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The great interest to the two and three dimensionally periodic structures,called photonic crystals (PCs), has begun with the pioneer works ofYablonovitch and John as one can efficiently control the propagation of theelectromagnetic (EM) waves in the same manner with semiconductors that affectthe electron conduction. One of the main peculiar properties of PCs is thatthey have photonic band gap in the transmission spectrum similar to electronicband gap and hence, they are able to prevent the light to propagate in certainfrequency regions irrespective of the propagation direction in space. Insidethe band gaps, neither optical modes nor spontaneous emissions exist. Breakingthe rotational and mirror symmetries of PC unit cells provides rich dispersivefeatures such as tilted self-collimation, and wavelength de-multiplexingeffects. Another important issue in PC designs is that it is feasible to designgraded index medium if the parameters of the two dimensional PCs isintentionally rearranged. That type of configuration is known as Graded indexphotonic crystals (GRIN PCs). The implementations of GRIN via periodicstructures provide great flexibilities in terms of designing different indexgradient and photonic integrated circuit components such as couplers, lenses,and mode order converters. It is crucial to deliver optical signal without anyloss for the long distances where light diffraction plays an important role.Hence, dealing with the alternative solution to light diffraction phenomenausing 2D axicon shape annular type photonic structure is another topic of thisthesis. In addition to conventional photonic all dielectric structures, we haveproposed gain-loss modulated parity-time (PT-) symmetric photonic structures toobtain strong asymmetric light transmission close to the crystallographicresonances or, equivalently, close to high-symmetry points.

Photonic Crystals Engineering For Light Manipulation: Low Symmetry, Graded Index and Parity Time Symmetry