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Applied Optics

Mixed binary multiplication of optical signals by convolution in an inhomogeneously broadened absorber

William Randall Babbitt, THOMAS W. MOSSBERG

Published Mar 15, 1986• 18 citations
Publisher

Abstract

We have employed the recently developed technique of real-time optical waveform convolution in inhomogeneously broadened absorbers [ Appl. Phys. Lett.45, 714 ( 1984)] to perform mixed binary multiplication of digital optical signals. We demonstrate that an output signal representing the mixed binary product of up to three numbers encoded into discrete input signals can be generated in a single convolution cycle. We have studied the effect of material relaxation on output signal shapes and intensities. We find that mixed binary product signals up to ∼0.5% as intense as the input signals can be expected in weakly relaxing materials. This method of all-optical multiplication may be useful in high-speed applications, since its bit rate is limited fundamentally only by the inhomogeneous absorption bandwidth of the material used.

DOI
10.1364/ao.25.000962

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We have employed the recently developed technique of real-time optical waveform convolution in inhomogeneously broadened absorbers [ Appl. Phys. Lett.45, 714 ( 1984)] to perform mixed binary multiplication of digital optical signals. We demonstrate that an output signal representing the mixed binary product of up to three numbers encoded into discrete input signals can be generated in a single convolution cycle. We have studied the effect of material relaxation on output signal shapes and intensities. We find that mixed binary product signals up to ∼0.5% as intense as the input signals can be expected in weakly relaxing materials. This method of all-optical multiplication may be useful in high-speed applications, since its bit rate is limited fundamentally only by the inhomogeneous absorption bandwidth of the material used.
We discuss the light signals that are coherently emitted by some optical absorbers sub-sequent to excitation by a series of three laser excitation pulses. In some cases, the light signal emitted by the material duplicates the temporal shape of one of the laser in-put pulses. In other cases, the emitted signal represents the convolution or cross-correlation of two of the laser input pulses. In principle, digitally encoded signals of multi-gigahertz bandwidth can be convolved in real time, or, in suitable materials, stored for long periods. Output signals on the order of a few percent as intense as the inputs are possible. We provide experimental demonstrations of these effects, and discuss their implementation in optical signal processing and data storage systems.
When a sequence of temporally modulated optical waveforms illuminate an inhomogeneously broadened absorbing medium, the resultant optical coherent transient output signal's represents the cross-correlation or convolution of the input temporal waveforms.1 The projected performance characteristics of coherent transient processors include data rates greater than 10 GHz, time-bandwidth products far in excess of 10,000, and the ability to fully process both amplitude and phase modulated waveforms.1,2 Previously it was assumed that the input data stream and pattern stream must both be shorter than the absorbing transition's homogeneous dephasing time and must both be reentered in order to process longer or multiple data streams.1 It has recently been proposed that patterns could be permanently stored in an inhomogeneously broadened solid and that input data streams of indefinite length could be continuously processed in real time without the need to reenter the input pattern.3,4 In this paper, we present a proof of concept demonstration of an optical coherent transient continuous correlator.
The phase conjugation property of backward-stimulated photon echo (BSE) has numerous potential applications in optical data storage and processing. We demonstrate mixed binary multiplication of spatially encoded bit patterns, by taking advantage of the fact that the geometry of BSE is analogous to that of conventional holography or four-wave mixing of nonlinear optics, where an object (data) and a reference (write) beams interfere to create a grating inside the medium, and another reference (read) beam is diffracted from that grating. When all three input beams contain structures, the output pattern is the convolution and correlation of the input patterns, which, with certain arrangements and interpretation, can be used for multiplication of binary numbers. The experiments were done by using a 477.8 nm transition of praseodymium ion-doped in single-crystal lanthanum trifluoride.
After the absorption profile of an inhomogeneously broadened solid is programmed by two temporally modulated pulses (at least one encoded with a pattern), it can be gated to fix the ground-state spectral population distribution permanently. The subsequent illumination of the solid by an uninterrupted, temporally modulated optical beam results in a coherent transient output signal that represents the correlation of the signal with the stored pattern. Multiple patterns can be stored at different locations on the sample and accessed randomly, enabling fast reprogramming of the processor. A performance analysis of this optical signal processor predicts that real-time continuous processing is possible with a processor bandwidth that exceeds 5 GHz, a time-bandwidth product that exceeds 10(4), and a pattern storage density that exceeds 10(5) patterns per square centimeter.
We demonstrate mixed binary multiplication of two or three numbers represented as spatial bit patterns by using a backward stimulated photon echo in a low-temperature solid activated by rare-earth ions. The photon-echo output image is the convolution-correlation of input images in a holographic arrangement, which can be interpreted as multiplication in a mixed binary format. The computation is extremely fast (~ 50 ns) and may be combined with temporal data processing for a versatile vector and matrix processor.
As a high-intensity monochromatic light pulse passes through a material containing two-level systems, saturable absorption or amplification of the radiation may occur. The resultant ``shaping'' of the intensity-vs-time curve as a function of distance into the sample is the subject of this paper. A theory is developed based on the Einstein rate equations, and pulse-shape functions are derived which depend on the absorption and loss coefficients of the material, the relaxation time of the systems, the input-pulse intensity and width, the initial ``state-of-pump'', and number density of absorbers in the sample.