Transmission properties in a photonic crystal with a Dirac-like point located at the Brillouin zone center

¹ Department of Physics, Capital Normal University - Beijing 100048, China
² School of Science, China University of Geosciences - Beijing, 100083, China

^(a) gaohua@cugb.edu.cn
^(b) 263zys@263.net

Received: 22 September 2017
Accepted: 23 January 2018

Abstract

Light transmission properties of a two-dimensional dielectric photonic crystal (PC) with a Dirac-like point located at the Brillouin zone center are studied. The results show that at the Dirac-like point, the transmittance remains constant rather than inversely varying with the PC's thickness, that is, this transmission does not follow the pseudo-diffusive phenomenon. Moreover, since the PC with a Dirac point at the Brillouin zone center can mimic zero index material (ZIM), transmittance of a real homogeneous ZIM layer is also theoretically investigated. Invariant transmittance is obtained again and the constant transmittance at the Dirac-like point is confirmed. Physical mechanisms of the pseudo-diffusive transmission as well as the constant transmission are both analyzed. It is found that the Dirac point is a critical state between band gaps and transmission bands, where the wave vector takes a complex number. It is the imaginary part of the wave vector which causes the decrease of the transmittance. While at the Dirac-like point at the center of the Brillouin zone, an additional flat band makes the Dirac point frequency fall into a transmission band where the wave vector is a real number, therefore the transmittance does not display any decrease tendency.