An approximate method of obtaining surface-wave band gap from reflection phase plots for mushroom structures

This paper proposes an approximate method of obtaining the surface-wave band gap from reflection phase plots for mushroom structures. The upper bound of the band gap can be found by observing the first in-phase frequency on the reflection phase plot of TE plane waves under grazing incidence, and the lower bound of the band gap can be approximated by the three specific frequencies on reflection phase plots of TM plane waves: the first in-phase frequencies under normal and grazing incidence and the frequency where the first +90° reflection phase occurs. By comparing surface-wave band gaps obtained from dispersion plots and from reflection phase plots through the approximate method in the commercial software CST, results show that the errors of estimated values are less than 10% in different cases of mushroom structures.