“…Moreover, most previous studies on metamaterials have lacked rigorous theoretical calculations and derivations. Subwavelength gratings (SWGs), in part, can be considered as subwavelength-scale photonic crystals and are emerging as an enabling technology for implementing compact, high-performance photonic integrated devices and circuits [6,7], including reflectors [8], directional couplers [9], filters [10], splitters [11], sensors [12], and modulators [13], among others. Moreover, certain subwavelength gratings with novel surface structures can greatly improve device performance [14].…”