Photonic Crystals Engineering For Light Manipulation: Low Symmetry,   Graded Index and Parity Time Symmetry
  The great interest to the two and three dimensionally periodic structures, called photonic crystals (PCs), has begun with the pioneer works of Yablonovitch and John as one can efficiently control the propagation of the electromagnetic (EM) waves in the same manner with semiconductors that affect the electron conduction. One of the main peculiar properties of PCs is that they have photonic band gap in the transmission spectrum similar to electronic band gap and hence, they are able to prevent the light to propagate in certain frequency regions irrespective of the propagation direction in space. Inside the band gaps, neither optical modes nor spontaneous emissions exist. Breaking the rotational and mirror symmetries of PC unit cells provides rich dispersive features such as tilted self-collimation, and wavelength de-multiplexing effects. Another important issue in PC designs is that it is feasible to design graded index medium if the parameters of the two dimensional PCs is intentionally rearranged. That type of configuration is known as Graded index photonic crystals (GRIN PCs). The implementations of GRIN via periodic structures provide great flexibilities in terms of designing different index gradient and photonic integrated circuit components such as couplers, lenses, and mode order converters. It is crucial to deliver optical signal without any loss for the long distances where light diffraction plays an important role. Hence, dealing with the alternative solution to light diffraction phenomena using 2D axicon shape annular type photonic structure is another topic of this thesis. In addition to conventional photonic all dielectric structures, we have proposed gain-loss modulated parity-time (PT-) symmetric photonic structures to obtain strong asymmetric light transmission close to the crystallographic resonances or, equivalently, close to high-symmetry points. 
Mirbek Turduev
physics.optics