New Analytical Approach for Computation of Band Structure in One-dimensional Periodic Media

In this paper, we present a new approach for the exact calculation of band structure in one-dimensional periodic media, such as photonic crystals and superlattices, based on the recently reported differential transfer matrix method (DTMM). The media analyzed in this paper can have arbitrary profile of refractive index. We derive a closed form dispersion equation using differential transfer matrix formalism, and simplify it under the assumptions of even symmetry and real-valued wavenumber. We also show that under normal incidence both TE and TM modes must have the same band structure. Several numerical test cases are also studied and discussed.