Enhanced self-collimation effect by low rotational symmetry in hexagonal lattice photonic crystals

In this study, we present the design of a photonic crystal (PC) structure with a hexagonal lattice, where adjustments to the PC unit cell symmetry reveal an all-angle self-collimation (SC) effect. By optimizing opto-geometric parameters, such as the rotational angle of auxiliary rods and adjacent distances, we analyze the SC property in detail, leveraging group velocity dispersion (GVD) and third-order dispersion (TOD) characteristics. We also investigate the relationship between symmetry properties and their influence on dispersion characteristics. Through symmetry manipulation, we gain a comprehensive understanding of the underlying mechanisms governing light collimation and confinement in the proposed configurations. The PC structure with a C1 symmetry group exhibits all-angle SC effect within the range of a/λ = 0.652 and a/λ = 0.668 normalized frequencies, with a bandwidth of Δω/ωc=2.4% Further breaking the symmetry, transforming from C1 to C2 group symmetry enhances the SC bandwidth to Δω/ωc=6.5% and reveals the perfect linear equi-frequency contours (EFC) at two different frequency bands: all angle SC between a/λ = 0.616 and a/λ = 0.344 normalized frequencies in the 4th transverse magnetic (TM) band and between a/λ = 0.712 and a/λ = 0.760 in the 5th TM band. Here, GVD and TOD values of the TM 4th band vary between 7.3 (a/2πc2)–254.3 (a/2πc2) and 449.2 (a2/4π2c3)–1.3×105 (a2/4π2c3), respectively. Also, GVD and TOD values of the TM 5th band vary between 182.5 (a/2πc2)–71.3 (a/2πc2) and −24380(a2/4π2c3)–−9619 (a2/4π2c3) values, respectively. Additionally, we propose a composite/hybrid PC structure resembling C2 group symmetry, where two auxiliary rods are replaced by rectangular photonic wires with the same refractive index and width equal to the diameter of auxiliary rods. This hybrid structure exhibits an all-angle SC effect with an operating bandwidth of Δω/ωc=11.7%, which displays near-zero GVD and TOD performance and offers enhanced robustness against potential fabrication precision issues.

Keywords: photonic crystal, self-collimation, symmetry reduction, low symmetry