Sensitive gas absorption coefficient measurements based on Q reduction in an optical cavity.

1
Sensitive gas absorption coefficient measurements
based on Q reduction in an optical cavity.
Three measurement methods to consider

1. Pulsed laser ring-down time measurements
2. Chopped CW laser resonant excitation of cavity
   and measurement of ring-down time
3. Continuous CW laser resonant excitation of
   cavity and measurement of cavity Q from optical
   power detection

1) Basic time-domain analysis, laser emitting one
large pulse of short duration (and thus not so
narrowband).
P1
P1T1T2 e-t/?
T1 lt 1-R1
T2 lt 1-R2
2
Resonant cavity model Assume all transmissions T
and losses L ltlt1
Fine Piezo control
Photodetector
E1
E2
E4
E42
LASER
E3
E5
Mirror 2 T2 , R2 , L2 ,
E52
Photodetector
Additional round-trip losses L0 various power
losses (diffraction, Rayleigh scattering,
etc.) 2 D ? absorption loss (what we're
trying to measure!)
Mirror 1 T1 power transmission R1 1 T1
L1 L1 power loss
Net cavity loss LCAV T1 T2 L0 L1 L2
2 D ? ? (2D / c) / LCAV (Photon lifetime
ring-down time const.) Q 2?fopt ?
BW fopt / Q F 2? ??/ (2D / c) 2? /
LCAV (Finesse)
3
D
E2
E4
E1
E3
E5
Intra-cavity waves E2 and E3(at position of
mirror 1 surface) E3 R11/2 (1 LCAV / 2)
ej 2kD E2 (1 LCAV / 2) ej? E2 Resonance when
?? 0 (that is, 2D N ?) Find that amplitude
increased inside cavity at resonance E2 / E1
T11/2 2 / LCAV On general principles Since
detection of sample absorption depends on loss of
energy (photons) passing through sample,
increasing the intracavity power E22 increases
the potential detectivity.
4
Direct measurement of cavity Q
All sources of cavity loss
Photodetector
E1
E2
E4
E3
E5
L0 2 D ?
Computer etc.
T1 L1
T2 L2
Net cavity loss LCAV T1 T2 L0 L1 L2
2 D ? Output power relative to incident laser
power E42/ E12 4 T1 T2 / L2CAV (at
resonance) Thus most sensitive to ? when T1, T2,
L0, L1, L2 reduced (high Q cavity).
5
Better scheme Measure peak ratio (thus at
resonance) of transmitted power E42 to
reflected power E52
Photodetector
E1
E2
E4
E3
E5
E42
L0 2 D ?
E52
T1 L1
T2 L2
Computer etc.
Photodetector
Output power relative to reflected power (at
resonance) E42/ E52 4 T1 T2 / (LCAV -
2T1)2 We assume that T1
accounts for less than ½ of Lcav otherwise
E52 will not be monotonically reduced with
reduced Lcav (E5 will actually go through zero
and reappear in opposite phase!). This will
always be assured when using two identical
mirrors M1 and M2 (and most other realistic
cases). Again, we get the best sensitivity to ?
by reducing losses L0, L1, L2 (of course) and
also reducing the mirror transmitances T1 and T2
when they are a large part of Lcav (after
reducing the actual loss terms).
6
E42/ E12
E52/ E12
This computation (if I didn't make any mistake!)
plots the transmission through the etalon and
reflection at the input vs. frequency. This is
for a very short etalon D.1mm, T1 T2 .001,
L0 .0005., so LCAV .0025, measured around ?1
micron (300 THz).
7
Cavity ring-down time measurement using a highly
reflecting mirror 2 in order to further reduce
LCAV (increasing the cavity Q)
E1
E2
E3
E5
L0 2 D ?
E52
T1 L1
T20 R 1-L2
Computer etc.
Photodetector
Net cavity loss LCAV T1 0 L0 L1 L2
2D ? ---gt Higher Q Method 1) Computer
dithers piezo to point of minimum reflected power
E52 2) Laser beam is interrupted. 3) Ring-down
time constant is measured at mirror 1 cavity
output. Again, we are assuming that T1 lt ½ LCAV

8
Practical (and energy efficient) implementation
of separation of incident laser beam and
reflected wave from cavity
Circularly polarized waves
PolarizingBeamsplitter
E2
E1
LASER
E3
Shutter
Quarter wave plate _at_ 45o
E5
Photodetector