Oscillations, Waves, and Interactions - GWDG

Large ring laser gyroscopes 285
Ring Laser Area, m 2 Perimeter, m fSagnac, Hz ∆Ω/ΩE
C-II 1 4 79.4 1 · 10 −7
GEOsensor 2.56 6.4 102.6 1 · 10 −7
G0 12.25 14 288.6 4 · 10 −7
G 16 16 348.6 1 · 10 −8
UG1 366.83 76.93 1512.8 3 · 10 −8
UG2 834.34 121.435 2177.1 5 · 10 −8
Table 1. Summary of physical properties of a number of large ring lasers.
the Earth with the exception of G0, which is located vertically along an east/west
wall. For this table only one parameter, namely the theoretical sensitivity, has been
regarded. This does not necessarily mean that the performance is readily obtained at
all times. The enhanced scaling factor comes on the expense of mechanical stability
and also a faster degradation of the laser gain medium over time. In order to draw
conclusions from ring laser measurements with respect to global geophysical signals
it is important to rigidly connect the interferometer to the Earth crust. Naturally
it is easier to do that with larger constructions. However, a heterolithic structure
inside an artifical cave suffers substantially from thermo-elastic deformations and
atmospheric pressure variations. The following section looks at the various error
mechanisms of ring lasers in more detail.
5 Sensor resolution
According to Refs. [4, 15] and also others the sensitivity limit of a ring laser gyroscope
from the irreducible quantum noise for a rotation measurement is given by
δΩ = cP
�
hf
, (3)
4AQ Pxt
where P is the perimeter, A the area encircled by the light beams of the gyro, Q = ωτ
the quality factor of the ring cavity, h is Planck’s constant, Px the beam power loss
corresponding to the photon flux on the photodetector and t the integration time.
For the large ring laser G in Germany P = 16 m and A = 16 m 2 . The ring-down
time was first measured to be τ = 1 ms in 2001. Over the years it reduced to a value
of τ = 500 µs in 2007 due to gradual mirror degradation. Figure 5 shows the current
quantum limit for G as a function of the respective integration time. Currently G
reaches a sensitivity of 10 −12 rad/s at an integration time of approximately 1000
seconds, which is believed to be a world record.
All these ring lasers are very large compared to an aircraft gyro. The optical
path length varies between several meters and 121.44 m. With total cavity losses at
the level of 108 parts per million, this translates into a very narrow linewidth. The
theortically expected Schawlow-Townes linewidth for G is
∆νL =
N2
N2 − N1
2πf0∆νc
, (4)
PL