  A theoretical study of photonic bands for one-dimensional (1D) lattices
embedded in planar waveguides with strong refractive index contrast is
presented. The approach relies on expanding the electromagnetic field on the
basis of guided modes of an effective waveguide, and on treating the coupling
to radiative modes by perturbation theory. Photonic mode dispersion, gap maps,
and intrinsic diffraction losses of quasi-guided modes are calculated for the
case of self-standing membranes as well as for Silicon-on-Insulator structures.
Photonic band gaps in a waveguide are found to depend strongly on the core
thickness and on polarization, so that the gaps for transverse electric and
transverse magnetic modes most often do not overlap. Radiative losses of
quasi-guided modes above the light line depend in a nontrivial way on structure
parameters, mode index and wavevector. The results of this study may be useful
for the design of integrated 1D photonic structures with low radiative losses.
