Open dielectric waveguides are of prime importance in the field of integrated optics. Almost all of the published literature concerned with guiding, radiating or scattering effects on open dielectric structures involves a surface wave striking a structural discontinuity at normal incidence. Under those conditions, the TE and TM modes remain independent of each other. When the surface waves are incident at an arbitrary angle, however, the TE and TM modes couple to each other at the geometrical discontinuity, giving rise to a rich variety of interesting and sometimes unexpected new physical effects. We have previously examined such TE-TM mode coupling, and the interesting new physical effects that result from it, in the context of uniform open waveguiding structures. We found that on most dielectric strip waveguides leaky modes can occur instead of the previously expected purely-bound modes, and that resonance effects appear in the leakage process. Furthermore, these leaky modes constitute a new class of leaky modes, since the leaking energy possesses a polarization opposite to tl~at present in the main body of waveguide, in contrast to customary leaky modes. Here we are concerned with periodically-grooved open dielectric waveguides, involving a wide planar dielectric layer. We find that guidance in a direction oblique to the grooves produces four stop bands instead of the usual two in the Bragg reflection region; also produced are interesting anisotropy phenomena such as beam steering and focusing, radiation at peculiar skew angles, and surprisingly large cross-polarization effects. The physical effects are relevant to integrated optics components such as multiplexers, filters and mode deflectors. The guidance of optical surface waves propagating in a direction normal to the grooves on a periodically:corrugated planar dielectric waveguide is well known, and various theoretical treatments are available. Such structures have been used in grating couplers and in distributed-feedback lasers, for example. The electromagnetic boundary-value problem for the case of normal incidence is scalar, however, where the TE and TM surface waves remain independent of each other. When the
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