Temporal behavior of low-amplitude two-photon screening-photovoltaic grey spatial solitons

Abstract

The time-dependent formation of one-dimensional two-photon screening-photovoltaic (PV) grey spatial solitons under low-amplitude conditions is presented theoretically. The time-dependent propagation equation of two-photon screeningphotovoltaic solitons is obtained by the numerical method. The results indicate that as the time evolves, the intensity width of grey screening-photovoltaic spatial solitons decreases monotonously to a minimum value towards the steady state. The higher the ratio of soliton peak intensity to the dark irradiation intensity, the narrower the width of grey solitons within the propagation time.Photorefractive (PR) spatial solitons have attracted much attention because of their possible applications for optical switching and routing. To date, there are four types of PR spatial solitons, i.e., quasi-steady-state solitons [1] , screening solitons [2] , photovoltaic (PV) solitons [3][4][5] and screeningphotorefractive (SP) solitons [6] . All of the above-mentioned solitons are about the steady-state propagation of the solitons. In 2003, Chauvet M [7] reported the temporal behavior of the dark PV solitons under open-circuit. Later, the temporal characteristics of bright PV solitons and SP solitons were investigated by Lu et al [8][9][10] . At the same time, CastroCamus and Magana [11] introduced a new model for PR spatial solitons, which involved two-photon PR effect. This model includes a valance band (VB), a conduction band (CB) and an intermediate allowed level (IL). A gating beam is used for maintaining a fixed number of excited electrons from the VB, which are then excited to the CB by the signal beam. Based on the model of two-photon PR spatial solitons, the screening solitons [12] , PV solitons [13] and SP solitons [14][15][16] were predicted one after another. However, the temporal behavior of two-photon PR solitons has not been fully investigated yet. In this paper, we present the time-dependent nonlinear wave equation of the two-photon SP spatial solitons and discuss the temporal characteristics of the normalized intensity profiles and width for grey solitons. The numerical results show that the width of solitons decreases monotonically to a minimum value towards the steady state. The temporal behaviors of the screening solitons and PV solitons can also be obtained from our results.To start, we consider an optical beam that propagates in a biased two-photon PV-PR crystal along the z-axis and is permitted to diffract only along the x direction. The crystal with the optical c-axis along the x direction is illuminated by the gating beam. Moreover, it is assumed that the optical beam is linearly polarized along the x direction. As usual, we express the optical field of the incident beam in terms of slowly varying envelope , i.e., E=x (x,z)exp(ikz), where k=k 0 n e = ( 0 )n e , n e is the unperturbed extraordinary index of refraction, and 0 is the free-space wavelength. Under these conditions the optical beam satisfies the following envelope evolution equation: 0 2 2 1 i sc 33 3 e 0