Abstract

The discrete Bessel representation in cylindrical (or spherical) geometry is presented that is analogous to the discrete Fourier scheme for a Cartesian coordinate. In other words, the integral Fourier–Bessel or Hankel transform is adequately discretized, and the underlying quadrature algorithm achieves Gaussian accuracy. The relevant discrete Bessel transform can be straightforwardly extended to the azimuthally dependent case. Efficient pseudospectral schemes are thus made possible in the resolution of the scalar Helmholtz and paraxial-wave equations in cylindrical coordinates. The superiority of the discrete Bessel scheme is illustrated by the calculation of the propagation constants for a multimode optical fiber.

© 1997 Optical Society of America

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