Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver

Abstract

The incidence of thin-film-guided, in-plane unguided waves at oblique angles on straight discontinuities of dielectric slab waveguides, an early problem of integrated optics, is being reconsidered. The 3-D frequency domain Maxwell equations reduce to a parametrized inhomogeneous vectorial problem on a 2-D computational domain, with transparent-influx boundary conditions. We propose a rigorous vectorial solver based on simultaneous expansions into polarized local slab eigenmodes along the two orthogonal cross section coordinates (quadridirectional eigenmode propagation QUEP). The quasi-analytical scheme is applicable to configurations with -in principle -arbitrary cross section geometries. Examples for a high-contrast facet of an asymmetric slab waveguide, for the lateral excitation of a channel waveguide, and for a step discontinuity between slab waveguides of different thicknesses are discussed.

Full Resonant Transmission of Semiguided Planar Waves Through Slab Waveguide Steps at Oblique Incidence

“…Details of the quasi-analytical solver (vQUEP, [24]), that has been applied to generate the numerical results of this paper, can be found in Refs. [12,11]. In all cases the numerical parameters have been selected such that results are converged on the scale of the figures as given, where the power balance (conservation of energy) serves as one of the criteria for convergence.…”

“…Still, for a distance h = 1.83 µm, a lossless configuration with virtually full transmission can be identified. The transmission is mostly TE polarized (reciprocity arguments apply [11]), with a TM contribution of about 2%. The field plot in Figure 8(a) shows a major TM contribution to the resonance in the vertical slab, visible through the strong electric field contributions next to the vertical core edges, similar to Figure 5(c).…”

Oblique quasi-lossless excitation of a thin silicon slab waveguide: a guided-wave variant of an anti-reflection coating

“…We shall see in this paper that things change drastically, if we step to a 2.5-D framework [5,6] with oblique incidence of the semi-guided waves at the junction, as illustrated in Figure 1(a). One retains a configuration where the structure is constant along one axis, but where optical fields are considered that vary harmonically along that axis, according to the given angle on incidence.…”

“…While a more formal, general description of the vectorial effective-2-D ("2.5-D") frequency domain scattering problem can be found in Refs. [7,8], for the present discussion we rely primarily on simulations on the basis of a semi-analytical solver, using simultaneous eigenmode expansions along the two cross sectional coordinate axes x, z (vectorial quadridirectional eigenmode propagation, vQUEP) [6,28]. We consider the abrupt interface (w = 0) first.…”

“…In this context, we thus deal with non-leaky modal solutions that are confined along the out-of-plane axis, but are not confined along the lateral in-plane axis. This motivates the notion of "semi-guided waves", as introduced in [5,6], to distinguish the fields from e.g. the guided modes of channel waveguides with two-dimensional cross section, or from the wave bundles with confinement along two cross-sectional axes as considered in Section 4.…”