It is proposed that the process of nonlinear optical phase conjugation can be utilized to compensate for channel dispersion and hence to correct for temporal pulse broadening. Specifically, a four-wave nonlinear interaction is shown to achieve pulse renarrowing. Spectral bandwidth phase-conjugate interaction parameters.Recent theoretically and experimental" 5 ' 7 -l 0 studies indicate that the generation of phase-conjugate replicas of incident optical waves has certain formal aspects of time reversal and that this property can be used to correct for spatial-propagation distortion. In addition, chirp compensation using four-wave mixing has been analyzed." In this Letter we explore theoretically what happens following conjugation to a short electromagnetic pulse that has traversed a dispersive channel. We find, reassuringly, that the group delay of the pulses is not time reversed, i.e., pulses retain their relative temporal order. The effect of group velocity dispersion, dvg/dw, however, is time reversed to first order. This implies that pulses broadened in propagation can be renarrowed following conjugation by merely propagating through a second channel. We remark here that the notion of equalization or estimation and chirp techniques as applied to phase compensation due to pulse propagation is a well-known concept in data communication systems and in radar applications.1 2 The application of nonlinear optical techniques with respect to this problem has not, to our knowledge, been analyzed and is the topic of this Letter.The model analyzed is shown in Fig. 1. An input pulse,is incident on a dispersive channel. wo is the optical carrier frequency; the pulse envelope is g(t). The Fourier transform of g(t) is F(Q)so thatSince the width of g(t) is very large compared with the optical period 2,r/wo, it follows that Q << wo over the region where F(Q) is appreciable. where fOo -(wo). The term (aol/do)Ll can be written as Ll/vg, where vg = wl/aO is the group velocity. The term a 2 l/dcW 2 , which can be written as [- (I/vg 2 ) (dOgi do)], is the group velocity dispersion term and causes f 2 (t) to be broader than fI(t) when f,(t) is a transform-limited pulse.The pulse f 2 (t) undergoes phase conjugation-the result being the pulse f 3 (t). To be specific, we will assume that the phase conjugation is achieved by fourwave mixing in a nondispersive medium with two (essentially cw) pump waves, Al and A 2 , at wo. We further assume that the response time of the nonlinear interaction is faster than the pulse duration. This causes a Fourier component at wo + Q to be reflected' 3 at a frequency wo -Q, so that the sum 2wo of the pump frequencies is equal to the sum of the incident and reflected frequencies. In general, an incident Fourier

We have realized a (GaAs1−xSbx-InyGa 1−yAs)/GaAs bilayer-quantum well (BQW), which consists of two adjacent pseudomorphic layers of GaAs1−xSbx and InyGa1−yAs sandwiched between GaAs barriers. Photoluminescence was observed at longer wavelengths than those found for corresponding InyGa1−yAs/GaAs and GaAs1−xSbx/GaAs single quantum wells (SQW), which indicates a type-II band alignment in the BQW. The longest 300 K emission wavelength achieved so far was 1.332 μm. For an accurate determination of the band offset between GaAs1−xSbx and GaAs, required for a theoretical modeling of the interband transition energies of these BQWs, a large set of GaAs1−xSbx /GaAs SQWs was prepared from which a type-II band alignment was deduced, with the valence band discontinuity ratio Qv found to depend on the Sb concentration x (Qv=1.76+1.34 x). With this parameter it was possible to calculate the expected interband transition energies in a BQW structure without any adjustable parameters. The calculations are in agreement with experimental data within a range of ±4%.

A nonlinear optical technique is described that performs, essentially instantaneously, the functions of spatial correlation and convolution of spatially encoded waves. These real-time operations are accomplished by mixing spatially dependent optical fields in the Fourier-transform plane of a lens system. The use of a degenerate four-wave mixing scheme eliminates (in the Fresnel approximation) phase-matching restrictions and (optical) frequency-scaling factors. Spatial bandwidth-gain considerations and numerical examples, as well as applications to nonlinear microscopy, are presented.In recent years, coherent and incoherent image processing has been demonstrated in a variety of applications, including pattern recognition, guidance systems, and other data-processing techniques. Present methods used to generate convolution and correlation operations of spatially encoded optical images include digital processing and Van der Lugt-type holograms. 1 ' 2 It has been proposed by one of the authors (A. Yariv) that nonlinear optical techniques can be used to perform real-time holographic functions.3 ' 4 The specific application of nonlinear three-wave mixing to perform the operation of convolution and correlation has been proposed by Eremeeva et al. 5 The proposed scheme was demonstrated in the case of simple (luminous spot) images. These schemes, as well as that proposed inRefs. 3 and 4, suffered from restrictions on the spatial bandwidth of the information, which were due to the need for phase matching. Second, the use of multiple wavelengths introduces spatial scaling that may be objectionable.In the analysis that follows we propose the use of four-wave mixing for real-time correlation and convolution operations. The process of four-wave mixing, which has recently been applied to the problem of "time-reversed" propagation, 7 is shown to be free of the phase-matching problem and to require a single frequency. Consider the nature of the field produced as a result of the simultaneous mixing of three optical fields, all of radian frequency co, incident upon a thin medium possessing a third-order nonlinear optical susceptibility, XNL 3 ), centered at the common focal plane of two identical lenses (or mirrors) of focal length f. The geometry is illustrated in Fig. 1. Each field is specified spatially at the front focal plane of its respective lens with the following amplitudes:where After propagating through lens LI, A 1 has the following form (in the Fresnel approximation),where 7ja} = & is the Fourier transform of a, andis the transmission function of a thin lens. 2 The argu- Fig. 1. Convolution/correlation geometry. All input optical fields are at frequency a. BS is a beam splitter necessary to view the desired output, E 3 , which is evaluated at a plane located a distance f from the lens L 1 .0146-9592/78/O700-0007$0.50/O

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