Subfemtowatt Laser Phase Tracking.

Low power optical phase tracking is an enabling capability for intersatellite laser interferometry, as minimum trackable power places significant constraints on mission design. Through the combination of laser stabilization and control-loop parameter optimization, we have demonstrated continuous tracking of a subfemtowatt optical field with a mean time between slips of more than 1000 s. Comparison with analytical models and numerical simulations verified that the observed experimental performance was limited by photon shot noise and unsuppressed laser frequency fluctuations. Furthermore, with two stabilized lasers, we have demonstrated 100 min of continuous phase tracking of Gravity Recovery and Climate Experiment (GRACE)-like signal dynamics with an optical carrier ranging in power between 1-7 fW with zero cycle slips. These results indicate the feasibility of future interspacecraft laser links operating with significantly reduced received optical power.

Absolute frequency readout derived from ULE cavity for next generation geodesy missions: erratum.

We found a calculation error affecting the scaling of results presented in Figure 7 of our article "Absolute frequency readout derived from ULE cavity for next generation geodesy missions" [Opt. Express2926014 (2021)10.1364/OE.434483] . The corrected Figure 7 is published here.

Large dynamic range, high resolution optical heterodyne readout for high velocity slip events.

We present a free-space optical displacement sensor for measuring geological slip event displacements within a laboratory setting. This sensor utilizes a fiberized Mach-Zehnder based optical heterodyne system coupled with a digital phase lock loop, providing a large dynamic range (multiple centimeters), high displacement resolution (with an amplitude spectral density of <10-10 m/Hz for frequencies above 100 Hz), and high velocity tracking capabilities (up to 4.96 m/s). This displacement sensor is used to increase the displacement and the time sensitivity for measuring laboratory-scale earthquakes induced in geological samples by using a triaxial compression apparatus. The sensor architecture provides an improved displacement and time resolution for the millisecond-duration slip events, at high containment and loading pressure and high temperatures. Alternatively, the sensor implementation can be used for other non-contact displacement readouts that required high velocity tracking with low noise and large dynamic range sensing. We use 13 high-velocity slip events in Fontainebleau sandstone to show the large dynamic range displacement tracking ability and displacement amplitude spectral densities to demonstrate the optical readout's unique sensing capabilities.

Improved cross-talk suppression for digitally enhanced interferometry using Golay complementary pairs.

We demonstrate digitally enhanced interferometry with better than 100 dB mean cross-talk suppression with Golay complementary pairs using a combination of numerical simulations and experiments. These results exceed previously reported cross-talk suppression using conventional maximal length sequences by more than 48 dB.

Absolute frequency readout derived from ULE cavity for next generation geodesy missions.

The next generation of Gravity Recovery and Climate Experiment (GRACE)-like dual-satellite geodesy missions proposals will rely on inter-spacecraft laser interferometry as the primary instrument to recover geodesy signals. Laser frequency stability is one of the main limits of this measurement and is important at two distinct timescales: short timescales over 10-1000 seconds to measure the local gravity below the satellites, and at the month to year timescales, where the subsequent gravity measurements are compared to indicate loss or gain of mass (or water and ice) over that period. This paper demonstrates a simple phase modulation scheme to directly measure laser frequency change over long timescales by comparing an on-board Ultra-Stable Oscillator (USO) clocked frequency reference to the Free Spectral Range (FSR) of the on-board optical cavity. By recording the fractional frequency variations the scale correction factor may be computed for a laser locked to a known longitudinal mode of the optical cavity. The experimental results demonstrate a fractional absolute laser frequency stability at the 10 ppb level (10-8) at time scales greater than 10 000 seconds, likely sufficient for next generation mission requirements.

High stability laser locking to an optical cavity using tilt locking.

This paper describes, to our knowledge, the first demonstration of high performance tilt locking, a method of stabilizing laser frequency to an optical reference cavity using a spatial-mode readout technique. The experiment utilized a traveling wave cavity with a finesse of approximately 10,000, housed in a thermally controlled vacuum chamber. The tilt locking method in a double pass configuration has promising performance in the 100 µHz-1 Hz band, including surpassing the Gravity Recovery and Climate Experiment (GRACE) Follow-On laser ranging interferometer requirement. Tilt locking offers a number of benefits such as high sensitivity, low cost, and simple implementation and therefore should be considered for future applications requiring high performance laser locking, such as future laser-based satellite geodesy missions and the Laser Interferometer Space Antenna.

