Oscillations, Waves, and Interactions - GWDG

Split-mode Sagnac [Hz]
282.800
282.750
282.700
282.650
282.600
Large ring laser gyroscopes 289
282.550
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Time [day 304 in 2002]
Figure 7. Earth strain changes the perimeter in UG1. The black dots show the variation
in the FSR, while the line represents the expected variations from a global strain model.
An additional linear term accounts for the increase of temperature in the Cashmere Cavern
over the course of these measurements.
6.3 The effect of Earth strain on large cavities
Large ring laser cavities such as UG1 and UG2 are subject to Earth strain effects
caused mainly by the gravitational attraction of the moon. The deformation in
response to the lunar gravitational pull stretches the cavity with an amplitude of
about 20 nanostrain, which adds up to a total of approximately 1.5 µm for UG1,
thus changing the geometrical part of the scale factor 4A/λP by a small amount. In
the absence of any shear forces these strain effects will change both the perimeter
and the area of the ring laser at the same time. Since the perimeter has to contain
an integer number of waves (P = Iλ) in order to maintain lasing, the scale factor can
be reduced to (I/4) for a square ring, where I is the longitudinal mode index. This
means that in this case all the changes in the area and perimeter are compensated
by a corresponding shift in the optical frequency of the laser, provided that the shift
is less than one free spectral range and the laser mode does not change. While this
self-compensation is strictly speaking only valid for a true square ring, one can find
that it also applies to near square rings.
Figure 7 gives an example from UG1. For the purpose of this measurement UG1
was operated on 2 neighbouring longitudinal modes per sense of propagation. The
beat note between these two modes ∆f = c/P ∼ = 3.9 MHz corresponds to the free
spectral range and is a direct measure of the effective length of the cavity. The
beat frequency was down-converted to an audio signal of about 288 Hz with the help
of a GPS controlled reference oscillator and continuously recorded with an A/Dconverter
and a computer. While the black dots in Fig. 7 represent the variation
of the length of the cavity expressed as a shift of the measured FSR, the red line
gives the corresponding FSR shift computed from an Earth strain model. In order
to account for an upward drift of the ambient temperature in the Cashmere Cavern
over the course of the measurements an additional linear drift term was added. A