Classification of time-domain waveforms using a speckle-based optical reservoir computer.

Reservoir computing is a recurrent machine learning framework that expands the dimensionality of a problem by mapping an input signal into a higher-dimension reservoir space that can capture and predict features of complex, non-linear temporal dynamics. Here, we report on a bulk electro-optical demonstration of a reservoir computer using speckles generated by propagating a laser beam modulated with a spatial light modulator through a multimode waveguide. We demonstrate that the hardware can successfully perform a multivariate audio classification task performed using the Japanese vowel speakers public data set. We perform full wave optical calculations of this architecture implemented in a chip-scale platform using an SiO2 waveguide and demonstrate that it performs as well as a fully numerical implementation of reservoir computing. As all the optical components used in the experiment can be fabricated using a commercial photonic integrated circuit foundry, our result demonstrates a framework for building a scalable, chip-scale, reservoir computer capable of performing optical signal processing.

Demonstration of speckle-based compressive sensing system for recovering RF signals.

We demonstrate measurement of RF signals in the 2-19 GHz band using a photonic compressive sensing (CS) receiver. The RF is modulated onto chirped optical pulses that then propagate through a multimode fiber that produces the random projections needed for CS via optical speckle. Our system makes 16 independent measurements per optical pulse and we demonstrate several calibration techniques to obtain the CS measurement matrix from these measurements. Then a standard penalized l1 norm method recovers amplitude, phase, and frequency of single-tone and two-tone RF signals with about 100 MHz resolution in a single 4.5 ns pulse. A novel subspace method recovers the frequency to about 20 kHz resolution over 100 pulses in a 2.8 microsecond time window. These experiments use discrete fiber-coupled optical components, but all necessary functions can be realized in photonic and electronic integrated circuits.

Compressive sensing of sparse radio frequency signals using optical mixing.

We demonstrate an optical mixing system for measuring properties of sparse radio frequency (RF) signals using compressive sensing (CS). Two types of sparse RF signals are investigated: (1) a signal that consists of a few 0.4 ns pulses in a 26.8 ns window and (2) a signal that consists of a few sinusoids at different frequencies. The RF is modulated onto the intensity of a repetitively pulsed, wavelength-chirped optical field, and time-wavelength-space mapping is used to map the optical field onto a 118-pixel, one-dimensional spatial light modulator (SLM). The SLM pixels are programmed with a pseudo-random bit sequence (PRBS) to form one row of the CS measurement matrix, and the optical throughput is integrated with a photodiode to obtain one value of the CS measurement vector. Then the PRBS is changed to form the second row of the mixing matrix and a second value of the measurement vector is obtained. This process is performed 118 times so that we can vary the dimensions of the CS measurement matrix from 1×118 to 118×118 (square). We use the penalized ℓ(1) norm method with stopping parameter λ (also called basis pursuit denoising) to recover pulsed or sinusoidal RF signals as a function of the small dimension of the measurement matrix and stopping parameter. For a square matrix, we also find that penalized ℓ(1) norm recovery performs better than conventional recovery using matrix inversion.