Non-paraxial Split-step Finite-difference Method for Beam Propagation

A method based on symmetrized splitting of the propagation operator in the finite difference scheme for non-paraxial beam propagation is presented. The formulation allows the solution of the second order scalar wave equation without having to make the slowly varying envelope and one-way propagation approximations. The method is highly accurate and numerically efficient. Unlike most Padé approximant based methods, it is non-iterative in nature and requires less computation. The method can be used for bi-directional propagation as well

Numerical analysis

Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in compu