Abstract

We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a dielectric corner. Although certain components of the electric field have long been known to be infinite at the corner, it is shown that all components of the magnetic field are finite, and that finite-difference equations may be derived for these fields that satisfy correct boundary conditions at the corner. These finite-difference equations have been combined with those derived in the previous paper to form a full-vector waveguide solution algorithm of unprecedented accuracy. This algorithm is employed to provide highly accurate solutions for the fundamental modes of a previously studied standard rib waveguide structure.

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  1. G. R. Hadley and R. E. Smith, "Full-vector waveguide modeling using an iterative finite-difference method with transparent boundary conditions", J. Lightwave Technol., vol. 13, pp. 465-469, Mar. 1995.
  2. A.-E. Abid, K. L. Johnson and A. Gopinath, "Analysis of dielectric guides by vector transverse magnetic field finite elements", J. Lightwave Technol., vol. 11, pp. 1545-1549, Oct. 1993.
  3. M. Koshiba, S. Maruyama and K. Hirayama, "A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems", J. Lightwave Technol., vol. 12, pp. 495-502, Mar. 1994 .

J. Lightwave Technol. (3)

G. R. Hadley and R. E. Smith, "Full-vector waveguide modeling using an iterative finite-difference method with transparent boundary conditions", J. Lightwave Technol., vol. 13, pp. 465-469, Mar. 1995.

A.-E. Abid, K. L. Johnson and A. Gopinath, "Analysis of dielectric guides by vector transverse magnetic field finite elements", J. Lightwave Technol., vol. 11, pp. 1545-1549, Oct. 1993.

M. Koshiba, S. Maruyama and K. Hirayama, "A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems", J. Lightwave Technol., vol. 12, pp. 495-502, Mar. 1994 .

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