Mitigation of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave LiDAR.

We present a detailed analysis of techniques to mitigate the effects of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave (RAMCW) LiDAR. The analysis focuses specifically on a technique which uses coherent dual-quadrature detection to enable a sum of squares calculation to remove the input signal's dependence on carrier phase and frequency. This increases the correlation bandwidth of the matched-template filter to the bandwidth of the acquisition system, whilst also supporting the simultaneous measurement of relative radial velocity with unambiguous direction-of-travel. A combination of simulations and experiments demonstrate the sum of squares technique's ability to measure distance with consistently high SNR, more than 15 dB better than alternative techniques whilst operating in the presence of otherwise catastrophic phase noise and large frequency offsets. In principle, the technique is able to mitigate any sources of phase noise and frequency offsets common to the two orthogonal outputs of a coherent dual-quadrature receiver including laser frequency noise, speckle-induced phase noise, and Doppler frequency shifts due to accelerations.

Fast beam steering with an optical phased array.

Optical phased arrays (OPAs) are devices that use the coherence of light to control the interference pattern in the far field, which enables them to steer a laser beam with no moving parts. As such, OPAs have potential applications in laser communications, target acquisition and tracking, metrology, and directed energy. In this Letter, we present a control architecture for an actively phase-locked OPA, capable of steering a laser beam at speeds limited by the actuation bandwidth of electro-optic modulators. The system achieved an output phase stability of λ/770 and steering speeds up to 1 MHz. The digital control architecture can be extended to GHz steering speeds, is readily scalable to hundreds of emitters, and is compatible with high-power arrays.

Crosstalk reduction for multi-channel optical phase metrology.

Digitally enhanced heterodyne interferometry (DEHI) combines the sub-wavelength displacement measurements of conventional laser interferometry with the multiplexing capabilities of spread-spectrum modulation techniques to discriminate between multiple electric fields at a single photodetector. Technologies that benefit from DEHI include optical phased arrays, which require the simultaneous phase measurement of a large number of electric fields. A consequence of measuring the phase of multiple electric fields is the introduction of crosstalk, which can degrade measurement precision. This work analytically and experimentally investigates the crosstalk when using DEHI to measure the phase of an arbitrarily large number of electric fields at a single photodetector. Also considered is the practical limit the dynamic range of the photodetector and shot noise imposes on the number of electric fields that can be discriminated. We describe how to minimize crosstalk by design. Experimental results demonstrate up to 55 dB suppression of crosstalk between two electric fields with a phase measurement bandwidth of 20 kHz and 1-10 pm/Hz displacement sensitivity for audio frequencies. Additionally, we demonstrate scaling of crosstalk proportional to the square-root of the number of electric fields when using an M-sequence modulation. Based on this analysis, we estimate that digitally enhanced heterodyne interferometry should be capable of measuring the phase of several hundreds of electric fields at a single photodetector while maintaining the same measurement bandwidth.

Observation of Squeezed Light in the 2 µm Region.

We present the generation and detection of squeezed light in the 2 µm wavelength region. This experiment is a crucial step in realizing the quantum noise reduction techniques that will be required for future generations of gravitational-wave detectors. Squeezed vacuum is generated via degenerate optical parametric oscillation from a periodically poled potassium titanyl phosphate crystal, in a dual resonant cavity. The experiment uses a frequency stabilized 1984 nm thulium fiber laser, and squeezing is detected using balanced homodyne detection with extended InGaAs photodiodes. We have measured 4.0±0.1 dB of squeezing and 10.5±0.5 dB of antisqueezing relative to the shot noise level in the audio frequency band, limited by photodiode quantum efficiency. The inferred squeezing level directly after the optical parametric oscillator, after accounting for known losses and phase noise, is 10.7 dB.

Interferometric wavefront sensing with a single diode using spatial light modulation.

