Oscillations, Waves, and Interactions - GWDG

288 Schreiber
and it is currently believed that the respective mirror coatings exhibit some minute
non-isotropy, causing the cavity Q to be different for the two senses of propagation.
For a model accounting for dispersive frequency detuning and hole burning [12] the
bias due to the corresponding null shift offset becomes
∆f0 = c
2P ·
�
ξ Zi(ξ)
L(ξ)
η Zi(0) G
�
· ∆I , (7)
with ξ the cavity detuning from line center, Z(ξ) the imaginary part of the dispersion
function, G the gain, and ∆I the observed difference in intensity. Equation (7) also
shows that it is very important to keep the gain constant, which is very difficult for a
gas laser in the presence of gain medium degradation through outgassing inside the
cavity.
6.2 Backscatter coupling
In the presence of strong backscattering, light of one sense of propagation is coupled
into the beam travelling into the opposite direction. According to Ref. [9] the beat
frequency disappears if the experienced rotation rate falls below a threshold value of
ωL = cλ2√rs . (8)
32πAd
A is the area enclosed by the cavity, d the diameter of the beam, and rs the amount
of backscatter contribution of the mirror. In the most general case the shifted beat
frequency then becomes
∆f = 4A
�
ω
λP
2 − ω2 L , (9)
where ω is the experienced rate of rotation of the gyro. For ring lasers of the size
of C-II or smaller, ωL can be of a significant amount, however far from locking up
with the Earth rate as the only source of rotation, while neither G nor any of the
UG ring lasers ever showed much evidence for the presence of backscatter at all. For
this situation the contribution to backscatter is best expressed as
∆fbs = c
2P (ρ2 sin(ψ + ɛ2) + ρ1 sin(ψ + ɛ1)) , (10)
where ɛ1 and ɛ2 are the respective backscatter phase angles and ρ1 and ρ2 the corresponding
backscatter amplitudes. Following Ref. [12] one can write
ρ1 = rsλ
�
I1
, ρ2 =
4d I2
rsλ
�
I2
, (11)
4d I1
with I1, I2 the respective intensities of the two beams. As one can see from Eqs. (10)
and (11) together, the effect of backscattering reduces with growing size of the cavity
and lower scattering amplitude. In particular, the reduction of backscattering
through a limited acceptance angle of the solid angle where all the light was scattered
into, seems to be a very effective process.