“…Photonic crystals (PCs) are meta-materials patterned with a periodicity in dielectric constant, which can alter radiation-matter interactions and shape the flow of light [1,2]. PCs have shown to exhibit a multitude of interesting properties, such as photonic band gaps (PBGs), Anderson localization with designed defects, negative refraction (NR), self-collimation (SC), slow light (SL) and zero refraction (ZR), which have found important technological and scientific applications spanning many disciplines, including semiconductor lasers [3], filters [4], couplers [5], solar cells [6], superlens [7], high-quality resonant cavities [8], etc. Recently, annular photonic crystal (APC) has attracted considerable attention due to its extraordinary properties and wide promising applica- * Authors to whom any correspondence should be addressed.…”