We present a new technique for the fine alignment sensing of optical interferometers. Unlike conventional wavefront sensing systems, which use multielement photodiodes, this approach works with a single-element photodiode, in combination with a spatial light modulator (SLM) and digitally enhanced heterodyne interferometry. As all signals pass through a single photodetection and analog path, the technique exhibits high common-mode rejection to low frequency errors present in conventional systems. By changing the modulation pattern on the SLM, the technique can also be extended to sensing higher-order wavefront errors. In this paper, we demonstrate the technique experimentally and compare performance with a conventional heterodyne wavefront sensing system. This may improve and simplify alignment systems in space-based interferometers such as the planned LISA gravitational wave detector and provide a way to optimize the power in laser cavities not possible with the traditional segmented diode approach.

Algebraic cancellation of polarisation noise in fibre interferometers.

This experiment uses digital interferometry to reduce polarisation noise from a fiber interferometer to the level of double Rayleigh backscatter making precision fiber metrology systems robust for remote field applications. This is achieved with a measurement of the Jones matrix with interferometric sensitivity in real time, limited only by fibre length and processing bandwidth. This new approach leads to potentially new metrology applications and the ability to do ellipsometry without polarisation elements in the output field.

High power compatible internally sensed optical phased array.

The technical embodiment of the Huygens-Fresnel principle, an optical phased array (OPA) is an arrangement of optical emitters with relative phases controlled to create a desired beam profile after propagation. One important application of an OPA is coherent beam combining (CBC), which can be used to create beams of higher power than is possible with a single laser source, especially for narrow linewidth sources. Here we present an all-fiber architecture that stabilizes the relative output phase by inferring the relative path length differences between lasers using the small fraction of light that is back-reflected into the fiber at the OPA's glass-air interface, without the need for any external sampling optics. This architecture is compatible with high power continuous wave laser sources (e.g., fiber amplifiers) up to 100 W per channel. The high-power compatible internally sensed OPA was implemented experimentally using commercial 15 W fiber amplifiers, demonstrating an output RMS phase stability of λ/194, and the ability to steer the beam at up to 10 kHz.

Suppressing Rayleigh backscatter and code noise from all-fiber digital interferometers.

We configure an all-fiber digital interferometer to eliminate both code noise and Rayleigh backscatter noise from bidirectional measurements. We utilize a sawtooth phase ramp to upconvert code noise beyond our signal bandwidth, demonstrating an in-band noise reduction of approximately two orders of magnitude. In addition, we demonstrate, for the first time to our knowledge, the use of relative code delays within a digital-interferometer system to eliminate Rayleigh-backscatter noise, resulting in a noise reduction of a factor of 50. Finally, we identify double Rayleigh-backscatter noise as our limiting noise source and suggest two methods to minimize this noise source.

A squeezed light source operated under high vacuum.

Non-classical squeezed states of light are becoming increasingly important to a range of metrology and other quantum optics applications in cryptography, quantum computation and biophysics. Applications such as improving the sensitivity of advanced gravitational wave detectors and the development of space-based metrology and quantum networks will require robust deployable vacuum-compatible sources. To date non-linear photonics devices operated under high vacuum have been simple single pass systems, testing harmonic generation and the production of classically correlated photon pairs for space-based applications. Here we demonstrate the production under high-vacuum conditions of non-classical squeezed light with an observed 8.6 dB of quantum noise reduction down to 10 Hz. Demonstration of a resonant non-linear optical device, for the generation of squeezed light under vacuum, paves the way to fully exploit the advantages of in-vacuum operations, adapting this technology for deployment into new extreme environments.

Homodyne digital interferometry for a sensitive fiber frequency reference.

Digitally enhanced homodyne interferometry enables robust interferometric sensitivity to be achieved in an optically simple configuration by shifting optical complexity into the digital signal processing regime. We use digitally enhanced homodyne interferometry in a simple, all-fiber Michelson interferometer to achieve a frequency reference stability of better than 20 Hz/√Hz from 10 mHz to 1 Hz, satisfying, for the first time in an all fiber system, the stability requirements for the Gravity Recovery and Climate Experiment Follow On mission. In addition, we have demonstrated stability that satisfies the future mission objectives at frequencies down to 1 mHz. This frequency domain stability translates into a fractional Allan deviation of 3.3 × 10(-17) for an integration time of 55 seconds.

Coherent beam combining using a 2D internally sensed optical phased array.

