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.

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.

Scalable all-fiber coherent beam combination using digital control.

This paper describes a filled-aperture coherent beam combining (CBC) system based on locking of optical coherence via single-detector electronic-frequency tagging (LOCSET). The sensing and control architecture is implemented using a field-programmable gate array and high-bandwidth electro-optic phase modulators. The all-fiber optical configuration consists of a narrow linewidth 1560 nm seed laser separated into three channels, each containing 7 W erbium-doped fiber amplifiers. The system was demonstrated experimentally, achieving a total stabilized output power of 20 W, a combination efficiency greater than 95%, and an output RMS phase stability of λ/493. As this architecture employs an entirely digital sensing and control scheme based on LOCSET, it presents a highly scalable and cost-effective solution for CBC that is wavelength agnostic and can support an arbitrarily large number of channels.

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.

Detection statistics for coherent RMCW LiDAR.

This paper presents an analytical model and experimental validation for the detection performance and false-alarm rates for phase-encoded random modulation continuous-wave (RMCW) LiDAR. Derivation of the model focuses on propagating the effects of relevant noise sources through the system to determine an analytical expression for the detection rate, expressed by the probability of detection. The model demonstrates that probability of detection depends only on three factors: i) the mean signal-to-noise ratio (SNR) of the measurement; ii) the measurement integration time; and iii) speckle-induced intensity noise. The predicted analytical relationship between measurement SNR and probability of detection was validated by numerical simulations and experimental demonstrations in both a controlled fiber channel and under fully-developed speckle conditions in an uncontrolled free-space channel.

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.

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.

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.

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.

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.