The Design And Simulation Of Two Dimension Four Channel Photonic Crystal Filter

Photonic crystal, an artificial material in which the dielectric material of different dielectric constant is arranged periodically, is proposed simultaneously by E.Yablonvitch and S.John in 1987. Similar to the semiconductors of the solid state theory, photonic crystal is considered as the semiconductor of photons. The characteristic of a photonic crystal is"photonic band gap", and the propagation of electromagnetic wave is highly prohibited in the"photonic band gap". By fabricating accurately designed defects in a perfect photonic crystal, the defects modes can be introduced into the photonic band gap. And these defects modes possess more far-ranging application, such as photonic crystal micro resonant cavity, photonic crystal waveguide etc. Furthermore, photonic crystals can be served as the conductors of photons to realize a variety of optical devices. Comparing with traditional optical waveguide devices, Photonic crystal devices have compact structure, small volume, and numerous applications in optical region,such as all-optical communication networks and optical integration chips. Related researches have drawn wide attention and become the research forefront of optical communications. Optical filters ,the key devices in WDM optical communication system, is to deal with the signal of specific channel or multiple channels. The designs of the optical photonic crystal multi-channel filter has become a significant research.The main contents of this article are given below: Firstly, according to the characteristics of periodicity distribution photonic crystal structure, the solutions of the Maxwell equation has been derivated out, and the electromagnetic field expression in the photonic crystals has also been given. A brief discussion about time-domain coupled-mode theory is proceeded, and the coupling efficiency expression of photonic crystal filters is obtained. Secondly, the influences of photonic crystals composition structures on photonic band gap has been firstly discussed. Through discussion, we concluded that photonic-crystals band-gap has a very strong relation to the relative permittivity, the unit shape of photonic crystals, and the lattice structure. And the duty ratio of the photonic crystal dielectric materials also have marvelous influence on the band gap size. Last but not the least, the coupling relation between the bus waveguide and the resonant cavity has been discussed, and according to the time-domain coupled-mode theory, transmission coefficient expression of each port has been derived. Then the coupling relation between the bus waveguides and symmetrical resonant cavities has been discussed. According to the discussion above, the structure parameters of photonic crystal filters has been obtained when the biggest transmission coefficient is satified. According to the discussion all above, a square-lattice four-channel photonic-crystal symmetrical filter has been designed.