We introduce a new method allowing rigorous electromagnetic analysis of scattering through photonic crystals comprising polygonal or round rods. For this purpose, we reformulate the C method with adaptive spatial resolution by utilizing the hybrid-spectrum connection method, permitting the use of nonidentical trapezoidal profiles. Considering polygonal rods as gratings consisting of different piecewise-differentiable surfaces, we are able to analyze the reflection and the transmittance of crystals by means of the C method. To enhance computational efficiency, we apply the recursive <i>S</i>-matrix approach with Redheffer’s star product to solve the transfer matrix for structures of numerous successive layers of rods.
© 2003 Optical Society of America
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(250.5300) Optoelectronics : Photonic integrated circuits
(260.2110) Physical optics : Electromagnetic optics
(290.0290) Scattering : Scattering
Tuomas Vallius and Markku Kuittinen, "Novel electromagnetic approach to photonic crystals with use of the C method," J. Opt. Soc. Am. A 20, 85-91 (2003)