Transport model for the propagation of partially coherent, partially polarized, polarization-gradient vector beams.

Recently we predicted and experimentally validated a new physical mechanism for altering the propagation path of a monochromatic beam [Opt. Express30, 38907 (2022)OPEXFF1094-408710.1364/OE.467678]. Specifically, we showed that by properly tailoring the spatial distribution of the linear state of polarization transverse to the direction of propagation, the beam followed a curved trajectory in free space. Here we extend the model to the partially coherent and partially polarized polychromatic case by redefining the beam amplitude, phase, and polarization angle as appropriate statistical quantities. In particular, the definition of polarization angle represents a fundamentally new quantity in modeling beam propagation and is shown to be consistent with recent works on energy and momentum flow. In the new model, the beam curvature matches that of our previous work in the fully coherent case but is predicted to vanish for an unpolarized, spatially incoherent beam. Simulated beam trajectories are shown for varying levels of initial partial coherence and for different polarization profiles. A new class of non-diffracting beams is also suggested by way of example.

Vector beam bending via a polarization gradient.

We propose, analyze and demonstrate experimentally an entirely new optical effect in which the centroid of a coherent optical beam can be designed to propagate along a curved trajectory in free space by tailoring the spatial distribution of linear polarization across the transverse beam profile. Specifically, a non-zero spatial gradient of second order or higher in the linear state of polarization is shown to cause the beam centroid to "accelerate" in the direction transverse to the direction of propagation. The effect is confirmed experimentally using spatial light modulation to create the distribution in linear polarization and then measuring the transverse location of the beam profile at varying propagation distances. The observed displacement of the beam centroid is shown to closely match the theory out to 34m propagation distance.

Transport-based model for turbulence-corrupted imagery.

A new model for turbulence-corrupted imagery is proposed based on the theory of optimal mass transport. By describing the relationship between photon density and the phase of the traveling wave, and combining it with a least action principle, the model suggests a new class of methods for approximately recovering the solution of the photon density flow created by a turbulent atmosphere. Both coherent and incoherent imagery are used to validate and compare the model to other methods typically used to describe this type of data. Given its superior performance in describing experimental data, the new model suggests new algorithms for a variety of atmospheric imaging and wave propagation applications.

Distribution of splice loss in single mode optical fiber.

This work investigates a probabilistic model for splice loss in single mode optical fibers. We derive the probability density function for loss values as a function of lateral and angular misalignment. We then use observed data to estimate these model parameters; both Bayesian and maximum likelihood estimation procedures are described. These estimates can then be used to provide an indication of the relative importance of various loss mechanisms. Alternatively, if one is given values for maximum lateral and angular misalignment, our results allow for predictions of expected distribution of loss values. An overall goal of this paper is to demonstrate that, beyond the mean and variance of splice loss, there is significant information in the shape of the distribution of values. A second goal is to understand the trade-off between the number of splice loss measurements and the confidence in estimates of parameters in the splice loss model.

Moving off the grid in an experimental, compressively sampled photonic link.

Perhaps the largest obstacle to practical compressive sampling is an inability to accurately, and sparsely describe the data one seeks to recover due to poor choice of signal model parameters. In such cases the recovery process will yield artifacts, or in many cases, fail completely. This work represents the first demonstration of a solution to this so-called "off-grid" problem in an experimental, compressively sampled system. Specifically, we show that an Alternating Convex Search algorithm is able to significantly reduce these data model errors in harmonic signal recovery.

Characterization of a compressively sampled photonic link.

The emerging field of compressive sampling has potentially powerful implications for the design of analog-to-digital sampling systems. In particular, the mathematics of compressive sampling suggests that one can recover a signal at a smaller sampling interval than is dictated by the rate at which the samples are digitized. In a recent work the authors presented an all-photonic implementation of such a system and experimentally demonstrated the basic operating principles. This paper offers a more in-depth study of the system, including a more detailed description of the hardware, issues involved in real-time implementation, and how choice of signal model and model fidelity can influence the reconstruction.

