A boundary integral equation for two-dimensional (2D) photonic crystals, which is based on the Green's function of the 2D scalar Helmholtz equation and Huygen's principle, is formulated, discretized with the Nystr"{o}m method, and solved with generalized minimal residuals (GMRES). In order to validate the accuracy of the method, the scattering of the plane wave by a single cylinder is calculated and compared with the analytical solution. Then, the simulation is extended to the multiple rods with various configurations.

Keywords: Photonic crystal, Maxwell's equation, Helmholtz equation, Integral equation, Numerical analysis