(𝜈) ∝ 𝑃𝑖𝑛
2ln( ) 2 0i thT R N L 𝛾 = 𝑁𝜎(𝜈)
Ti internal transmission
Ri reflectivity of the mirrors R = R1R2
Nth threshold inversion
L length of the gain medium
Pin: pump power
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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
1
th
inS
P
P thinslopeCW PPP hfor 𝑃𝑖𝑛 > 𝑃𝑡ℎ laser power:
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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
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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
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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
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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 = 10-10 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
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Q-Switch
Time dependencies for cw and pulsed pumping
a) continuous wave b) pulsed mode
pump
intensity
loss
inversion
laser
pulse
Ref.: M. Kaschke
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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
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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
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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
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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
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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
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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
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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
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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
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Fiber Laser
Ref: B. Böhme
outer cladding
inner cladding
core Double clad structure for efficient pumping
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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|| )(
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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
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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
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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
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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.
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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