Semivectorial polarised H̃ field solutions for dielectric waveguides with arbitrary index profiles

Abstract

Following recent successes with semivectorial polarised £ field solutions for rib, channel, embedded, and buried waveguides a method is presented for the determination of corresponding polarised H field modes for similar and other rectangular waveguide structures which may contain any arbitrary distribution of horizontal and vertical dielectric discontinuities. The new finite difference schemes take full account of the discontinuities in the normal gradients of magnetic field components across all internal dielectric interfaces. The polarised H field results, which are presented for various rib and embedded waveguide structures, are found to be in excellent agreement with the corresponding polarised £ field modes. Application of the zero divergence constraint prevents the occurrence of spurious modes.

Norm-conserving finite-difference beam-propagation method for TM wave analysis in step-index optical waveguides

“…We now demonstrate the effectiveness of the modified FD formula, comparing it with the well-known Stern formula [13]. Before discussing propagating beam problems, we assess the accuracy of each formula through the eigenmode analysis.…”

Application of modified finite-difference formulas to the analysis of z-variant rib waveguides

“…Modified FD formulas, which are regarded as the extension of Stern's formula [7], have been developed for semivectorial fields by several authors [6], [8]- [11]. The formulas are derived assuming a planar geometry where all the discontinuities are either parallel or orthogonal to axes.…”

Modified finite-difference formula for semivectorial H-field solutions of optical waveguides

“…The continuity relations at the interface, which are different from those in E-fields [4], require that where is the free-space wavenumber and . After some manipulations similar to those in [4], we finally obtain (1) where in which It is worth mentioning that the coefficient of vanishes when either 0.5 or 0 (note that 0 is approximately realized in the limit where approaches zero). Equation (1) similar to (1) is also derived when the discontinuity lies between and .…”

“…T O IMPROVE accuracy of a propagating beam analysis in a step-index optical waveguide, care has to be exercised in evaluation of the second derivatives of transverse fields, since the accuracy of the conventional finite-difference formula deteriorates at an interface between different refractive indices [1], [2]. In the analysis of a step-index waveguide, a semivectorial approach is often sufficient, unless one needs minor field components [3].…”