Signal design using nonlinear oscillators and evolutionary algorithms: application to phase-locked loop disruption.

This work describes an approach for efficiently shaping the response characteristics of a fixed dynamical system by forcing with a designed input. We obtain improved inputs by using an evolutionary algorithm to search a space of possible waveforms generated by a set of nonlinear, ordinary differential equations (ODEs). Good solutions are those that result in a desired system response subject to some input efficiency constraint, such as signal power. In particular, we seek to find inputs that best disrupt a phase-locked loop (PLL). Three sets of nonlinear ODEs are investigated and found to have different disruption capabilities against a model PLL. These differences are explored and implications for their use as input signal models are discussed. The PLL was chosen here as an archetypal example but the approach has broad applicability to any input∕output system for which a desired input cannot be obtained analytically.

Beating Nyquist with light: a compressively sampled photonic link.

We report the successful demonstration of a compressively sampled photonic link. The system takes advantage of recent theoretical developments in compressive sampling to enable signal recovery beyond the Nyquist limit of the digitizer. This rather remarkable result requires that (1) the signal being recovered has a sparse (low-dimensional) representation and (2) the digitized samples be incoherent with this representation. We describe an all-photonic system architecture that meets these requirements and then show that 1 GHz harmonic signals can be faithfully reconstructed even when digitizing at 500 MS/s, well below the Nyquist rate.

Bayesian estimation of weak material dispersion: theory and experiment.

This work considers the estimation of dispersion in materials via an interferometric technique. At its core, the problem involves extracting the quadratic variation in phase over a range of wavelengths based on measured optical intensity. The estimation problem becomes extremely difficult for weakly dispersive materials where the quadratic nonlinearity is very small relative to the uncertainty inherent in experiment. This work provides a means of estimating dispersion in the face of such uncertainty. Specifically, we use a Markov Chain Monte Carlo implementation of Bayesian analysis to provide both the dispersion estimate and the associated confidence interval. The interplay between various system parameters and the size of the resulting confidence interval is discussed. The approach is then applied to several different experimental samples.

Chaotic signal detection and estimation based on attractor sets: applications to secure communications.

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.

Characterization and modeling of drift noise in Fourier transform spectroscopy: implications for signal processing and detection limits.

A theoretical analysis of long-term drift noise in Fourier transform spectroscopy is presented. Theoretical predictions are confirmed by experiment. Fractional Brownian motion is employed as a stochastic process model for drift noise. A formulation of minimum detectable signal is given that properly accounts for drift noise. The spectral exponent of the low-frequency drift noise is calculated from experimental data. A frequency-dependent optimal spectrum averaging time is found to exist beyond which the minimum detectable signal increases indefinitely. It is also shown that the minimum detectable signal in an absorbance or transmission measurement degrades indefinitely with the time elapsed since background spectrum acquisition.

Measurement and origin of magnetostrictive noise limitation in magnetic fiber-optic sensors.

Fiber-optic magnetic sensors based on magnetostriction yield l/f-type noise, which has typically been limiting the sensors' resolution at frequencies below 1 Hz. To study the origin of this noise, we devised a new experimental technique that discriminates between the transducer self-noise and various other noise sources and determines under which conditions the limiting noise source is the material's self-noise.

Effects of parasitic Fabry-Perot cavities in fiber-optic interferometric sensors.

We show theoretical and experimental evidence for increased quadrature point fluctuations and amplitude and phase noise in interferometric fiber sensors owing to the presence of parasitic Fabry-Perot cavities. We demonstrate greater than 2 orders of magnitude reduction of such effects.

Thermal noise spectrum of a fiber-optic magnetostrictive transducer.

We report the observation of the thermal equilibrium strain fluctuation spectrum in a transducer using a fiber interferometer. The thermal noise power spectrum in the range of 20-30 kHz of the metallic glass cylinder in this experiment is determined by the dynamic elastic susceptibility and has peak value corresponding to approximately 0.8 microrad/ radicalHZ at 25.5 kHz. The data are analyzed by using the fluctuation-dissipation theorem and a coupled-mode model for dynamic response in metallic glass.