The effect of low symmetry on self-collimation in photoni̇c crystal structures

The advantages of photonic crystals in optical transmission, particularly in directional control and light confinement, underscore their critical role in optoelectronic devices. As the demand for novel crystal structures capable of effectively manipulating light increases, hexagonal lattice-based photonic crystals have emerged as a promising solution due to their ability to induce self-collimation at various angles. In this thesis, the self-collimation effect in hexagonal lattice photonic crystals is achieved by systematically adjusting the symmetry of the unit cell. The opto-geometric parameters of the proposed structure are optimized, and the self-collimation effect is analyzed through group velocity dispersion (GVD) and third-order dispersion (TOD) characteristics. It is determined that a low-symmetry hexagonal lattice photonic crystal with a single dielectric rod exhibits self-collimation in all directions within the normalized frequency range of 0.652 to 0.668, corresponding to a bandwidth of 2.4%. Further symmetry reduction, achieved by introducing a second dielectric rod, leads to an increased self-collimation bandwidth of 6.5% and the formation of welldefined linear equal-frequency contours in two distinct frequency bands. Specifically, the fourth transverse magnetic (TM) band exhibits self-collimation within the normalized frequency range of 0.616 to 0.652, while the fifth TM band demonstrates this effect within 0.712 to 0.760. Additionally, a hybrid photonic crystal structure is proposed, replacing the two dielectric rods with rectangular photonic wires of the same refractive index and rod diameter. This hybrid structure exhibits self-collimation in all directions with an expanded bandwidth of 11.7% and provides near-zero GVD and TOD values, enhancing robustness against potential fabrication tolerances. The findings presented in this study contribute to the advancement of photonic crystal design, with potential applications in nextgeneration light manipulation technologies.