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The fast development of laser technique opened up new possibilities for optical computing and optical communication. In fact, present-day lasers are capable of generating pulses of femtosecond duration. It is obvious that such short pulses can only be effectively controlled by pulses of the same short duration. This performance range lies beyond the abilities of present-day microelectronics; it also exceeds the abilities of optical information processing based on conventional dynamic holograms, which operate on the principle of the modulation of the refractive index of a light-sensitive material. A promising new approach to this problem presents a method of cross-correlation of two optical wavefields based on the principle of the modulation of the polarization of a nonlinear material. This process is much faster than the process of changing the refractive index of the medium. In fact, this method permits one to transform light wavefields at the moment when they intersect each other. The cross-correlation operation of two wavefields can be performed using either up-conversion when the frequency of the resulting wavefield is doubled, or down-conversion when the frequency of the resulting wavefield decreases. In fact, the cross-correlation method of wavefields shares many properties with the holographic method. Because of this similarity, we refer to the method considered as “second-harmonic generated hologram” (SHG hologram). Using this similarity, we have proven theoretically and experimentally that the SHG hologram generates 3D holographic images of an object. These images are characterized by diffraction-limited resolution. The regularities that determine the position and scale of reconstructed images have been deduced and checked in experiments. For the case when down-conversion is used, the regularities of the holographic image formation are different from those that are valid for the SHG hologram, but the way of their deducing is the same as in the case of the SHG hologram. From the point of view of practical applications, the most important property of the SHG hologram is its ability to perform the mutual transformation of wavefronts of light using the principle “light is controlled by light.” In principle, this property opens up the way for the creation of completely optical computing. One example of this kind of operation presents the switching of light communication lines.4 The switching in this case can be performed with almost no time delay. Another possible application of the method considered is the implementation of superfast logical elements for optical computing. The main drawback of the systems considered is the fact that each operation of wavefront transformation is followed by the doubling of the light frequency. The situation can be improved and the signal wave can be returned to its initial frequency by using the effect of down-conversion.
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