New method for nonparaxial beam propagation

Abstract

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Numerical simulation of inhomogeneous and nonlinear diffusion

“…Thus, by writing Eqs. (2) and (4) at the collocation points j x and carrying out some algebraic manipulations (see, e.g., [6,7,13] for details), we can transform the partial differential equation (2) to the following ordinary differential equation for the matrix { : ( ),…”

“…In the case of the expansion functions defined in Eq. (5), this diagonal matrix reduces to a number and we have [13] 1 T…”

A new finite-difference-based method for wide-angle beam propagation

“…Recently, we have proposed a new method . [10] based on symmetrized splitting of the operator for non-paraxial propagation using the collocation method [11]. In this paper, we show that the splitstep non-paraxial scheme can be implemented efficiently in the finite-difference based propagation method without resorting to the paraxial approximation.…”

“…As a measure of accuracy, we computed the overlap integral and an error (ERR), which includes the effects of both the dissipation in power as well as the loss of shape of the propagating mode [10]. We have used 900 computation points for this calculation.…”

Propagation of a localized wavepacket in a metamaterial with a negative index of refraction

“…Other numerical methods used to model the distribution of beams also have their drawbacks. For example, calculations based on a parabolic approximation impose limitations on the allowed deviations [19] and do not always effectively describe multiple reflection of the wavepacket [20]. Let us examine two limiting cases.…”