Spectral analyses of low-symmetric and graded index photonic crystals

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 (PBG) 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 PBG, neither optical modes nor spontaneous emissions exist. Breaking the rotational and mirror symmetries of PC unit cells provides rich dispersive features such as super-collimation, polarization insensitive self-collimation, complete band gap and 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). Specifically, re-orientation of PC unit cells gives rise to the implementation of graded index (GRIN) mediums. 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 super-bending.