Dielectric Function Versus Frequency Two-dimensional Photonic Crystal Band-gap Structures

Photonic band structures of two-dimensional photonic crystal composed of GaAs dielectric, in which air cylinders are set in triangular lattice, are investigated with the use of expanded basis method. In the thesis, we devote the studies to two topics: (1) The characteristics of band structures and field distributions in two-dimensional polaritonic photonic crystal (PPC); (2) Interactions between the photonic band gaps (PBG) of the PPC and the polariton gap (PG) of the GaAs medium..Firstly, the band structures and field distributions of two-dimensional PPC are calculated. The results show that some flattened bands appear in the frequency range below ω_T (thetransverse-optical-phonon frequency of polar semiconductor), the corresponding electric fields distribute in dielectric instead of air cylinders, that is owed to the total reflection causedby the great value of dielectric function of the polar material when frequency nearing ω_T. Band structures are observed in PG (between ω_T and ω_L), where the dielectric fields arelocated in air cylinders for the reason of resonance cavity effect; furthermore, the field distribution pictures of TM and TE modes present different symmetry due to their different polarizing directions. These results are helpful for understanding the band structure properties and for further investigations of two-dimensional PPC.Secondly, we study the interactions between the PBG for two-dimensional PPC and PG of polar medium. The calculated results show that the interactions can be observed when the PBG approached to PG or they overlap each other by varying the lattice constant. PBG is divided by PG and some new extra bands appear within original PBG region; the width of PG become narrower owing to the effect of PBG, and the PG can be divided for some values of lattice constant. The results help to fully understand the characteristics of the two kind band gaps and their interactions in two-dimensional PPC, they also give a theory base for fabrications and further applications of PPC.