We propose and simulate integrated optical devices for accelerating numerical linear algebra (NLA) calculations. Data is modulated on chirped optical pulses and these propagate through a multimode waveguide where speckle provides the random projections needed for NLA dimensionality reduction.
Optical speckle in a multimode waveguide has been proposed to perform the function of a compressive sensing (CS) measurement matrix (MM) in a receiver for GHz-band radio frequency (RF) signals. Unlike other devices used for the CS MM, e.g. the digital micromirror device (DMD) used in the single pixel camera, the elements of the speckle MM are not known before use and must be measured and calibrated. In our system, the RF signal is modulated on a repetitively pulsed chirped wavelength laser source, generated from mode-locked laser pulses that have been dispersed in time or from an electrically addressed distributed Bragg reflector laser. Next, the optical beam with RF propagates through a multimode fiber or waveguide, which applies different weights in wavelength (or equivalently time) and space and performs the function of the CS MM. The output of the guide is directed to or imaged on a bank of photodiodes with integration time set to the pulse length of the chirp waveform. The output of each photodiode is digitized by an analog-to-digital converter (ADC), and the data from these ADCs are used to form the CS measurement vector. Accurate recovery of the RF signal from CS measurements depends critically on knowledge of the weights in the MM. Here we present results using a stable wavelength laser source to probe the guide.
We demonstrate that speckle patterns at the output of multimode optical waveguides can be used for a compressive sensing (CS) measurement matrix (MM) to measure sparse RF signals in the GHz band (1-100 GHz). In our system mode-locked femtosecond laser pulses are stretched to a width on the order of the interpulse time, modulated by the RF, and injected into a multimode waveguide. The speckle pattern out of the guide is imaged onto an array of photodiodes whose output is digitized by a bank of ADCs. We have measured the CS MM for multimode fibers and used these MMs to demonstrate that sparse RF signals (sparsity K) modulated on a chirped optical carrier can be recovered from M measurements (the number of photodiodes) consistent with the CS relation M ~ K log(N/K) (N is the number of samples needed for Nyquist rate sampling). We demonstrate experimentally that speckle sampling gives comparable results to the photonic WDM sampling system used previously for periodic undersampling (multi-coset sampling) of RF chirp pulses. We have also calculated MMs for both multimode fibers and planar waveguides using their respective mode solutions to determine optimal waveguide parameters for a CS system. Our results suggest a path to a CS system for GHz band RF signals that can be completely constructed using photonic integrated circuit (PIC) technology.
Direct digitization of long, wideband chirped RF signals in the GHz band requires power hungry ADCs and produces large data sets. Here we present an optical scheme to perform multi-coset sampling of such signals with reduced power consumption and smaller data sets. In our scheme a repetitively pulsed femtosecond laser is dispersed to the interpulse time, the RF is modulated on the optical field, and the field is directed to a pair of wavelength-division demultiplexers (WDM). The channels of the WDM are attenuated with a pseudo-random sequence to form a coset pattern that repeats at the laser repetition rate. After a photodiode, the photocurrent is integrated for the duration of the dispersed optical pulse so that the coset pattern non-uniformly samples the RF signal. Since the laser repetition rate is uncorrelated with the RF, each coset provides an independent measurement of the RF. Experimental and numerical results show that 4 properties of the RF chirp pulse can be determined from the multiple coset samples: carrier frequency, chirp rate, start time, and pulse duration. Results are presented for a 20MHz chirp on a 13 microsecond pulse at a carrier of 2.473 GHz.
