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June 15,1998 / Vol. 23, No. 12 / OPTICS LETTERS 897 Primarily isotropic nature of photorefractive screening solitons and the interactions between them Hongxing Meng and Gregory Salamo Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701 Mordechai Segev Department of Electrical Engineering and Center for Photonics and Opto-Electronic Materials, Princeton University, Princeton. New Jersey 08544 Received January 16, 1998 We present experimental evidence demonstrating that the photorefractive-index change responsible for the formation of photorefractive spatial screening solitons and coherent collisions between them is primarily isotropic in nature, even though the photorefractive medium is inherently anisotropic. O 1998 Optical Society of America OCIS codes: 160.1190, 120.5710, 060.5530. Optical spatial solitons' are created when a selfinduced index change exactly compensates for the natural diffraction of the optical beam. In this sense the beam induces its own waveguide and offers the potential to guide, steer, and switch another optical beam. These ideas are particularly apparent in the case of collisions between photorefractive solitons. Although there have been several types of photorefractive solit~n~-~~ reported, our study is focused on the isotropic nature of screening photorefractive solitons and the interactions between them.5-16 Intuitively, one can view the formation of bright screening photorefractive solitons by picturing a focused laser beam passing through an electrically biased photorefractive crystal. The beam excites charge carriers from dopant with energy levels deep in the forbidden energy gap, thereby increasing the conductivity (decreasing the resistivity) in the illuminated region. Therefore the applied voltage creates an electric field primarily in the dark high-resistance regions, whereas the electric field in the bright region is considerably lower. Since the index change created by the electro-optic effect is proportional to the electric field, the index is lowered (for an appropriate choice of direction of the applied field with respect to the principal crystalline axes) primarily in the dark region, and a graded-index profile is created that mimics the laser intensity distribution. This index profile leads to trapping of the beam and to the formation of an individual screening spatial photorefractive soliton.5-' Observed photorefractive screening solitons have been so robust that they have presented a playing field on which to investigate soliton collision^.'^-^^ For example, if the colliding solitons are coherent, the two beams interfere in the crystal as they propagate. When the relative phase between the two beams is zero and the collision angle is small, the interference produces a pattern that is predominantly one bright fringe that develops into a single soliton and two solitons that can fuse into one.16 On the other hand, when the relative phase between the two beams is .rr the interference is predominantly two bright fringes centered about a dark fringe. The two bright fringes then develop into repelling solitons.16 Photorefractive screening solitons5-' that have one transverse dimension are characterized by an existence curve that relates the soliton width A5 = h~kn~~(r,~~V/1)"~, where Ax is the actual soliton intensity FWHM, k = 27r/A, reff is the effective electro-optic coefficient, and V is the voltage applied across the crystal of width 1, to Uo2 = Io(Ib + Id), the ratio between the incident soliton peak intensity I. and the sum of the background intensity Ib and the effective dark intensity Id. Solitons exist only for parameters that follow the existence curve, and large deviations (> 10%) cannot support a soliton, as shown experimentally in many papers (see, e.g., Refs. 10, 12, and 16). Although one-dimensional (1-D) screening solitons are well understood theoretically, little has been noted about the nature of the self-induced index change for a single 2-D soliton or for a collision between two 2-D solitons. An analytic theoretical analysis exists only for the 1-D case, whereas the theory for 2-D screening solitons relies mostly on numerics." For example, despite the large amount of direct experimental evidence demonstrating the existence of circular screening soliton^.^^^^^^^^'^ all numerical attem~ts have either failed completely to yield a soliton or have found an approximately nonevolving beam of an elliptical shape. Intuitively, the circular symmetry is broken by the boundary conditions as the voltage is applied between two planar electrodes. Furthermore, the electro-optic effect is fundamentallv anisotro~ic. In fact. it is rather surprising that many photorefractive crystals can support circular solitons. Given the lack of a full 2-D theory and the inherent anisotropic nature of the photorefractive nonlinearity, the interaction behavior between 2-D screening solitons is not so intuitive as in the 1-D case. In this Letter we present experimental evidence demonstrating that the photorefractive-index change responsible for the formation of individual photorefractive screening solitons and the behavior 0146-9592/98/120897-03$15.00/0 O 1998 Optical Society of America
Journal of Electronic Materials, Vol. 27, No. 7, 1998 Regular Issue Paper Evaluation of 1nP:Fe Parameters by Measurement of Two Wave Mixing Photorefractive and Absorptive Gain M. CHAUVET,' G.J. SALAMO,' D.F. BLISS,^ and G. BRYANT~ 1.-University of Arkansas, Physics Department, Fayetteville, AK 72701, 2.-Rome Laboratory, U.S.A.F., Hanscom AFB, MA 01731 In this paper, we present two-wave mixing absorption gain measurements in 1nP:Fe in the 960-1035 nm wavelength range. The measured absorption gain is shown to be positive for long wavelength but changes sign for shorter wavelength. By simultaneously measuring the photorefractive gain and the absorption gain, we deduce the values of the photo-ionization cross sections related to the iron deep level trap. Finally, the study of the temperature dependence of the absorption gain allows us to evaluate a temperature shift of the iron level with respect to the conduction band of -4 x lo4 eV/K. Key words: Absorptive gain, InP:Fe, photorefractivity, two wave mixing INTRODUCTION Semi-insulating iron doped indium phosphide (1nP:Fe) is of interest for the development of optoelectronic components. For this reason, it is important to understand the role of iron on the electronic and optical performance of 1nP:Fe devices. This role is strongly related to the position and behavior of the iron level, as well as to the iron optical cross sections. In this paper, we exploit photorefractive two wave mixing (TWM) experiments to determine the optical cross sections as well as the temperature dependence of the iron energy level. These TWM experiments are based on observing the mutual influence of two coherent beams of unequal intensity crossing in a 1nP:Fe crystal. We measure the change of intensity level of the weaker beam (signal beam) after propagation in the crystal under the presence of the strong beam (pump beam). A TWM gain r can then be calculated assuming that the intensity of the weak beam follows the solution: Where Iso and I,, are the intensity of the signal in the (Received August 25, 1997; accepted January 26, 1998) absence and in the presence of the strong beam, respectively. The TWM gain is composed of rEO, the electro-optic gain, Ta, the absorption gain and T, the absorption-induced index gain. These gains all come initially from a redistribution of the charges on the iron deep level under the influence of the interference grating formed by the two beams. Specifically, rEO is the electro-optic gain that is measured when the energy coupling is created by the space charge field associated with the linear electro-optic effect. This electro-o tic gain has been extensively studied in 1nP:Fe 1s as well as in numerous photorefractive and is commonly named the photorefractive gain. The absorptive gain5 ra takes place because of the absorption grating formed by the ~ e" and ~ e sinusoidal ~ ' redistribution resulting in a spatial modulation of the absorption. The absorption gain is usually neglected but it has been reported for photorefractive crystal such as6 BaTi03 and G~As.~" This absorption grating is accompanied by an index grating giving energy coupling or a gain T,. The total gain is simply the sum of the contribution of each individual gain: r = rEO + ra + ran THEORY The photorefractive effect is present in 1nP:Fe because of a spatial redistribution of the free carriers
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