Wide-Angle Spectral Split-Step Method for 2D or 3D Beam Propagation

Abstract

We develop a method for non-paraxial beam propagation that obtains a speed improvement over the Finite-Difference Split-Step method (FDSSNP) recently reported by Sharma et al. The method works in the eigen-basis of the Laplace operator, and in general requires half as many operations to propagate one step forward so that a 2X speedup can be realized. However, the new formulation allows the Fast Fourier Transform (FFT) algorithm to be used, which allows an even greater speedup. The method does not require a numerical matrix inversion, diagonalization, or series evaluation. The diffraction operator is not approximated, and in the absence of refractive index fluctuations the method reduces to an exact solution of the Helmholtz equation.

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Document Details

Document Type
Technical Report
Publication Date
Jul 23, 2010
Accession Number
ADA526251

Entities

People

  • C. D. Clark Iii
  • Robert J. Thomas

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Birds
  • Boundaries
  • Cartesian Coordinates
  • Coordinate Systems
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Fast Fourier Transforms
  • Grids
  • Helmholtz Equations
  • Refractive Index
  • Square Roots
  • Three Dimensional
  • Two Dimensional
  • Wave Equations
  • Wide Angles

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Wave Propagation and Nonlinear Chaotic Dynamics.