Multipole method for modeling linear defects in photonic woodpiles

We extend the multipole method to allow for rod-type defects in woodpiles composed of infinitely long cylinders. A coupled-resonator optical waveguide and a linear waveguide are considered, where each waveguide is embedded in a woodpile cladding. For both structures, low-loss waveguiding is observed (Q̃1×10⁴-3×10⁴). Decreasing the radius of the defect rod shifts the transmission resonances to shorter wavelengths. The reflection and transmission coefficients of the woodpile are derived for the case of normal incidence in the longwavelength limit, and it is shown that both the individual layers and the entire assemblage of layers homogenize to one-dimensional dielectric slabs. Expressions for the effective permittivities are given.