Long-range sensing can be critical, whether for detecting incoming weapons before they become immediate threats, tracking the locations and health of satellites in orbit, or locking two satellites together across many kilometers, tracking and correcting their drift so they can take long-exposure interferometric measurements. This can be accomplised by reducing noise, which was used by the LIGO Laboratory, or by amplifying the signal coherently, resulting in greater signal amplification than noise amplification. While Samurai Scientists has worked on both technologies, our greatest successes--and all our publications--come from coherent amplification.

The main method we have used for coherent amplification is photorefractivity, a nonlinear optical technique that enables a transfer of power from one laser beam into another. We tested a variety of photorfractive crystals, such as BGO, BTO, BaTiO3, and Cu:KNSBN, and used two-wave as well as four-wave mixing. In the course of our experiments, we demonstrated the capability of photorefractive-enhanced laser radar to meaure the vibrometric signatures of objects 200 km distant -- the equivalent of tracking and probing satellites in low-earth orbit. We showed measurement resolution better than 5 nm (limited by our manual technology) with a theoretical range exceeding 2000 km (dependent on beam propagation delay and processing time). Our publications in this area include:

1. Kurtz, R.M. “Optimizing the Amplifier Bandwidth for Pulse Reception.” TechRXiv Preprint. Palos Verdes Estates, California: Samurai Scientists LLC; 2023. 13 pp. doi: 10.36227/techrxiv.14955456.v1.
        Detecting and recognizing pulses is a critical task, in fields as widely separated as telecommunications, lidar, and target illumination. In all cases, the signal-to-noise ratio (SNR) is a key parameter that can be used to determine both the potential rate of errors and the probability of correct detection. In this paper the relationship among pulse width, amplifier bandwidth, and SNR is determined through modeling four approximations to pulse shapes and four amplifier lowpass filter configurations. The analysis determined that, given a specific filter and pulse shape, the bandwidth that maximizes SNR is a constant divided by the pulse width. For example, if the pulse has a Gaussian shape and the amplifier incorporates a second-order Chebyshev lowpass filter, this constant is 0.3389. Applying this, if the pulse width is 20 ns the maximum SNR comes for a filter bandwidth of 16.95 MHz, while if the pulse width is 50 μs the SNR is maximized at a 6.778-kHz bandwidth. Passing the signal through a filter also distorts the signal shape; the temporal shift and pulse lengthening are also determined. The calculated values are offered as inputs to a potential trade space that includes SNR, pulse distortion by the filter, and cost.
2. Kurtz, R.M.; Lu, W.; Piranian, J.; Okorogu, A.O. “Photorefractive Amplification at High Frequencies.” In: Bjelkhagen, H.I., editor. Practical Holography XXV: Materials and Applications. San Francisco, California: SPIE; 7957, 2011. p. 79570K. doi:doi:10.1117/12.875761.
         Photorefractive optical amplification, while useful, is a slow process. Under some circumstances, however, it amplifies optical signals effectively even when one is modulated at a relatively high frequency. We determine the reasons for this capability (what we have called the “Fast Photorefractive Effect”) and analyze its enhanced bandwidth, improvements over standard photorefractivity, and limitations.
3. Kurtz, R.M.; Lu, W.; Piranian, J., et al. “The Fast Photorefractive Effect and Its Application to Vibrometry.” J Hologr Speckle. 5: 149-155; 2009. doi:10.1166/jhs.2009.1008.
         We previously reported on what we describe as the “fast photorefractive effect,” photorefractive signal amplification at much greater frequencies than predicted by its grating formation speed. In this paper we explain the effect and its potential for application to vibrometry. We demonstrated photorefractive amplification in Cu:KNSBN (whose grating formation speed is <5 Hz), matching the standard model with CW illumination. We then demonstrated photorefractive amplification of vibrometric signals at frequencies up to 4 MHz. Our theory of the fast photorefractive effect indicates that the amplification bandwidth of Cu:KNSBN at 488 nm illumination could exceed 800 GHz.
4. Kurtz, R.M.; Pradhan, R.D.; Aye, T.M., et al. “Long-Range Phase Conjugate Interferometry.” Spaceborne Sensors. Orlando, FL: SPIE; 5418, 2004. p. 115-126.
         The most accurate method of measuring distance and motion is interferometry. This method of motion measurement correlates change in distance to change in phase of an optical signal. As one mirror in the interferometer moves, the resulting phase variation is visualized as motion of interferometric fringes. While traditional optical interferometry can easily be used to measure distance variation as small as 10 nm, it is not a viable method for measuring distance to, or motion of, an object located at a distance grater than half the coherence length of the illumination source. This typically limits interferometry to measurements of objects within <1 km of the interferometer. We present a new interferometer based on phase conjugation, which greatly increases the maximum distance between the illumination laser and the movable target. This method is as accurate as traditional interferometry, but is less sensitive to laser pointing error and operates over a longer path. Experiments demonstrated measurement accuracy of <15 nm with a laser-target separation of 50 times the laser coherence length.