Haifeng_Columbus_2008.ppt
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Transcript Haifeng_Columbus_2008.ppt
Non-ideal Cavity Ring-Down Spectroscopy:
Linear Birefringence, Linear Polarization
Dependent Loss of Supermirrors, and Finite
Extinction Ratio of Light Modulator
Haifeng Huang and Kevin K. Lehmann
Chemistry Department, University of Virginia
63rd International Symposium on Molecular Spectroscopy
Columbus OH, June 20, 2008
Cavity ring-down spectroscopy
(mV)
Ring
1400
down
decay
signal
154.66±0.08µs, χ2 = 0.99
1200
1000
800
600
400
Laser
Modulator
Cavity
Detector
200
0
0
1
1
y(t ) A Be
1
( ) (
)
c ( ) 0
1.1 10
10
cm
1
200
per shot
Absorption enhancement:
400
1
( N 3) 2
2
L (c )
F
600
800
(µs)
1000
t
noise
N 1
y(i) A B exp( i / )
i 0
L
2
Experimental setup
He-Ne laser
Laser control board
Computer
DFB diode laser
Isolator
Trigger signal
AOM driver
Flat mirror
Detector
Curved mirror
Lens
AOM
Mode matching optics
Polarizer or
Isolator
Cavity
3PZTs
Pockel’s cell
Mode structure 02/25/2007
2.5
TEM00
0.30
TEM00
0.25
2.0
1.5
0.15
Vpzt
Signal
1.0
0.10
0.0
-0.03
TEM02
TEM02
TEM01
TEM11
TEM11
TEM10
TEM20
TEM20
TEM02
0.5
-0.02
TEM01
TEM11
TEM10
TEM20
-0.01
0.00
Time [s]
0.05
0.00
0.01
0.02
0.03
Signal [V]
0.20
Vpzt/100 [V]
λ/2 plate
Two polarization eigenmodes
There exist two special angles of the analyzer, perpendicular with each other, at which we
have the lowest noise level of τ.
Cavity is excited by circular polarization light, but these two angles are independent of the
polarization of the incident light.
Cavity under vacuum
Low stress conditions:
760 torr and tightening
screws loosened (front
mirror)
Polarization dependent loss
(PDL) (Linear dichroism)
Cavity under vacuum
Back mirror at 7 degree
Two modes: 2.5 and 92.5 degree
Cavity under vacuum
Back mirror at -53 degree
Two modes: 14 and 104 degree
Δτ
PDL with back mirror rotation
τ strongly depends on local conditions (e.g. defects) of mirrors.
The incident polarization angle of max τ changes more smoothly.
Physical picture diagram
HR coating
x
Laser
Fast
Axis
AR coating
α2
Slow
Axis
z
Waveplate
β2
x
Fast
Axis
Slow
Axis
α1
r2max
β1
y
r2min
y
r1max
r1min
Single pass phase retardance: ε1 and ε2
The model
Jones matrices for
reflection and wave
plate transmission:
Round trip Jones
matrix with linear
approximation:
Round trip net PDL
parameters and
birefringence values:
0
1 bi
r r
r r
R( i ), with ai i max i min , bi i max i min
Gi ai R(i )
1 bi
2
ri max ri min
0
0
exp( j i 2)
R( i )
Fi R( i )
0
exp( j i 2)
M i Fi Gi Fi
M M1 M 2
1 0 b cos( 2 ) j cos( 2 ) b sin( 2 ) j sin( 2 )
M a1a2
0
1
b
sin(
2
)
j
sin(
2
)
b
cos(
2
)
j
cos(
2
)
b 2 b12 b22 2b1b2 cos( 2( 1 2 ))
b b
1
tan 1 1 2 tan( 1 2 )
2
2
b1 b2
2 12 22 2 1 2 cos( 2(1 2 ))
1 2
1 2
2
1
tan 1 1 2 tan( 1 2 )
2
1 2
The Model
(continued)
Two eigenvalues:
1, 2 a1a2 1 [b2 2 2 jb cos(2( ))]1 2
Frequency splitting
of two modes:
arg( 1 ) arg( 2 )
FSR
FSR
Im [b 2 2 2 jb cos( 2( ))]1 2
2
130 s, max min 5 s, i 10 6 , bi 10 8 , then 0.1kHz
tr
2 ln( i )
Decay time constant:
i
τ versus Incident
polarization direction:
With FSR 1 and
b FSR 1
cos( )
cos( )
tr
u
u M u M
( )
2 ln( u )
sin( )
sin( )
Two polarization eigenvectors are no longer orthogonal, but almost perpendicular with each
other and almost linearly polarized. Both polarization directions can be calculated from M.
