  We present a semi-analytic method to calculate the dispersion curves and the
group velocity of photonic crystal waveguide modes in two-dimensional
geometries. We model the waveguide as a homogenous strip, surrounded by
photonic crystal acting as diffracting mirrors. Following conventional
guided-wave optics, the properties of the photonic crystal waveguide may be
calculated from the phase upon propagation over the strip and the phase upon
reflection. The cases of interest require a theory including the specular order
and one other diffracted reflected order. The computational advantages let us
scan a large parameter space, allowing us to find novel types of solutions.

Optics