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IEEE Journal of Quantum Electronics

Basic considerations of four-wave mixing and dynamic gratings

Y. Ron Shen

Published Aug 1, 1986• 34 citations
Publisher

Abstract

The basic principles of four-wave mixing are reviewed. Emphasis is on the coupling between light waves and material excitational waves. Only cases where material excitations are excited by optical mixing of input waves are considered. The material excitations appear in the form of a dynamic grating that would coherently scatter the incoming radiation. Probing of the dynamic grating allows the deduction of information about the material excitations.

DOI
10.1109/jqe.1986.1073131

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The basic principles of four-wave mixing are reviewed. Emphasis is on the coupling between light waves and material excitational waves. Only cases where material excitations are excited by optical mixing of input waves are considered. The material excitations appear in the form of a dynamic grating that would coherently scatter the incoming radiation. Probing of the dynamic grating allows the deduction of information about the material excitations.
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Recording of localized transmission gratings by four-wave mixing in non-local photorefractive media with strong response is considered. The input conditions to record dynamic gratings with a stable grating amplitude distribution as well as grating amplitude oscillations are defined. They are determined both by intensities and by a phase difference of input waves. The influence of fluctuations of wave phases on stability of the recorded gratings is considered. Methods of optical control of both the grating amplitude localization degree and the grating amplitude location are defined.
We explore dynamic media, such as plasmas and photorefractive materials, as generators of phase conjugated replicas of transient optical signals via four-wave mixing. The characterizing element of dynamic media is a population of free charge carriers that leads to induced charge density gratings on probe illumination. In steady-state conditions, phase conjugation in such media normally appears with smaller pump intensities than are required in Kerr media but at the expense of potentially slow response times.1
The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].