Coherent combination of multiple lasers using an optical phased array (OPA) is an effective way to scale optical intensity in the far field beyond the capabilities of single fiber lasers. Using an actively phase locked, internally sensed, 2D OPA we demonstrate over 95% fringe visibility of the interfered beam, λ/120 RMS output phase stability over a 5 Hz bandwidth, and quadratic scaling of intensity in the far field using three emitters. This paper presents a new internally sensed OPA architecture that employs a modified version of digitally enhanced heterodyne interferometry (DEHI) based on code division multiplexing to measure and control the phase of each emitter. This internally sensed architecture can be implemented with no freespace components, offering improved robustness to shock and vibration exhibited by all-fiber devices. To demonstrate the concept, a single laser is split into three channels/emitters, each independently controlled using separate electro-optic modulators. The output phase of each channel is measured using DEHI to sense the small fraction of light that is reflected back into the fiber at the OPA's glass-air interface. The relative phase between emitters is used to derive the control signals needed to stabilize their relative path lengths and maintain coherent combination in the far field.

Laser link acquisition demonstration for the GRACE Follow-On mission.

We experimentally demonstrate an inter-satellite laser link acquisition scheme for GRACE Follow-On. In this strategy, dedicated acquisition sensors are not required-instead we use the photodetectors and signal processing hardware already required for science operation. To establish the laser link, a search over five degrees of freedom must be conducted (± 3 mrad in pitch/yaw for each laser beam, and ± 1 GHz for the frequency difference between the two lasers). This search is combined with a FFT-based peak detection algorithm run on each satellite to find the heterodyne beat note resulting when the two beams are interfered. We experimentally demonstrate the two stages of our acquisition strategy: a ± 3 mrad commissioning scan and a ± 300 µrad reacquisition scan. The commissioning scan enables each beam to be pointed at the other satellite to within 142 µrad of its best alignment point with a frequency difference between lasers of less than 20 MHz. Scanning over the 4 alignment degrees of freedom in our commissioning scan takes 214 seconds, and when combined with sweeping the laser frequency difference at a rate of 88 kHz/s, the entire commissioning sequence completes within 6.3 hours. The reacquisition sequence takes 7 seconds to complete, and optimizes the alignment between beams to allow a smooth transition to differential wavefront sensing-based auto-alignment.

Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling.

The GRACE Follow-On mission will monitor fluctuations in Earth's geoid using, for the first time, a Laser Ranging Interferometer to measure intersatellite distance changes. We have investigated the coupling between spacecraft rotation and the intersatellite range measurement that is incurred due to manufacturing and assembly tolerances of the Triple Mirror Assembly (TMA), a precision retroreflector to ensure alignment between in- and outgoing laser beams. The three TMA mirror planes intersect in a virtual vertex to which satellite displacements are referenced. TMA manufacturing tolerances degrade this ideal vertex, however, a Point of Minimal Coupling (PMC) between spacecraft rotation and displacement exists. This paper presents the experimental location of the PMC under pitch and yaw rotations for a prototype TMA. Rotations are performed using a hexapod, while displacements are monitored with heterodyne laser interferometry to verify the PMC position. Additionally, the vertex of the three TMA mirror planes is measured using a Coordinate Measuring Machine and compared to the PMC position. In the pitch and yaw axes, the biggest deviation between TMA vertex and PMC was 50 ± 64 µm. Thus, within the measurement uncertainties, no difference between TMA vertex and PMC could be observed. This is a key piece of information for integration of the TMA into the spacecraft: It is sufficient to use the readily-available TMA vertex location to ensure minimal rotation-to-displacement coupling during the mission.

Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset.

A method based on phase-shifting Fizeau interferometry is presented with which retroreflectors with large incoming-outgoing beam separations can be tested. The method relies on a flat Reference Bar that is used to align two auxiliary mirrors parallel to each other to extend the aperture of the interferometer. The method is applied to measure the beam coalignment of a prototype Triple Mirror Assembly of the GRACE Follow-On Laser Ranging Interferometer, a future satellite-to-satellite tracking device for Earth gravimetry. The Triple Mirror Assembly features a lateral beam offset of incoming and outgoing beam of 600 mm, whereas the acceptance angle for the incoming beam is only about ±2 mrad. With the developed method, the beam coalignment of the prototype Triple Mirror Assembly was measured to be 9 µrad with a repeatability of below 1 µrad.