Fourier analysis of reflection and refraction in two-dimensional photonic crystals

We investigate the reflection and refraction at an interface between a homogeneous medium and a photonic crystal with a negative effective refractive index. For this purpose a two-dimensional finite-difference time-domain method and Fourier analysis are combined to study the fields in spatial and momentum spaces. This technique allows us to study the Fourier components of the excited Bloch modes individually. It is shown that their amplitude profiles and propagation directions are to a large extent determined by the shape of the Fourier coefficient function for the Bloch-mode plane wave expansion.