Influence of filling fraction on the defect mode and gap closing of a one-dimensional photonic crystal: An analytical approach

Study of the optical properties of the one-dimensional defective photonic crystals using the gap map is improving through the emergence of new analytical methods, which are easy and without any physical restrictions. Gap map is able to monitor the changes in the defect mode frequencies and photonic band gap regions as a function of filling fractions, and all visible spectra in a single graphic presentation. In this paper, by utilizing a novel technique based on Green's function method for analyzing the defect modes, the gap map and gap closing point of a one-dimensional defective photonic crystal have been demonstrated. This method enables study of the defect modes inside the omnidirectional band gap, which is an important object in the designing of the optical filters. Moreover, as a designing criterion, obtaining the gap closing points inside the gap map enables finding of some filling fraction intervals that each one contains several distinct omnidirectional band gaps simultaneously, using a single photonic crystal. This method has been employed for the design of an optical filter at 1.3 and 1.55 μm, which is applicable for telecommunication.