Analysis of two-dimensional waveguides with misaligned or curved gratings

Periodic corrugated waveguides with wave confinement in both transverse dimensions are analyzed. The description includes the cases of grating misalignment (tilt) and curvature; for a tilt angle θ, the resonant wavelengths vary as
(\cos \theta)^{-1}
. Coefficients for intramode coupling (identical contradirectional modes) and hybrid (intermode) coupling are calculated as functions of θ. Numerical results for a GaAlAs waveguide, of the type employed in distributed Bragg reflector (DBR) lasers, are included.