Influence of an external electric field on self-focusing of light beams in cubic photorefractive crystals

Abstract

535.012.22Self-focusing of an optical paraxial beam in a photorefractive cubic crystal exposed to a strong external electric field E 0 of arbitrary orientation has been considered with regard to the Pockels effect. The best localization of radiation is shown to be attained when the vector E 0 is oriented along diagonals of the cubic cell. Numerical modeling revealed that the beam width increased significantly for non-optimal electric field orientations.Introduction. Self-focusing of optical beams in photorefractive crystals has been well studied experimentally and theoretically [1][2][3][4][5][6][7][8]. Thus, the dielectric permeability tensor was expanded into a Taylor series [9] around an external electric field. The linear term corresponded to the Pockels effect; the quadratic, to the Kerr effect. These effects make the formation of solitons dependent on the orientation of the external electric field E 0 and the wave normal n. A cubic crystal becomes biaxial under the influence of a strong field. If the direction of vector E 0 is changed, both induced optical axes change their orientation over broad limits. The dynamics of the optical axes and refractive indices of a perturbed cubic crystal with various orientations of the external field E 0 and wave normal have been investigated [10].Applications require light radiation to be localized in small areas. The localization of a beam can be improved by selecting the direction of the wave normal and the external electric field. Vectors E 0 and n in theoretical studies [2][3][4] were directed along the crystallographic axes. The properties of screened solitons with the external field E 0 oriented in certain fixed planes have also been studied [5, 6]. Self-focusing with E 0 oriented in the (1 1 2 _ ) plane was examined theoretically [5]. It has been reported that the electric field vector belongs to the (1 _ 1 _ 0) plane [6]. It was shown [5, 6] that the best conditions for self-focusing of a light beam are attained for E 0 directed along [111] and for the beam polarized parallel to this direction. The same orientation of the vectors is frequently selected for experimental studies of self-focusing in cubic photorefractive crystals [7,8].Herein we determine the optimum orientations of the vectors of the external electric field, wave normal, and polarization. All possible orientations of E 0 in space are examined. This vector is not required to reside in any fixed plane.The properties of the solitons depend on the direction because of the anisotropy of the linear and nonlinear responses of the crystal that are described by tensors of different ranks. It has been shown [11][12][13][14][15] that the coordinate-free (covariant) Fedorov method is effective for studying anisotropy in optics and acoustics. In the present work this method is used to study the properties of photorefractive solitons in cubic nongyrotropic crystals.Nonlinear Schro .. dinger Equation for Cubic Crystals. Maxwell's equation for the electric field E frequency