1. 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

2. Cavity ring-down spectroscopy
(mV)
Laser
Cavity
Modulator
Detector
Absorption enhancement:

3. Experimental setup Lens He-Ne laser DFB diode laser
Laser control board
AOM
AOM driver
Detector
Isolator
Computer
3PZTs
Flat mirror
Curved mirror
Mode matching optics
Cavity
Trigger signal
Isolator
Polarizer or
Pockel’s cell
λ/2 plate

4. 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.

5. Cavity under vacuum
Low stress conditions:
760 torr and tightening screws loosened (front mirror)

6. 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

7. PDL with back mirror rotationΔτ
τ strongly depends on local conditions (e.g. defects) of mirrors.
The incident polarization angle of max τ changes more smoothly.

8. Physical picture diagram
Slow Axis
Fast Axis
r1max
r2max
r1min
r2min α1 β1 β2 α2 x y z
HR coating
Waveplate
AR coating
Laser
Single pass phase retardance: ε1 and ε2

9. 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:

10. The Model (continued) Two eigenvalues:
Frequency splitting of two modes:
Decay time constant:
τ versus Incident polarization direction:
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.

11. 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.

12. 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

13. PDL and back mirror rotation
The main axis direction of polarization dependent loss is less localized.

14. Depolarization and stress
♣ cavity under vacuum
♣ 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

15. Noise from light leakage
Decay amplitude: 1.5V
Detector noise: 2mV
Extinction ratio: 20dB
Fitting residue of one decay

16. 50dB is not enough! Detector noise limited CRDS
Noise from light leakage, laser always on resonant
K. K. Lehmann and H. Huang, Frontiers of Molecular Spectroscopy, chapter 18, Elsevier 2008

17. Noise vs. extinction ratio

18. 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

19. Acknowledgements Paul Johnston and Robert Fehnel
Dr. Brooks Pate’s Lab in UVA

20. AOM extinction ratio RF on RF off RF amplifier RF oscillator 80 MHz
Trigger signal
Switch 1
Switch 2
RF In 2 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
RF on
RF off