Contexts in source publication

Context 1

... two-wave coupling in electro-optic crystals has been studied extensively for its potentials in many applications. Much attention has been focused on materials of cubic symmetry such as the optically active sillenite crystals Bi 12 SiO 20 and Bi 12 TiO 20 ( 23 symmetry group) and the isotropic crystals GaAs, InP, and CdTe (4 ̄ 3 m symmetry group) because of their high carrier mobility, which permits achievement of fast response time. The symmetry properties of the photorefractive two-beam coupling in such crystals have been studied both theoretically and experimentally by several research groups. 1 – 5 These properties provide possibilities to realize effective energy exchange between two coherent beams in a two- wave coupling geometry, which has been demonstrated to be very useful in signal and image processing 6 and in in- terferometric measuring systems. 7 Moreover, two-beam coupling and a coherent amplification of weak beams un- derlie the photorefractive beam-fanning effect 8 that in turn is the base of photorefractive optical oscillators 9 and of both self-pumped and mutually pumped phase conjugators. 10,11 An optimal design of these devices should take into account an orientational dependence of light-induced scattering, which is mainly defined by symmetry properties of two-wave coupling. For example, the asymmetrical scattering-light distribution in a Bi 12 SiO 20 crystal under external electric field can be matched by mapping the two-wave-coupling gain of a variable grating orientation. 12 In the cited work, 12 the external electric field was parallel to the ͗ 001 ͘ axis while the interacting beams were propagating under small angles to the ͗ 110 ͘ axis. Since the early paper of Marrakchi et al. 13 this geometry was incorrectly considered as a most effective one for two-beam coupling in cubic crystals. Only six years later it was pointed out by Stepanov 14 (and confirmed by other authors 15,16 ) that the optimal geometry of two-wave coupling is achieved in these crystals when both the ex- ternal electric field and the grating vector are parallel to the ͗ ̄ 1 11 ͘ axis. Two-wave coupling in photorefractive crystals was theoretically investigated in a number of papers. 17 – 20 The most advanced theory was recently presented by Pedersen and Johansen, 21 which includes almost all effects of photorefractive beam coupling under a general angle of incidence: optical activity, externally induced linear birefringence, self diffraction, and depleted pump beam. However, this theory does not consider piezoelectric and photoelastic effects despite the importance of these effects for the explanation of the experimental results, which was pointed out by several research groups. 12,22,23 Un- fortunately, each of these works neglects one or more effects listed above. Moreover, to the best of our knowl- edge, no attempt has been made before to compare the two-wave-coupling gain for the beams propagating along the ͗ 110 ͘ axis with the counterdirectionally propagating beams. The only exception is the early paper of Fabre et al. , 24 where the particular case of the grating vector’s being parallel to the ͗ 001 ͘ axis was considered, but, as we show in this work, there is no asymmetry of the gain factor in this geometry if the counterpropagating beams are considered. The present paper is devoted to detailed theoretical and experimental study of the most effective geometry of two-wave coupling in the (110) cut of cubic crystals, when both the grating vector and the electric field are parallel to the ͗ ̄ 1 11 ͘ axis. Particularly, we demonstrate that the gain for beams propagating along the ͗ 110 ͘ axis significantly differs from the gain for the same beams but propagating backwards (along the ͗ 110 ͘ axis). If in one direction maximal beam coupling is observed for beams linearly polarized along the external electric field, then for counterpropagating beams the optimal polarization is the orthogonal one, and the net amplification is much weaker. We also show that the important peculiarities of light-induced scattering (angular distribution of the fan- out light) in sillenite crystals can be explained by mapping the two-wave-coupling gain with the obligatory con- sideration of the piezoelectric and photoelastic effects. Referring to Fig. 1, we consider the intersection of two coherent polarized beams, R and S , inside a cubic photorefractive crystal with the angle 2 ␪ between them. The bulk refractive index of the crystal is n 0 at the wavelength ␭ . These beams produce an interference pattern, which is recorded in the crystal as a space-charge-field grating with the vector K G , given by K G ϭ k R Ϫ k S , where k R and k S are the wave vectors of the beam R and S , respectively. This grating modulates the permittivity tensor of the crystal in the ...

Context 2

... k B is the Boltzmann constant, T is the absolute tem- perature, e is the electron charge, N A is the trap density, ␶ is the photoelectron lifetime, ␮ is the charge mobility, ⑀ is the low-frequency dielectric constant, ⑀ 0 is the free- space permittivity, and D is the diffusion coefficient. The optical fields R and S are assumed to be of transverse nature and these are characterized by transverse- electric and transverse-magnetic components, denoted by the subscripts E and M , respectively (see Fig. 1). R M , R E , S M , and S E are of a complex nature (to describe a general state of polarization) and are dependent on the coordinate z . 21 The modulation of the interference pattern created by these beams is given ...