The Band Gaps Properties Of Hexangular-lattice Photonic Crystal With Poor Symmetric Scatterers

Photonic crystal (PC) is a type of dielectric structure whose dielectric constant variesperiodically in space with the lattice constant comparable to the wavelength and can controlphotons behavior easily. Due to the ability to control the propagation of electromagneticwaves, various applications of PCs are associated with their absolute photonic band gaps(PBGs), such as photonic crystal waveguide, photonic crystal fiber, photonic crystalwavelength division multiplexing (WDM) and high efficiency light-emitting diodes (LEDs).Generally speaking, photonic crystal devices will have good performance if the PBG is wideenough. So achieving large width of absolute PBGs is one of the most important goals in theresearches on PCs. The study of band gap properties of two dimensional hexangular latticephotonic crystal (HLPC) provides a theoretical basis for the application of the photoniccrystal devices in optical integration, optical information transmission and processing andother areas of the optical communication.In this paper, we change the chape of the traditional rods and utilized HLPC strctureswith five different shape scatterers (circle, circle with square hole, circle with rectangularhole, semicircle, and Taiji-shaped) whose symmetries are broken in turn. With the Theplane wave expansion method (PWM), We find that the number of PBGs of E-andH-polarization obviously increase with breaking the symmetry of scatterers, so thatthe possibility of coinciding with PBGs of E-and H-polarization to form absolutePBGs increases. So the width and number of absolute PBG increase. The largestPBG of E-polarization exhibit red shift with breaking the symmetry of scatterers, butthe H-polarization is just the reverse. The Taiji scatterer with the poorest symmetry canget the optimum band gaps properties.Then we study thoroughly the influence of the dielectric constant contrast and threegeometric parameters of Taiji-shaped rods on PBG. The calculations show that: with thedielectric constant contrast and filling ratio increase，the absolute PBG width doesn’talways increase, but there is a peak. By optimizing the parameter ε、R、r and θ, theTaiji scatterer attains optimum structure with at best eight absolute PBG and the largestabsolute PBG0.0541(ωa/2πc).Finally, we study the PBG properties of Taiji scatterers in the E and H polarization with the dielectric constant contrast and duty cycle changed. In addition,we utilize Taiji scatterer with air rods and analysis its PBG chatacteristics of TE andTM polarized mode. The results show that it is easier for the dielectric rods typephotonic crystal to form TE-polarized mode PBG; while the air rods type is conduciveto the formation of TM-polarized-mode PBG.