Exact Solutions And Numerical Solutions Of Equations Describing Photovoltaic Photorefractive Media With An External Electric Field

Since the first experimental observation, photorefractive spatial solitons have been the focus of considerable attention. Until now, it has been predicted and proved that there exist four types of scalar photorefractive spatial solitons:quasi-steady-state soliton, screening soliton, photovoltaic soliton, and photovoltaic photorefractive(PP) soliton. The three latters are steady-state solitons. Recently, the PP soliton which forms in PP crystal with the external electric field has attracted much more interest. The PP soliton is possible when the process of diffraction is exactly balanced by the nonlinearity due to both the photovoltaic effect and the spatially nonuniform screening of the external electric field. In fact, the screening soliton and photovoltaic soliton in the closed-circuit case are a special case of the PP soliton. So, the screening soliton and photovoltaic soliton may be integrated in the PP soliton. There are differences between using an external field and adding background illumination in PP crystal.In this paper, using the classical Lie-group method, we study the evolution equation in photovoltaic photorefractive media with an external electric field. Until now, many people have studied this work with the numeric method and the PP bright, dark, and gray solitons were obtained. However, few analytically exact solutions of this equation have been investigated. The classical Lie-group method is effective for searching analytically the exact solutions of non-integrable system. We show theoretically that the evolution equation of the optical beam in PP media with external electric field not only has the numerical PP soliton solutions, but has analytical exact solutions.