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Fabry-Perot Interferometer
Broad Applications: laser wave meter; Raman spectrometer; Ultra-narrow bandwidth laser; optical filters etc….
M2
detector
o
1l
2l
1E
2E
M1
Michaelson interferometer
λ
r (distance)
Wave Propagation of Light
𝐸 = 𝐴𝑒𝑖𝑘.𝑟
𝑘 =2𝜋
𝜆
r= ro + m λ 𝐸 𝑟 = 𝐴𝑒𝑖 𝑘.𝑟𝑜+𝑘𝑚𝜆
= 𝐴𝑒𝑖𝑘.𝑟𝑜𝑒𝑖2𝑚𝜋 = 𝐸(𝑟𝑜)
M2
detector
o
1l
2l
1E
2E
M1
Constructive Interference
𝐸 = 𝐴𝑒𝑖𝑘.𝑙
l2= l1 + 2d
If 2d= mλ
Phase difference δ = 𝑘. 2𝑑 = 2𝑚𝜋
Quiz!
M2
detector
o
1l
2l
1E
2E
M1
Initially, M2 at position do, and it is a dark circle in the middle.
(1)M2 moves by ¼ λ. Is the center bright or dark?
(2) M2 moves by ½ λ. Is the center bright or dark?
Quiz!
M2
detector
o
1l
2l
1E
2E
M1
Initially, M2 at position do, and it is a dark circle in the middle.
(1)M2 moves 7 μm. The center changes from dark to dark 20 times. What is the exciton laser wavelength?
Fabry-Perot Interferometer
r: reflection coefficientt: transmission coefficient
ConstructiveInterference
when 2dcosq = nl
OA
B
M1M2
OA+AB=OA (1+cos2θ)=2𝑐𝑐𝑜𝑠2 𝜃 𝑂𝐴
=2𝑐𝑐𝑜𝑠2 𝜃 𝑑
cos θ=2dcos(θ)
Eot’
Eot’r
Eot’rr’
Eot’r2r’
Fabry-Perot Interferometer
Hecht, Pg 422, Eq. 9.65
If there is no absorption, ( )t
o
IA
Iq
-
Fabry-Perot Interferometer
Coefficient of finesse
R~0.99->F~40,000 cos
4 dq
l
γ
Fabry-Perot Interferometer
cos4 d
q
l
Resolving power of instrument ~ frequency width of peaks
Hecht, Pg 423, Fig. 9.45Fabry-Perot fringes for (monochromatic light)
γ
Fabry-Perot Interferometer4 d
l
Free spectral range
2m 2( 1)m
same l4 d
l
4 'd
l ' / 2d d l
Central spot scanning
d
d’
γ
Fabry-Perot Interferometer4 d
l
Free spectral range
2m 2( 1)m
same l4 d
l
4 'd
l ' / 2d d l
4 d
l
4
'
d
lDifferent l
In this case, we cannot distinguish these two frequencies apart
'l l l Free spectral range
Central spot scanning
γ
Fabry-Perot InterferometerFree spectral range
FSRf
4 42( 1) 2
'
d dm
l l
' 1
' 2d
l l
l l
f cl 'l l
2FSR
cf
d
'
'
2 '
( )
1
/ 2
c f f
ff
c ff d
The round-trip time for light travels in the cavity
Fabry-Perot Interferometerresolving power ~ free spectral range
2 /Finess 4 4d df
c
l
1/2
4 d f
c
FSRf
Finesse
Resolving power: Δf=
f cl
2𝜋
𝛾Δ𝑓 =
𝐶
2𝑑
Fabry-Perot Interferometer
Fabry-Perot Interferometer
2FSR
cf
d
FSRf
Finesse
Resolving power:
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