Eigenvalue Problems in Fiber Optic Design

  • Authors:

  • Linda Kaufman

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 2006

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Abstract

Maxwell's equation for modeling the guided waves in a circularly symmetric fiber leads to a family of partial differential equation-eigenvalue systems. Incorporating the boundary condition into a discretized system leads to an eigenvalue problem which is nonlinear in only one element. In fiber design one would like to determine the index profile which is involved in Maxwell's equation so that certain optical properties, which sometimes involve derivatives of the eigenvalues, are satisfied. This contribution discusses how to handle the nonlinear eigenvalue problem and how to determine derivatives of the eigenvalue problem.