Superstructure gratings in the tight-binding approximation

The reflection properties of gratings, such as those found in the core of an optical fiber, previously have been interpreted in terms of evanescent or propagating wave behavior in different parts of the grating. According to this interpretation, nonuniform gratings can thus be understood in a similar way to one-dimensional quantum-well structures. Here we exploit this similarity to develop an analytic theory for deep Bragg superstructure gratings. Using a method similar to the tight-binding method from condensed matter physics, we find approximate analytic expressions for the high-and low-reflectance frequency regions of such gratings.