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Applied Physics Letters

Real-time optical waveform convolver/cross correlator

Yu Bai, William Randall Babbitt, N. W. Carlson, THOMAS W. MOSSBERG

Published Oct 1, 1984• 93 citations
Publisher

Abstract

We show that an inhomogeneously broadened sample, excited by a series of three resonant optical pulses, emits an optical signal whose electric field envelope closely approximates the convolution or cross correlation of the field envelopes belonging to two of the three excitation pulses. The convolution (cross correlation) function is obtained when the first (second) pulse in the excitation sequence is short compared to the temporal structure of the other two excitation pulses.

DOI
10.1063/1.95391

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We show that an inhomogeneously broadened sample, excited by a series of three resonant optical pulses, emits an optical signal whose electric field envelope closely approximates the convolution or cross correlation of the field envelopes belonging to two of the three excitation pulses. The convolution (cross correlation) function is obtained when the first (second) pulse in the excitation sequence is short compared to the temporal structure of the other two excitation pulses.
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 temporal processing operations of convolution and correlation are demonstrated through optical coherent transient techniques, in which two long, low-intensity frequency-chirped pulses replace the single, brief reference pulse of a traditional three-pulse excitation sequence (brief pulse, pattern pulse, and data pulse). Here, a four-pulse excitation sequence is used (two frequency-chirped pulses, pattern pulse, and data pulse) in which the particular order and timing of the chirped pulses with respect to the other waveforms determine the processing operation. An experiment is performed with biphase-coded pattern and data pulses to demonstrate both the correlation and the convolution operations. A new atomic rephasing process that we call delayed rephasing is demonstrated.
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 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.
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.