# Laser frequency stabilisation for GRACE Follow-On

GRACE Follow-On will augment the ranging capabilities of the existing microwave ranging system by equipping the spacecraft with a laser ranging instrument (LRI). By operating at a much shorter wavelength than microwaves (1 micrometre instead of 1 centimetre), laser ranging is expected to significantly increase the measurement resolution of the distance between the satellites. However, even high-quality lasers have some natural wavelength variation (usually called frequency noise); if uncontrolled, this frequency noise would limit the ranging precision to far worse than the mission requirements of 50 nm/√Hz. To solve this problem, the GRACE Follow-On consortium, led by ANU Centre for Gravitational Physics, is simultaneously exploring three strategies for laser frequency stabilisation on a spacecraft. One of these three techniques will be finally selected for the mission.

## The GRACE Follow-On measurement principle

In GRACE Follow-On two spacecraft are connected by an infrared laser link. A laser beam is sent by the first spacecraft, spacecraft A, to the second, spacecraft B. Spacecraft B, set in a transponder configuration, sends a copy of this light back to spacecraft A. This is shown in Figure 1. Here the outgoing and the returning beams are made to interfere and, by measuring changes in their relative phase, variations in the distance (L in Figure 1.) between the spacecraft are directly measured.

Thanks to advances in high precision interferometry in the past decades, we are now able to detect very small changes in optical phase, and thus length changes well below the laser wavelength. However, laser phase variations from any source will mimic a length change between the satellites, and thus confuse the signal. Laser frequency noise is one of the most important sources of these spurious laser phase fluctuations. It is thus critical to develop an onboard laser frequency stabilisation system.

## Laser frequency stabilisation

In laser frequency stabilisation systems, an independent, stable frequency reference is compared to the frequency of the laser. This measurement is then used by a feedback system to change the laser frequency so that it matches the independent reference. The stability of the frequency reference sets the ideal limit to the frequency stabilisation system.

These systems can be very complex, and many are not suited for space application, where simplicity, weight, volume and power consumption set rigid constraints on the onboard instrumentation. The GRACE Follow-On consortium is currently investigating two types of frequency reference: the resonance frequency of a rigid optical cavity and the resonance frequency of an optical fibre resonator. ANU in Canberra and the Jet Propulsion Laboratory (JPL) in Pasadena, California are exploring two variations of the first option, with differences in the frequency fluctuations readout technique; the Australian National Measurement Institute (NMI), in Sydney, is focusing on the second.

An optical cavity consists of two or more partially reflecting mirrors facing each other so that they reflect the light back on to the same path indefinitely. If the cavity length is equal to an integer number of half wavelengths, the light interferes constructively, optical power builds up and the cavity resonates. In other words, the light resonates every time the laser frequency is equal to an integer multiple of the cavity resonant frequency. If the cavity length is very stable, the cavity can be used as a frequency reference.

## Technique #1: Pound-Drever-Hall locking technique

Worldwide, the standard technique to readout frequency fluctuations around cavity resonance is the so-called Pound-Drever-Hall technique (PDH). This technique is the one used by the frequency stabilisation system being tested at the JPL. In this technique a high frequency phase modulation is placed on the laser light, generating two sidebands with equal and opposite frequency offset from the main laser light. All three frequencies of laser light are then sent to the optical cavity. The sidebands do not resonate in the cavity at the same time as the main laser frequency, and by appropriately comparing the relative phase of the main laser frequency and the two sidebands (a process called demodulation), it is possible to determine very precisely whether the main laser frequency is matched to the cavity resonance frequency. Although this PDH technique is well established, a system using it has never before been flown on a spacecraft.

## Technique #2: Tilt-locking technique

Tilt-locking is an alternative technique developed at ANU to sense the difference between the laser and cavity resonance frequencies using a secondary transverse spatial mode (i.e., a slightly different shape) of the laser beam in place of the phase modulation sidebands used in PDH locking. This time, the spatial mode is obtained by introducing a very small misalignment between the laser and the cavity. In the same way as in PDH locking, comparing the phase of the secondary spatial mode and the fundamental mode allows a precise determination of whether the laser frequency matches the cavity resonance frequency.

No phase modulation or beat note demodulation is needed in tilt locking, greatly reducing the complexity of the optical system, the weight, and the power consumption of the apparatus when compared to the standard PDH technique. These reasons make it a very interesting candidate for frequency stabilisation in space. In theory, tilt-locking and PDH locking have the same limits on ultimate precision, but tilt-locking has never been demonstrated in a high-performance setup. This is one of the primary goals of the ANU experiment.

### ANU tilt-locking frequency stabilisation experiment

At ANU Centre for Gravitational Physics we have designed and built a tilt-locking reference cavity based on double-pass tilt-locking, an improvement on the original tilt-locking technique. In this configuration (depicted in Figure 2) the laser is aligned to a triangular cavity and it is fully transmitted at resonance. A mirror is then placed at the cavity output, which reflects the light back into the cavity, with a small tilt added on the beam.

The cavity is held together by an Ultra Low Expansion (ULE) glass spacer (shown in Figure 3), one of the hardest materials suited for this purpose. A low-noise quadrant photodetector developed in collaboration with the Albert Einstein Institute in Hanover, Germany measures the beam displacements. To remove the disturbances due to air currents and temperature fluctuations, the cavity is placed inside of a vacuum chamber, which is in turn enclosed by a temperature-controlled container (shown in Figure 4).

The goal of the experiment is to stabilise the laser frequency noise down to 30 Hz/√Hz across the GRACE Follow-On bandwidth, which ranges from 2 to 200 mHz.

In order to measure the absolute stabilisation obtained through this system, we built two identical setups. By measuring the phase noise between the two independently stabilised lasers, we will be able to estimate the mean frequency noise of each system.

## Technique #3: Fiber laser frequency stabilisation

The third option being investigated by our consortium uses a segment of an optical fibre in a similar way to an optical cavity (Figure 5). The National Measurement Institute in Sydney is currently leading the research in that direction.

## System down selection

By the 31st of December 2012 the consortium will converge on one of these three technologies to make it the choice for GRACE Follow-On. Such an early decision is necessary in order to have later enough time later to develop the actual flying system, and demonstrate its ability to survive launch, before the launch date in 2016.