ABSTRACT
Periodic structures or gratings in a waveguide are one of the most important elements for integrated optics. They can perform various passive functions on guided waves, such as deflection and reflection, input and output coupling, mode conversion, wavelength filtering, wavelength dispersion, wavefront conversion, phase matching in directional coupling between waveguides, and phase matching for nonlinear-optic interactions. Periodic structures for integrated optics include fiber gratings, which are fabricated by UV-light-induced refractive index change of an optical fiber. The characteristics of waveguide gratings can be analyzed based on the coupled-mode theory. Coupling between guided modes propagating along the same axis is classified into codirectional and contradirectional couplings. In a planar waveguide with a grating of appropriate orientation, coplanar coupling takes place between guided waves of different propagation directions. This type of coupling is also called diffraction or deflection, since it involves a change of propagation direction.
