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

shotpercm

c110

0

101.1

)1

)(

1(

1)(

noiseBeAty

t

)(

1

0

22

2 )/exp()()3(

1 N

i

iBAiyN

Detector

0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

Ring down decay signal

154.66±0.08µs, χ2 = 0.99

(µs)

(mV)

Absorption enhancement: LF

cL

)(

Laser CavityModulator

Experimental setup

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.030.0

0.5

1.0

1.5

2.0

2.5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

TEM02

TEM11

TEM20

TEM02

TEM11

TEM20

TEM02

TEM11

TEM20

TEM01

TEM10

TEM00

Vpzt

Vpz

t/10

0 [V

]

Time [s]

TEM00

TEM01

TEM10

Signal

Sig

nal [

V]

Mode structure 02/25/2007

Lens

He-Ne laser

DFB diode laser

Laser control board

AOM

AOM driver

DetectorIsolator

Computer

3PZTs

Flat mirror Curved mirror

Mode matching opticsCavity

Trigger signal

IsolatorPolarizer or

Pockel’s cell

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

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.

Δτ

Physical picture diagram

Slow Axis

Slow Axis

Fast Axis

Fast Axis

r1max

r2max

r1min

r2min

α1 β1

β2

α2

x

y

z

x

y

HR coating

WaveplateAR coating

Laser

Single pass phase retardance: ε1 and ε2

The model

Round trip Jones matrix with linear approximation:

)2cos()2cos()2sin()2sin(

)2sin()2sin()2cos()2cos(

10

0121

21

jbjb

jbjbaaM

MMMFGFM iiii

Round trip net PDL parameters and birefringence values:

minmax

minmaxminmax ,2

),(10

01)(

ii

iii

iiii

i

iiii rr

rrb

rrawithR

b

bRaG

Jones matrices for

reflection and wave plate transmission:

)()2exp(0

0)2exp()( i

i

iii R

j

jRF

)tan(tan2

1

2

))(2cos(2

)tan(tan2

1

2

))(2cos(2

2121

21121

212122

21

2

2121

21121

212122

21

2

bb

bb

bbbbb

The Model (continued)

Two eigenvalues: 2122212,1 ))](2cos(2[1 jbbaa

kHzthenbss ii 1.0,10,10,5,130 86minmax

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.

212221 ))](2cos(2[Im2

)arg()arg(

jbbFSR

FSRFrequency splitting of two modes:

Decay time constant:)ln(2 i

ri

t

τ versus Incident polarization direction:

)ln(2)(

)sin(

)cos(

)sin(

)cos(

11

u

tMuMuu

FSRbandFSRWith

r

Cavity under vacuum

Back mirror at ~56 degree, both slow (fast) axes parallel

Cavity under low stress conditions

Back mirror at ~36 degree, the slow (fast) axis of it is along the x axis.

b21 3.3

b

21 6

1

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

]))2sin()2sin(())2sin()2sin(([ 22211

222112

222

bbF

EE outx

outy

1221211

2

2

222 ,)1()],4sin(1[

2

)2cos(21

andfaaFwith

ffF

♣ cavity under vacuum

rad

rad7

2

61

101.3

100.1

rad

rad7

2

81

100.5

103.8

♣ 700 torr, tightening screws not loosened (front mirror)

♣ low stress conditions: 760 torr and all tightening screws loosened (front mirror)

Back mirror at 62 degree

Noise from light leakage

Decay amplitude: 1.5V

Detector noise: 2mV

Extinction ratio: 20dB

Fitting residue of one decay

12

50dB is not enough!

Noise from light leakage, laser always on resonant

Detector noise limited CRDS 2

2

2

8)(

t

d

Itk

k

k

tr I

I

k

k 02

2

27

64)(

%31.0)(

5.2,101

%28.0)(

100,01.0

0

5

k

k

I

I

k

kItk

tr

d

t

K. K. Lehmann and H. Huang, Frontiers of Molecular Spectroscopy, chapter 18, Elsevier 2008

Noise vs. extinction ratio

ratesweepingsGHzlineDotted

IIlineSolid t

4.11

2.1 0

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

RF amplifier

RF oscillator 80 MHz

Trigger signal

Switch 1 Switch 2

RF In RF In

2 2

1 1

Attenuator 20 dB

Step attenuator 0 – 69 dB

Combiner

1512 nm laser diode

Optical fiber

0th order

1st order to cavity

AOM crystal

Isolator

Output coupler

TTL TTL

AOM extinction ratio

RF on

RF off