Generalized dispersion properties of a four-layer thin-film waveguide.

A general analytic expression is derived, which describes the dispersion properties of a four-layer thin-film optical waveguide. The formula describes the variation of the effective refractive index with respect to any physical parameter with which the refractive index of any layer or the thickness of the guiding layers may vary. Normalized parameters are used, and curves are presented which describe the contributions of the individual layers and waveguide geometry to the total dispersion. Uses of the formula are illustrated for the cases of temperature and wavelength dispersions. Results show that considerable control of the effective index of refraction is possible. Application to the control of chromatic dispersion in a thin-film Luneburg lens is also demonstrated.