PHYSICS OF THE COUNTER-PUMPED BRILLOUIN LASER
4.4 Earth’s rotation measurement
Figure 4.6 shows the conceptual illustration of the Earth’s rotation measurement by a resonator laser gyroscope. When the gyroscope is toward North and South, the effective cavity round-trips seen by the clockwise (CW) and counterclockwise (CCW) lights are different due to the Earth rotation. This round-trip difference
Figure 4.6: The Earth’s rotation measured by the resonator laser gyroscope. The Earth’s rotation is detected from the laser beating frequency change (δν) when the gyroscope is switching back and forth between North and South. There is no Earth rotation induced Sagnac shift if the gyroscope is toward East and West. Solid curve: cavity mode. Solid arrow: laser mode with Sagnac shift. Dashed line: laser mode without rotation. CW:
clockwise. CCW: counterclockwise.
causes the frequency splitting of the passive cavity modes, and the corresponding laser frequencies are shifted accordingly. When the counter-propagating lasers have an offset, both the magnitude and direction of the rotation are resolved by tracking the beating frequency change,δν. In contrast, no rotation couples into the gyroscope toward East and West, so the beating frequency change is zero.
Measuring the Earth’s rotation is a milestone for gyroscope development, not only because the measurement proves the sensitivity of the gyroscope, but also because the system drift is suppressed to a certain level such that the gyro shows the potential for a field test and North-finding. In our experiment, the full gyro system is installed on top of an automated air-bearing rotation stage (Figure 4.7). The rotation stage is installed firmly with a vibration absorbing pad on the ground to minimize the vibration noise and rotates freely on the horizontal surface. The gyro surface is vertically aligned (tilt angle< 0.1◦) to minimize the stage rotation induced signal.
Figure 4.7: Full rotation system. To measure the Earth’s rotation, we install the full system on an automatic air-bearing stage. The packaged gyro is installed in a damped and shielded environmental chamber. The gyro axis is well-aligned so the coupling from the stage rotation is minimized. Also, the whole system is well-balanced to minimize wobbling.
During measurement, the stage rotates toward specified directions and then stabilizes until the next cycle begins. We retrieve the stabilized data for analysis. (Photo: Yu-Hung Lai)
The system is balanced to minimize wobbling during rotation. The gyro orientation is flipped by 180◦every 60 seconds. In the first 15 seconds, the full system rotates.
In the following of 45 seconds, the system stops moving and is stabilized. We retrieve 30 seconds of data from each stabilized session, and run the drift reduction algorithm for the overall trace. Then, the shifts of the gyro readout at different orientations are measured.
When the orientation of the gyroscope changes from North to South locally, the gyro axis and Earth axis have an angle equal to the latitude (34.1◦at Caltech). The frequency shifts are normalized into the measured Earth rotation rates with latitude correction. Furthermore, we switch the sign of the detuning, such that the polarity of the frequency shifts reverses according to our model. We compare the North-South data and East-West data to check the validity of the measurement. Each data set is measured in a single trace without interruption.
The results show the opposite polarity in the North-South measurement, and the near zero response in the East-West measurement (Figure 4.8). According to the rate change measured in the experiment, the averaged Earth’s rotation vector is
the modal temperature may further reduce the thermal drift. This gyroscope paves the way towards an all-optical inertial guidance system that is both rugged and whose manufacturing process is scalable.
Figure 4.8: The Earth’s rotation measurements. a, The North-South measurement (top) and the East-West measurement (bottom) with negative pump detuning (∆νp,∆νs <
0). The Earth rotation is captured in the North-South measurement, while the East-West measurement has near zero response. Both measurements have similar residual long term drift. b,The Earth measurement with positive pump detuning (∆νp,∆νs > 0). Switching the relative frequency of the CW and CCW lights changes the sign of the Sagnac shift as predicted. (Dots/Thick lines/Dotted line: the 1s-averages/30s-averages/full-average of the gyro readout in each direction. The left axis shows the gyro readout in the frequency shift. The right axis is the rotation velocity normalized by the latitude correction and the corrected Sagnac factor.) Left Panels: The statistics of frequency changes of switching the gyro orientation. Each count is calculated by the 1s-average frequency change between consecutive cycles. (Bars: the histogram of frequency change of 1s-averages. Dashed curve: the Gaussian envelope. The error bar shows the standard deviation.)
control. Because this system dissipatively couples counter-propagating lightwaves in a single high-optical-Q resonator, it also functions as a sensitive gyroscope for measurement of rotations. As a result, our system is used to test the recent prediction of the EP-enhanced Sagnac effect [75, 76]. We are able to observe a Sagnac scale factor boost by over 4× by measuring the rotations applied to the resonator. Moreover, the amount of boost can be controlled by adjustment of system bias relative to the EP, and modeling confirms the measured enhancement. Besides verifying EP physics in a new system and application area, this work has practical importance for enhancement of optical gyroscope performance.