A new method of solution of the problem of difference frequency generation in a periodic medium with an arbitrary profile of modulation of optical parameters is proposed. It is shown that the amplitude of the wave at the difference frequency may be either a periodic or an exponentially increasing function of the sample length. The conditions making possible an increase of the amplitude of the wave at the difference frequency (quasi-phase matching) are found. Using a medium on the basis of AlGaAs as an example, it is shown that the periodicity of a material can provide a high efficiency of difference frequency generation.
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