Optical finite impulse response neural networks

Holographic method of cohering fiber tapped delay lines

We propose, analyze, and demonstrate the use of a holographic method for cohering the output of a fiber tapped delay line (FTDL) that enables the use of fiber-remote optical modulators in coherent optical processing systems. We perform a theoretical examination of the phase-cohering process and show experimental results for a radio frequency (RF) spectrum analyzer that uses a lens to spatially Fourier transform the output of a holographically phase-cohered FTDL providing 50 MHz resolution and bandwidths approaching 3 GHz. Substantial improvements in bandwidth should be achievable with better fiber length-trimming accuracy and improvements in resolution can be obtained with longer fiber delay lines. We also analyze and demonstrate the use of a parallel holographic technique that compensates for polarization state scrambling induced by propagation through an array of single-mode fibers. Both the phase-cohering holography and the polarization fluctuation compensation can operate on hundreds of fibers in parallel, enabling both coherent optical signal processing with FTDLs and coherent fiber remoting of optically modulated RF signals from antenna arrays.

Frequency-multiplexed logic circuit based on a coherent optical neural network

We propose an adaptive logic circuit whose function can be controlled by optical carrier frequency modulation. The circuit learns the desired functions by adjusting the delay time at a spatial light modulator with a complex-valued Hebbian learning rule. After the learning, the circuit can switch its function all at once. A high degree of mechanical stability is achieved by spatial phase-difference coding. Two orthogonal phase components are detected in parallel spatially. Experiments demonstrate that the system works as an AND circuit at a certain frequency and as an XOR at another. The proposal will enhance the design of optical plastic cell architectures.

Optoelectronic implementation of a 256-channel sonar adaptive-array processor

We present an optoelectronic implementation of an adaptive-array processor that is capable of performing beam forming and jammer nulling in signals of wide fractional bandwidth that are detected by an array of arbitrary topology. The optical system makes use of a two-dimensional scrolling spatial light modulator to represent an array of input signals in 256 tapped delay lines, two acousto-optic modulators for modulating the feedback error signal, and a photorefractive crystal for representing the adaptive weights as holographic gratings. Gradient-descent learning is used to dynamically adapt the holographic weights to optimally form multiple beams and to null out multiple interference sources, either in the near field or in the far field. Space-integration followed by differential heterodyne detection is used for generating the system's output. The processor is analyzed to show the effects of exponential weight decay on the optimum solution and on the convergence conditions. Several experimental results are presented that validate the system's capacity for broadband beam forming and jammer nulling for linear and circular arrays.

Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor

We present a spatio-temporal operator formalism and beam propagation simulations that describe the broadband efficient adaptive method for a true-time-delay array processing (BEAMTAP) algorithm for an optical beamformer by use of a photorefractive crystal. The optical system consists of a tapped-delay line implemented with an acoustooptic Bragg cell, an accumulating scrolling time-delay detector achieved with a traveling-fringes detector, and a photorefractive crystal to store the adaptive spatio-temporal weights as volume holographic gratings. In this analysis, linear shift-invariant integral operators are used to describe the propagation, interference, grating accumulation, and volume holographic diffraction of the spatio-temporally modulated optical fields in the system to compute the adaptive array processing operation. In addition, it is shown that the random fluctuation in time and phase delays of the optically modulated and transmitted array signals produced by fiber perturbations (temperature fluctuations, vibrations, or bending) are dynamically compensated for through the process of holographic wavefront reconstruction as a byproduct of the adaptive beam-forming and jammer-excision operation. The complexity of the cascaded spatial-temporal integrals describing the holographic formation, and subsequent readout processes, is shown to collapse to a simple imaging condition through standard operator manipulation. We also present spatio-temporal beam propagation simulation results as an illustrative demonstration of our analysis and the operation of a BEAMTAP beamformer.