Quantitative Analysis of Photon Density of States for One-Dimensional Photonic Crystals in a Rectangular Waveguide  
[PERSON]  
1 School of Information Technology, Guangdong Industry Polytechnic, Guangdong 510300, China; [EMAIL_ADDRESS]  
[PERSON]  
2 Multidisciplinary Computational Laboratory, Department of Electrical and Biomedical Engineering,  
Hanyang University, Seoul 04763, Korea 22 [EMAIL_ADDRESS]; Tel. : +82-2-2220-0358222011 August 201930 October 201  
metallic cavities [8], dielectric cavities [9], superlattices [10; 11; 12; 13; 14; 15], and 2D PCs [16] have been studied. The environmental effects have been described by the photon density of states (PDOS), which is related to the transition rate of the Fermi golden rule. In principle, a PC with a complete PBG can be best realized in a 3D system to prohibit the propagation of electromagnetic waves of any polarization traveling in any direction from any source [1]. However, the difficulty in fabricating such 3D crystals with PBGs in the optical regime prohibits the progress of many applications. On the other hand, there has been a lot of interest in microwave and millimeter wave applications of PBG, such as the significant progress in the design of filters [17; 18], microstrip antennas [19], and slow wave structures [20; 21], and so on. However, the design of PBG in this frequency range is still difficult due to complexities of the modeling. There are too many parameters affecting the PBG properties, such as the number of lattice periods [22], lattice shapes [23; 24], lattice spacing [25], and relative volume fraction [26; 27; 28; 29; 30]. Since the actual fabrication of 3D PCs remains difficult, another simpler choice is periodic dielectric or PC waveguides, which have only a one-dimensional periodic pattern [1]. The rigorous study of the PC waveguide can be traced back to the 1970s, where a more detailed review can be found [31; 32]. Recently, it was demonstrated that, by considering a quantum dot spin coupled to a PC waveguide mode, the light-matter interaction can be asymmetric, leading to unidirectional emission and a deterministic entangled photon source, which might have application in future optical quantum devices [5; 33]. One interesting feature of electromagnetism in dielectric media is that there is no fundamental length scale, namely the scaling properties of Maxwell's equations, i.e., the solution of problem at one length scale determines the solutions at all other length scale [1]. In a previous work [34], a multilayer dielectric window in a rectangular waveguide had been studied to achieve a wide-bandwidth transmission of a millimeter wave. A transfer matrix approach was successfully employed to discretize the dielectric function profile and the transmission functions could be calculated efficiently. In principle, the approach can be extended to study a quasi-1D PC, a PC confined in a waveguide. However, the transmission method is limited to study radiation modes in a finite-length system. In order to study the PBG phenomena such as the suppression of spontaneous emission [35] in a quasi-1D PC, the calculation of the dispersion relations or band structures (BS) and the PDOS are needed. Metallic waveguides and cavities are widely used to control microwave propagation. One of the main concerns is visible light energy is quickly dissipated within the metallic components, which makes this method of optical control almost impossible to generalize. Recently, an unconventional superconductivity in magic-angle graphene superlattices had been discovered and studied [36]. The superconductivity might help realize the metallic waveguide confinement of optics in the near future. In this work, light propagation in 1D PCs enclosed in a rectangular waveguide or quasi-1D PCs is investigated in order to achieve a complete PBG while avoiding the difficulty in fabricating 3D PCs.