At the National Ignition Facility (NIF), home of the world’s largest laser, a critical pulse screening process is used to ensure safe operating conditions for amplifiers and target optics. To achieve this, high speed recording instrumentation up to 34 GHz measures pulse shape characteristics throughout a facility the size of three football fields—which can be a time consuming procedure. As NIF transitions to higher power handling and increased wavelength flexibility, this lengthy and extensive process will need to be performed far more frequently. We have developed an accelerated highthroughput pulse screener that can identify nonconforming pulses across 48 locations using a single, real-time 34-GHz oscilloscope. Energetic pulse shapes from anywhere in the facility are imprinted onto telecom wavelengths, multiplexed, and transported over fiber without distortion. The critical pulse-screening process at high-energy laser facilities can be reduced from several hours just seconds—allowing greater operational efficiency, agility to system modifications, higher power handling, and reduced costs. Typically, the sampling noise from the oscilloscope places a limit on the achievable signal-to-noise ratio of the measurement, particularly when highly shaped and/or short duration pulses are required by target physicists. We have developed a sophisticated signal processing algorithm for this application that is based on orthogonal matching pursuit (OMP). This algorithm, developed for recovering signals in a compressive sensing system, enables high fidelity single shot screening even for low signal-to-noise ratio measurements.
The optical wideband converter (OWC) is a system for measuring properties of RF signals in the GHz band without use
of high speed electronics. In the OWC the RF signal is modulated on a repetitively pulsed optical field with a large
wavelength chirp, the optical field is diffracted onto a spatial light modulator (SLM) whose pixels are modulated with a
pseudo-random bit sequences (PRBSs), and finally the optical field is directed to a photodiode and the resulting current
integrated for each PRBS. When the number of PRBSs and measurements equals the number of SLM pixels, the RF
signal can be obtained in principle by multiplying the measurement vector by the inverse of the square matrix given by the PRBSs and the properties of the optics. When the number of measurements is smaller than the number of pixels, a compressive sensing (CS) measurement can be performed, and sparse RF signals can be obtained using one of the standard CS recovery algorithms such as the penalized l1 norm (also known as basis pursuit) or one of the variants of matching pursuit. Accurate reconstruction of RF signals requires good calibration of the OWC. In this paper, we present results using the OWC for RF signals consisting of 2 sinusoids recovered using 3 techniques (matrix inversion, basis pursuit, and matching pursuit). We compare results obtained with orthogonal matching pursuit with nonlinear least squares to basis pursuit with an over-complete dictionary.
We simulate an optical time-domain mixer that can be used to make a photonic analog-to-digital converter
(ADC) or a digital demodulator for high-speed optical communications signals. In the basic mixer, a high
frequency RF signal modulates a repetitively chirped optical carrier; this RF/optical waveform then is dispersed
in one transverse dimension, and imaged onto a 2-dimensional transparency or spatial light modulator whose
pixels are modulated with randomly chosen transmission or reflection coefficients (the optical mixing matrix).
Following transmission through or reflection from the mixing matrix, the optical waveform from each row of the
matrix is recombined and directed to a photodiode and electronics that integrate over the repetition period of the
chirped source. Finally, each of these signals is digitized by an independent ADC sampling at a rate equal to the
pulse repetition rate of the chirp source. A digital replica of the input RF signal can be recovered by digital
signal processing from the digital output of the ADCs and the values of the transmission or reflection
coefficients of the mixing matrix. The effective sampling rate is given by the number of pixels per row of the
mixing matrix times the repetition rate of the chirp source while the effective resolution is controlled by the
resolution of the electronic ADCs and the distortions introduced by the optical mixing process.
This paper documents the fundamental and practical limits on the performance of the demultiplexing class of photonic analog-to-digital converters (ADCs). First, we review the classes of photonic ADCs that have been investigated to date. Then the reported performance of several demultiplexing photonic ADCs is compared to performance recently obtained with high rate, high resolution electronic ADCs. Next, the paper derives the fundamental limits on ADC performance that are determined by amplitude noise, timing jitter and the finite width of the optical sampling pulse. Finally, we review practical limits for the demultiplexing ADC. These practical limits are generally determined by the performance of the electronic-to-optical and optical-to-electronic interfaces, the optical modulator and the photodetector, and by the requirements on component/path matching.
We have used a physically realistic model to investigate the
spatial and temporal behavior of reverse saturable absorption
and optical limiting in organometallic cluster compounds. An
algorithm was developed to solve numerically the model and is
used for the case of a collimated beam to determine various
material parameters by fitting theory to experimental optical
limiting data. Using these parameters, the algorithm was then
extended to the case of converging and/or diverging beams.