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Nonlinear Optical Properties of Materials

Two-Wave Mixing in Saturable Absorbers and Ranging Applications

S.A. Boothroyd, Jacek Chrostowski, M.S. O'Sullivan

Published Jan 1, 1988• 0 citations
Publisher

Abstract

When two coherent light beams overlap in a saturable absorber, the materials refractive index is altered in phase with the light intensity distribution and a volume phase and/or absorption grating is created. A frequency shift introduced on one of the beams causes the fringe pattern to move. In materials with a finite response time, τ, a phase lag between the grating and the intensity pattern is produced and exchange of energy between the beams can occur.

DOI
10.1364/nlopm.1988.mf4

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When two coherent light beams overlap in a saturable absorber, the materials refractive index is altered in phase with the light intensity distribution and a volume phase and/or absorption grating is created. A frequency shift introduced on one of the beams causes the fringe pattern to move. In materials with a finite response time, τ, a phase lag between the grating and the intensity pattern is produced and exchange of energy between the beams can occur.
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].
According to the theory of two-beam coupling in a thick Kerr medium, which is based on the firstorder coupled-wave method,1 the energy exchange between the two incident beams is forbidden because the phase shift between the intensity grating and refractive-index grating is zero in the Kerr media. The energy exchange must be achieved by artificially creating a phase shift, e.g., by moving the intensity grating with respect to the medium at a speed of the order of one fringe per response time of the medium.
Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.
We have studied two-wave mixing in resonant media. Illumination with two beams of the same frequency leads to the formation of a spatially local volume grating with no exchange of energy between the writing beams, each beam merely reducing the absorption experienced by the other beam. Nondegenerate two-wave mixing leads to gain for one beam and additional absorption for the other beam as they propagate through the medium. Starting from first principles, the explicit forms of the two-beam coupling constants are derived using third-order perturbation theory, and their dependence on material and experimental factors is examined.
Two-wave mixing allows one to change effectively Intensities, phases, space profiles, polarizations and time evolution of interacting beams [1,21. We will show, that two-wave mixing of partially coherent beams may be used to increase degree of coherence of these beams. The physics of the effect under discussion is as follows: two partially coherent beams write a refraction index grating in a nonlinear medium whose position and profile are practically stationary. Scattering of strong beam on this grating in the direction of the weak one means that this weak beam acquires an addition, that is coherent with the strong beam, thereby increasing degree of coherence of the beams. Similar effects were discussed in connection with scattering of different frequency components at the common running grating [3] and with Interaction of different polarization components [4,5].