Transmittance analysis of three-dimensional photonic crystals by the effective medium theory

A simple method for calculating the transmittance of three-dimensional photonic crystals is proposed. The crystals are divided into multilayer thin films, and each film is divided into rectangles with a minute width to calculate the effective permittivity of the film by the effective medium theory. Transmittance of the multilayer thin films is calculated with the matrix method. As the number of atomic layers increases, remarkable stop bands appear. When the refractive index of photonic atoms increases, the stop band shifts to a lower frequency, the band widens, and the number of bands increases. Polarization and incident angle dependences are also analyzed. The limit of application for this calculation method is also discussed.