The optical phenomena and nanophotonic applications provided by photonic crystals having low rotational symmetry

Most of the two-dimensional photonic crystals that are studied in the literature are based on the high rotational symmetric unit cells consisting of circular dielectric rods or circular air-holes. Inclusion of additional dielectric elements or modifying the shapes of existing circular elements gives rise to a reduction on the rotational symmetry order of two-dimensional photonic crystals' unit cells. Low rotational symmetric unit cells involve structural variety and pave the way for extraordinary optical properties. In this thesis, novel optical phenomena and photonic device designs, which are achieved by utilizing various dispersion properties of low rotational symmetric unit cells, were presented. The proposed concepts were investigated in both frequency and time domains by exploiting "plane wave expansion" and "finite-difference time-domain" methods, respectively. One of the studies is about the polarization beam splitters that use polarization-sensitive self-collimation phenomenon of photonic crystals consisting of C2 symmetric air holes. The proposed polarization beam splitters were investigated with different unit cell configurations. In addition, presented devices are novel and have high polarization extinction ratios. The device, which is 46.4 μm × 12.4 μm in size, has maximum polarization extinction ratios of 26 dB (TE) and 22 dB (TM) at λ = 1550 nm. Operational bandwidth of the device was measured to be 59 nm. Another study is about the numerical and experimental analyses of anisotropic zero-refractive-index materials that were achieved by performing a rotational symmetry reduction on the unit cells of photonic crystals exhibiting Dirac-like cone dispersion. Accidental degeneracy of two Bloch modes in the Brillouin zone center of C2 symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed photonic crystals expose impedance-matched zero-refractive-index feature (εeff ≈ 0, μeff ≈ 0) for one propagation direction and impedance-unmatched zero-refractive-index behavior (εeff ≈ 0, μeff ≠ 0) along transverse direction. A proper effective medium approach was utilized to verify proposed material's properties. The advantages of photonic crystals exhibiting semi-Dirac cone dispersion over periodic structures showing Dirac-like cone dispersion were stated in both frequency and time domains for photonic applications. By using anisotropic behavior of the proposed photonic crystals, photonic designs such as beam deflectors, beam splitters, and focusing lenses were proposed. In the last study, controlling the guided modes of waveguides, which consist of C1 symmetric unit cells, were investigated depending on the unit cell rotation. By controlling the geometrical properties of C1 symmetric unit cells lying along the air-defect, adjustable phase properties of guided electromagnetic waves were achieved. Using this property, Mach-Zehnder interferometers based photonic applications such as wavelength-selective transmission, gas sensing, and mode converters were investigated in frequency and time domains.