Photonic bandgap structures in planar waveguides

If a one-dimensional (1D) or two-dimensional (2D) photonic bandgap (PBG) structure is incorporated into a planar optical waveguide, the refractive-index nonuniformity in the direction perpendicular to the waveguide plane responsible for waveguiding may affect its behavior detrimentally. Such influence is demonstrated in the paper by numerical modeling of a deeply etched first-order waveguide Bragg grating. On the basis of physical considerations, a simple condition for the design of 1D and 2D waveguide PEG structures free of this degradation is formulated; it is, in fact the separability condition for the wave equation. Its positive effect is verified by numerical modeling of a modified waveguide Bragg grating that fulfills the separability condition. (C) 2001 Optical Society of America OCIS codes: 130.2790, 130.0130, 050.2770, 230.1480.