Simulation of photonic band gaps in metal rod lattices for microwave applications

Abstract

We have derived the global band gaps for general two-dimensional (2D) photonic band gap (PBG) structures formed by square or triangular arrays of metal posts. Such PBG structures have many promising applications in active and passive devices at microwave, millimeter wave, and higher frequencies. A coordinate-space, finite-difference code, called the photonic band gap structure simulator (PBGSS), was developed to calculate complete dispersion curves for lattices for a series of values of the ratio of the post radius (r) to the post spacing (a). The fundamental and higher frequency global photonic band gaps were determined numerically. These universal curves should prove useful in PBG cavity design. In addition, for very long wavelengths, where the numerical methods of the PBGSS code are difficult, dispersion curves were derived for the transverse-magnetic (TM) mode by an approximate, quasi-static approach. Results of this approach agree well with the PBGSS code for $\text{r/a<0.1.}$ The present results are compared with experimental data for transverse-electric (TE) and TM mode PBG resonators built at Massachusetts Institute of Technology (MIT) and the agreement is found to be very good.