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Applied Optics

Coherent transient optical signal processing without brief pulses

K.D. Merkel, William Randall Babbitt

Published Jan 10, 1996• 7 citations
Publisher

Abstract

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.

DOI
10.1364/ao.35.000278

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 1, 1991•2 citations
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.
A technique is proposed and experimentally demonstrated that achieves simultaneous optical pattern waveform storage and programmable time delay for continuous real-time signal processing by use of optical coherent transient technology. We achieve variable-time-delay and broadband signal processing by frequency shifting of two chirped programming pulses, the chirp rate of one being twice that of the other, without using brief reference pulses and without changing the timing of the programming sequence. We demonstrate the technique experimentally in Tm(3+): YAG at 5 K for 40-MHz chirps by performing temporal signal convolution with true-time delays that vary over a 250-ns range.
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.
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.
This final report of contract F49620-91-C-0088 describes the development of the analytical tools required to evaluate optical coherent transient memory, triple-product correlator, and continuous signal processor systems. One key tool is a coherent transient simulator based on the optical Bloch equations. The coherent transient output signal that results from an arbitrary sequence of pulses, each having an arbitrary amplitude, duration, center frequency, chirp, phase, and timing can be calculated. The simulator was used to study excitation pulse saturation and it effects on the output signal efficiency and fidelity and to study frequency chirped reference pulse saturation. Analytical tools were developed to assess the effects of local heating and spatial crosstalk. A performance evaluation of a coherent transient continuous optical correlator is reported, along with new implementation techniques. The continuous processor's predicted time-bandwidth product, data bandwidth, and pattern storage density are 10000, 5 GHz, and 100000 patterns per square centimeter, respectively. A proof of concept demonstration of the continuous optical processor was performed in europium doped yttrium silicate in collaboration with IBM Almaden Research Center. Research into divalent ion doped crystals as photon gated materials for coherent transient systems was performed.
Using multiple temporally-overlapped, frequency offset and phase-tuned, linear frequency chirps, a new method of multi-GHz optical coherent transient optical pulse shaping and processing in inhomogeneously broadened rare-earth doped crystals is proposed. Using this technique with properly chirped laser sources, multi-GHz processing can be controlled with conventional low-bandwidth electronics and optical modulators. Specifically, this technique enables pulse shaping in the MHz to THz frequency regime with time-bandwidth-products exceeding 100,000, filling the gap between the operating regimes of femtosecond pulse shaping and analog electronics. The low bandwidth (~20 MHz) proof-of-concept demonstrations presented in this paper include pulse train creation, selfconvolution, auto-correlation, and chirped pulse compression.
A theory is developed to describe the optical transient signals that arise when a sample of two-level atoms is irradiated by a sequence of two or 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. These pulses whose temporal width is much greater than the delay time are fully correlated with one another and can be strong enough to saturate the two-level atomic transition. In the case of three-pulse transients the third pulse is weak non-correlated with the first two and is delayed in time so that it does not overlap them. Taking into account the effects ofinhomogeneous and homogeneous broadening we calculate the intensity of the transient signals as a function of delay time. The signals are found to depend dramatically on the intensities of the excitation pulses. It is shown that for strong excitation pulses a direct dependence of the signal on the cross-correlation time of the pulses r occurs that does not exist when the pulses are weak. In particular for saturating pulses the signals exhibit a peak of width of order r . In the case of the two-pulse transient the peak is found to disappear when the Doppler width of the atomic ensemble becomes sufficiently large. This peak can have a very narrow dip near its maximum whose width is much