Abstract
The paper deals with finding of soliton solution for Schrödinger equation with periodic linear and nonlinear properties of medium in 1D case. Such structure is named as photonic crystal. To find soliton solution the corresponding problem for finding of eigenfunctions and eigenvalues is formulated. Iterative process is proposed for solution of this problem. Using the technique of continuation on parameter we investigate a dependence of soliton location on its maximum intensity, on ratio between light frequency and frequency of structure, on ratio between dielectric permittivity of alternating linear and nonlinear layers and on position between centre of initial distribution of eigenfunction and center of considered photonic structure area. The results of this paper confirm the features of soliton self‐formation investigated early in our papers [37, 38, 39, 40, 41, 42], in which one considered a propagation of femtosecond laser pulse through nonlinear layered structure.
Highlights
Interaction of laser pulse with photonic crystal (PC), which is a periodic structure, and with other periodic structure is one of the actual problems of modern laser physics [3, 11, 12, 13, 14, 17, 18, 26, 28, 45, 46]
In [37, 38, 39, 40, 41, 42] we have investigated a self-formation of soliton, which locates in some layers of nonlinear 1D PC and has intensity profile similar to ch−2(z)
In these papers we have considered the case when the optical radiation falls on PC in a direction that is perpendicular to PC layers
Summary
Interaction of laser pulse with photonic crystal (PC), which is a periodic structure, and with other periodic structure is one of the actual problems of modern laser physics [3, 11, 12, 13, 14, 17, 18, 26, 28, 45, 46]. It should be mentioned that for the observation of the Anderson localization it is necessary that the carrying frequency of an input optical pulse is near the band-gap or stronger PC layers thickness fluctuations take place. Under such conditions the light energy localises in a part of PC, but not in a definite layer as it realises at the nonlinear light localization. It is very important that nonlinear light localization can occur as well for light frequencies, which belong to the frequency range of a transparency of the linear PC In this case it is necessary that an input pulse intensity must be greater than its critical value [37], which decreases in disordered layered structure [37]. We investigate below a dependence of soliton formation on various parameters of optical pulse interaction with layered structure and an opportunity for controlling the soliton displacement in PC and their parameters
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