Numerical Calculation of Light Propagation

Abstract

An algorithm is presented for the numerical integration of the scalar wave equation is the Fresel approximation in inhomogeneous media. The wave equation is reduced by a variable transform to an equation describing the deviation from a Gaussian reference beam. Large phase shifts are handled analytically in combination with the longitudinal discretization using the Crank-Nicolson Scheme, This permits large step sizes. The discretization in the two transverse directions is performed with the Galerkin method, with spline functions as basis. An alternating-direction scheme is used in inverting the implicit finite-difference equations that result. An interaction of the longitudinal and transverse discretization is described. A method of handling a non-linear index of refraction is described, and the algorithm is applied to the thermal lens effect.

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Document Details

Document Type
Technical Report
Publication Date
Jul 12, 1971
Accession Number
ADA954864

Entities

People

  • Jeffrey W. Herrmann
  • L. C. Bradley

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Absorption
  • Accuracy
  • Algorithms
  • Amplitude
  • Computations
  • Difference Equations
  • Differential Equations
  • Equations
  • Frequency
  • Galerkin Method
  • Intensity
  • Partial Differential Equations
  • Phase Shift
  • Polynomials
  • Thermal Lens Effect
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Physics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.