Arm locking with the GRACE follow-on laser ranging interferometer

Arm locking is a technique for stabilizing the frequency of a laser in an interspacecraft interferometer by using the spacecraft separation as the frequency reference. A candidate technique for future space-based gravitational wave detectors such as the Laser Interferometer Space Antenna, arm locking has been extensive studied in this context through analytic models, time-domain simulations, and hardware-in-the-loop laboratory demonstrations. In this paper we show the laser ranging interferometer instrument flying aboard the upcoming Gravity Recovery and Climate Experiment follow-on (GRACE-FO) mission provides an appropriate platform for an on-orbit demonstration of the arm-locking technique. We describe an arm-locking controller design for the GRACE-FO system and a series of time-domain simulations that demonstrate its feasibility. We conclude that it is possible to achieve laser frequency noise suppression of roughly 2 orders of magnitude around a Fourier frequency of 1 Hz with conservative margins on the system’s stability. We further demonstrate that “pulling” of the master laser frequency due to fluctuating Doppler shifts and lock acquisition transients is less than 100 MHz over several GRACE-FO orbits. These findings motivate further study of the implementation of such a demonstration.

Figure 1

Bode plots of Open-Loop and Closed-Loop gain for proposed GRACE-FO arm-locking system.

Figure 2

Nyquist plot of Open-Loop gain for proposed GRACE-FO arm-locking system. The inset shows a zoom in of the low-gain region, showing the system’s interaction with the noise-enhancement region (interior of the dashed circle).

Figure 3

Spectra of representative Doppler shifts for the GRACE-FO LRI derived from microwave ranging data from GRACE. The blue curve shows the raw GRACE microwave ranging data [12, 13, 14] after finite differencing and scaling to Doppler shift for 1064 nm light. The red curve, which corresponds to the signal used in the simulations, has been low-pass filtered to reject excess high-frequency noise that originates in the GRACE microwave system.

Figure 4

Time series of master laser frequency and round-trip Doppler shift from a 10 ks simulation with the economized model. The top panels compare the drift from nominal frequency for a free-running laser (blue) and laser locked to the GRACE-FO arm (red). After an initial lock-acquisition transient lasting a few hundred seconds (top left panel) the arm-locked system undergoes roughly periodic drifts with an amplitude of $\sim 35\mathrm{MHz}$, well within an acceptable operating range for the GRACE-FO laser. The bottom panel shows the round-trip Doppler shift, which is also roughly equivalent to the drift in the optical beat note at the master spacecraft. The drift of the arm-locked laser is correlated with the Doppler shift at low frequencies due to the frequency-pulling effect described in the text.

Figure 5

Amplitude spectral density of frequency noise in a simulated GRACE-FO arm-locking system. The free-running frequency noise is shown in blue and the arm-locked frequency noise is shown in red. The green trace shows the expected residual frequency noise based on the system transfer function (gain limit) while the magenta trace shows the noise associated with the pulling of the laser frequency caused by the time-varying Doppler signal. All traces derived from two simulations with the high-fidelity model: a 10 s simulation with 100 kHz data sampling and a 500 s simulation with 10 Hz data sampling.