Wavelet method for computing band diagrams of 2D photonic crystals

A wavelet method is applied for the first time to the computation of band diagrams of photonic crystals (PhCs). The wavelet algorithm is described. Its numerical implementation is validated in the case of emblematic two-dimensional triangular and square lattice PhCs. Although these examples do not emphasize the full power of wavelet methods, the number of wavelets needed to achieve a prescribed accuracy is already shown to be orders of magnitude smaller than the number of waves used in the traditional plane wave method. Further extension to more complex photonic structures is discussed.