Cavity under vacuum
Back mirror at ~56 degree, both
slow (fast) axes parallel
1 3.3 2
b
Cavity under low stress conditions
Back mirror at ~36 degree, the slow
(fast) axis of it is along the x axis.
1
6
b
1 2
Polarization dependent loss
(Linear dichroism)
Cavity under vacuum
Back mirror at 7 degree
Two modes: 2.5 and 92.5 degree
Cavity under vacuum
Back mirror at -53 degree
Two modes: 14 and 104 degree
PDL and back mirror rotation
The main axis direction of polarization dependent loss is less localized.
Depolarization and stress
E
out 2
y
E
out 2
x
F2
2
[(1 sin( 21 ) 2 sin( 2 2 )) 2 (b1 sin( 21 ) b2 sin( 2 2 )) 2 ]
22 F 2 1 f 2 2 f cos( 2 )
2
[1 sin( 41 )], with F (1 a1a2 ) , f 1 2 and 2 1
2
♣ cavity under vacuum
1 1.0 10 6 rad
2 3.110 7 rad
♣ 700 torr, tightening screws not
loosened (front mirror)
♣ low stress conditions: 760 torr
and all tightening screws loosened
(front mirror)
1 8.3 10 8 rad
Back mirror at 62 degree
2 5.0 107 rad
Noise from light leakage
Decay amplitude:
1.5V
Detector noise:
2mV
Extinction ratio:
20dB
Fitting residue of one decay
2 1
50dB is not enough!
Detector noise limited CRDS
d
(k )
8k t
2
k
It
Noise from light leakage,
laser always on resonant
2 (k )
2
k2
kt 0.01,
It
d
r 110 5 ,
100
It
2. 5
I0
2
64 I 0
r
27 I t
(k )
k
(k )
k
0.28 %
0.31%
K. K. Lehmann and H. Huang, Frontiers of Molecular Spectroscopy, chapter 18, Elsevier 2008
Noise vs. extinction ratio
Solid line
I t 1.2 I 0
Dotted line
11.4GHz s sweeping rate
Conclusions
■ Linear birefringence (10-7~10-6 rad) of supermirrors will lift the
polarization degeneracy of TEM00 mode, generating two new
polarization eigenmodes with frequency splitting ~0.1 kHz. These two
modes are almost linearly polarized.
■ For the first time, we reported the linear polarization dependent loss
(~10-8) of supermirrors. The results can only be explained by including
both factors.
■ Birefringence of supermirrors can be reduced greatly by releasing the
stress on both mirrors.
■ Finite extinction ratio of the light modulator can cause significant noise
in CW-CRDS signal. For signal of S/N about 1000, 70 dB extinction ratio
is needed in order to reach the noise limit.
H. Huang & K. K. Lehmann, Applied Optics, accepted
H. Huang & K. K. Lehmann, in preparation
Acknowledgements
Paul Johnston and Robert Fehnel
Dr. Brooks Pate’s Lab in UVA
AOM extinction ratio
Optical fiber
Output
coupler
1512 nm laser diode
AOM crystal
0th order
Isolator
1st order to cavity
Trigger
signal
Switch 1
RF amplifier
Switch 2
TTL
2
TTL
2
RF In
1
RF In
1
RF oscillator
80 MHz
Attenuator
20 dB
RF on
RF off
Step attenuator
0 – 69 dB
Combiner