Post on 12-Sep-2020
Gaussian Beams &
Resonators
Electro-Optics & Applications Prof. Elias N. Glytsis
School of Electrical & Computer Engineering National Technical University of Athens
08/11/2018
Gaussian Beams r
z θ
R(z1) R(z2)
w0
z1 z2
2 Prof. Elias N. Glytsis, School of ECE, NTUA
TEM00 TEM10 TEM11
TEM20 TEM02 TEM21
TEM30 TEM31 TEM32
TEM33 TEM40 TEM63
Gaussian Beams Patterns
Hermite Polynomials Generator
3 Prof. Elias N. Glytsis, School of ECE, NTUA
Hermite Polynomials (recursive)
Experimental Patterns of Gaussian Beams
From A. Yariv and P. Yeh, “Photonics” 6th Ed. Oxford University Press, 2007
4 Prof. Elias N. Glytsis, School of ECE, NTUA
TEM00 TEM10 TEM01
TEM11 TEM21
Gaussian Beams Patterns
5 Prof. Elias N. Glytsis, School of ECE, NTUA
Laguerre-Gaussian Beams
Laguerre Polynomials Generator
6 Prof. Elias N. Glytsis, School of ECE, NTUA
Laguerre Polynomials (recursive)
Laguerre-Gaussian Beams Patterns
7 Prof. Elias N. Glytsis, School of ECE, NTUA
Gaussian Beams and ABCD Law
qin qout
Input Plane
Output Plane
8 Prof. Elias N. Glytsis, School of ECE, NTUA
Prof. Elias N. Glytsis, School of ECE, NTUA 9
θi
θt
θi
A
B
C
D
E
t nf
n0
n0
Transmitted Waves
Reflected Waves
Fabry-Perot Interferometer
Prof. Elias N. Glytsis, School of ECE, NTUA 10
Fabry-Perot Interferometer
Prof. Elias N. Glytsis, School of ECE, NTUA 11
Symmetric Fabry-Perot Interferometer
νm νm+1 νm-1 ν
FSR
Resonant Frequencies
Prof. Elias N. Glytsis, School of ECE, NTUA 12
Symmetric Fabry-Perot Interferometer
Coefficient of Finesse
Prof. Elias N. Glytsis, School of ECE, NTUA 13
Symmetric Fabry-Perot Interferometer
δ
δ/k0
mλ01 mλ02
2πm 2πm
1
1/2
Δδ
Minimum Wavelength Separation
Prof. Elias N. Glytsis, School of ECE, NTUA 14
νm νm+1 νm-1 ν
FSR
Symmetric Fabry-Perot Interferometer
Resolving Power
Finesse
Prof. Elias N. Glytsis, School of ECE, NTUA 15
Asymmetric Fabry-Perot Interferometer with Gain or Loss
G = eγt
Gain Loss
Fabry-Perot Interferometer
Prof. Elias N. Glytsis, School of ECE, NTUA 16
Two-Mirror Laser Resonator
17 Prof. Elias N. Glytsis, School of ECE, NTUA
http://www.optique-ingenieur.org/en/courses/OPI_ang_M01_C03/co/Contenu_11.html
ℓ
Two-Mirror Laser Resonator Example
R1 = Infinite
R2 = 1m (R2>0)
18 Prof. Elias N. Glytsis, School of ECE, NTUA
Two-Mirror Laser Resonator Example
R1 = Infinite, R2 = 1m (>0), L = R2/2 = 0.5m
z0 = 0.5m, w0 = 317.35μm, z1 = 0, z2 = 0.5m
19 Prof. Elias N. Glytsis, School of ECE, NTUA
Two-Mirror Laser Resonator Example
R1 = 0.3m (R1>0)
R2 = 0.5m (R2>0)
20 Prof. Elias N. Glytsis, School of ECE, NTUA
Two-Mirror Laser Resonator Example
R1 = 0.3m (>0), R2 = 0.5m (>0), L = 0.6m R1 = 0.3m (>0), R2 = 0.5m (>0), L = 0.2m
z0 = 0.15m, w0 = 173.82μm, z1 = -0.15m, z2 = 0.45m
z0 = 0.15m, w0 = 173.82μm, z1 = -0.15m, z2 = 0.05m
21 Prof. Elias N. Glytsis, School of ECE, NTUA
Two-Mirror Laser Resonator Example
R1 = -0.3m (R1<0)
R2 = 0.5m (R2>0)
22 Prof. Elias N. Glytsis, School of ECE, NTUA
Two-Mirror Laser Resonator Example
R1 = -0.3m (<0), R2 = 0.5m (>0), L = 0.25m R1 = -0.3m (<0), R2 = 0.5m (>0), L = 0.5m
z0 = 0.1382m, w0 = 166.84μm, z1 = 0.2083m, z2 = 0.4583m
z0 = 0.0928m, w0 = 136.71μm, z1 = 0.0321m, z2 = 0.4821m
23 Prof. Elias N. Glytsis, School of ECE, NTUA
http://www.optique-ingenieur.org/en/courses/OPI_ang_M01_C03/co/Contenu_12.html
Different Laser Resonator Geometries
24 Prof. Elias N. Glytsis, School of ECE, NTUA
Prof. Elias N. Glytsis, School of ECE, NTUA 25
Cavity Lifetime – Approximate Approach
Assume N round-trips in the cavity: ℓ
R1 R2
Prof. Elias N. Glytsis, School of ECE, NTUA 26
Cavity Lifetime – Accurate Approach
Rate of decrease in intensity (or number of photons) in the cavity:
Survival Ratio:
Round-Trip Time:
ℓ
R1 R2