Photonics Bandgap Computations using Novel Periodic Meshless Methods

─ Although many numerical methods have been developed to calculate photonic bandgap structure properties, but always improvement in numerical methods is necessary to have more efficient, accurate and flexible techniques. In the present work, novel periodic meshless shape functions including so-called direct and radial shape functions are presented. The meshless approaches, based on these periodic shape functions as real-space methods, can be used for simulation of periodic structures, like photonics bandgap structures, straightforwardly. The results on band structures derived from the proposed methods are then presented, discussed and compared with those available in the literature, and a very good agreement is seen. It shows that the proposed techniques are very promising to be robust techniques in the simulation of periodic structures such as photonic problems. Index Terms ─ Meshless methods, photonics bandgap, periodic shape functions.