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Annual Meeting Optical Society of America

Dynamics of refractive-index grating formation in a Kerr medium

Ragini Saxena, Pochi Yeh

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Light-induced change in the index of refraction of a Kerr medium is well known.1 Illumination with a spatially periodic light intensity leads to the formation of an index grating in the Kerr medium. We make a comparative study of the response time and power requirement for index grating formation in photorefractive and Kerr media. We examine the conditions in which the index grating in the Kerr medium will be spatially shifted from the light intensity that induces it. Two-beam coupling via Bragg diffraction from the nonlocal index grating is studied.2 The coupling constant is found to depend on the relaxation mechanism of the atoms in the Kerr media and the frequency detunings of the two beams from the line center.

DOI
10.1364/oam.1988.thc3

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Light-induced change in the index of refraction of a Kerr medium is well known.1 Illumination with a spatially periodic light intensity leads to the formation of an index grating in the Kerr medium. We make a comparative study of the response time and power requirement for index grating formation in photorefractive and Kerr media. We examine the conditions in which the index grating in the Kerr medium will be spatially shifted from the light intensity that induces it. Two-beam coupling via Bragg diffraction from the nonlocal index grating is studied.2 The coupling constant is found to depend on the relaxation mechanism of the atoms in the Kerr media and the frequency detunings of the two beams from the line center.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
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.
A review is given of the present state of theoretical and experimental work on the interaction of two coherent light beams of equal frequency in a nonlinear medium. It is shown that dynamic self-diffraction is substantially different for media with different types of response. Stationary energy transfer between interacting beams is possible in the case of nonlocal nonsymmetric response, whereas this type of transfer is forbidden in the case of local response. Different mechanisms for self-induced changes in the refractive index are examined together with the corresponding processes of energy transfer between the writing beams. The more important applications of dynamic self-diffraction are discussed.
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.
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].
We demonstrate a scheme for coherently induced grating based on a mixture of two three-level atomic species interacting with two standing-wave fields. As a result of interaction between the absorptive and amplified Raman resonances, the refractive index of the medium can be enhanced and modulated periodically. Then a sinusoidal grating, which can diffract the probe field into high-order directions, is coherently formed in the medium. The proposed scheme is theoretically investigated in a mixture of atomic isotopes of rubidium. The results show that the diffraction efficiency depends strongly on the two two-photon detunings of the two Raman transitions and the intensities of the two driving standing-wave fields. The proposed electromagnetically induced grating scheme may be applied to the all-optical switching and beam splitting in optical networking and communication.