Optical properties of planar colloidal crystals: Dynamical diffraction andthe scalar wave approximation

We present a quantitative comparison between two analytic theories for the propagation of electromagnetic waves in periodic dielectric structures. The se theories have both been used extensively in the modeling of optical spec tra of colloidal crystals exhibiting photonic band gap behavior. We demonst rate that dynamical diffraction theory is equivalent to the scalar wave app roximation, in the limit of small dielectric contrast. This equivalence all ows us to place quantitative limits on the validity of dynamical diffractio n, relative to the predictions of the more accurate scalar wave theory. We also note that dynamical diffraction is often applied with boundary conditi ons which neglect the strong interference between the incident and diffract ed waves within the periodic medium. These boundary conditions lead to expr essions for the transmission spectrum which cannot be generalized to the ca se of normal-incidence propagation. We provide a corrected form for these e xpressions, and use them in comparisons with experimental spectra. Excellen t agreement between theory and experiment is obtained for the widths of opt ical stop bands, for both positive and negative values of the dielectric co ntrast. These are among the first quantitative comparisons between theoreti cal and experimental optical spectra of colloidal photonic crystals. (C) 19 99 American Institute of Physics. [S0021-9606(99)70725-7].