Design And Study Of Highly Efficient Photonic Crystal Filters

Photonic crystal, proposed simultaneously by E.Yablonovitch and S.John in 1987, is an artificial "band gap" material in which the dielectric constant is arranged periodically. Analogous to the semiconductors considered in solid state theory, photonic crystals are called semiconductors of photons. A photonic crystal is characteristic of "photonic band gap", in which the propagation of electromagnetic wave is highly prohibited. The defects modes can be introduced into the photonic band gap by fabricating carefully designed defects in perfect photonic crystal, and these defects modes are of more plentiful applications, such as photonic crystal fiber, micro resonant cavity etc. Additionally, a photonic crystal can act as a conductor of photons. Additional, photonic crystals can be used as the conductor of photon to produce various optical devices. Compared with optical waveguide devices, photonic crstal devices have small volume and compact structure, and have tremendous application in optical integration chips and optical communication network. Related research have attracted wide attention and become the research forefront of optical communications.Optical filter is the key device in WDM optical communication system to deal with the signal of specific channel or multiple channels. The optical filter design of base on photonic crystal structure has become an important research. At present, though many researchers have been produced many types optical filters using photonic crystals,it needs deeply study to design high efficiency photonic crystal multi-channel filters. How to design highly effective optical filter is primary objective of this thesis. Based on the research of the composed elements of photonic crystal to the crystal characteristics. and in accordance with the time-domain coupled mode theory, the high efficiency coupling condition of between waveguide and resonance cavity has been educed.The square crystal lattice photonic crystal double resonance cavity four-channel optical filter and the triangle crystal lattice photonic crystal four-channel optical filter have been designed, which be simulated using finite-difference time-domain (FDTD) method. The primary factors of influence filter efficiency and the methods of improving the filter efficiency had been discovered by using simulation analysis. Through the improvement parameter's establishment of photonic crystal optical filter structure, filter efficiency of every channel has exceeded 90%.The main contents of the dissertation are given below:1. According to the characteristic of photonic crystal structure (dielectric periodicity distribution), the solution of the Maxwell equation has carried, and the electromagnetic field expression has also been solved in the photonic crystal .the scaling law and time reversal symmetry of photonic crystal have been improved,and the method of photonic band calculation has been educed.A good theory foundation has been obtained for solution photonic crystal.A brief introduction about FDTD (finite-difference time-domain) method is given, and the stable condition and the boundary condition have been discussed. The finite difference equation expression is obtained using the exponential difference format. A brief analysis about time domain coupled mode theory is given, and the coupling efficiency expression is obtained.2. The influence of photonic crystal composition structure to photonic band gap has been first analyzed. Through analysis, we discovered that photonic crystal band gap with the relative permittivity has a very strong relation, and the photonic crystal composition unit's shape, the lattice structure and the dielectric duty ratio also has the very tremendous influence to the band gap size. We can see from the analysis results, the photonic crystal band gap of circular cellular construction is the biggest under the same condition. The photonic crystal band gap of triangle crystal lattice is bigger than the photonic crystal band gap of square crystal lattice. In the photonic crystal of dielectric rod, the dielectric duty ratio is bigger and the band gap is wider. Then the influence of defect resonant cavity dielectric rod radius size to the coupling wave length has been analyzed, through the analysis simulation, we find that the wavelength increased with the defect resonant cavity dielectric rod radius increases and coupling efficiency is about 50% when defect dielectric rod radius is smaller than photonic crystal dielectric rod radius. When the defect dielectric rod radius is bigger than the photonic crystal dielectric rod radius, the coupling wave length is small, and the coupling efficiency is also lower than 20%, therefore, the defect dielectric rod radius is must smaller than the crystal dielectric rod radius when using the dielectric rod structure to carry on the waveguide resonant cavity coupling. Finally, the relations of the defect waveguide with the wave transmission and the method of improvement the coupling efficiency have been analyzed. Through the computation simulation, we find that the transmission efficiency is the highest and the reflect efficiency is the lowest when defect waveguide dielectric rod refractive index is 1.5 or 2.5 times of crystal refractive index. On the contrary, the transmission efficiency is the lowest and the reflect efficiency is the highest when defect waveguide dielectric rod refractive index is the integer times of crystal refractive index. Through the analysis, we also find that the change of defect waveguide edge dielectric rod radius and wave guide's width are advantageous for enhancing the coupling efficiency of waveguide with the resonant cavity.3. The coupling relation of between the resonant cavity and waveguide has been analyzed, and according to the coupled mode theory, transmission coefficient expression of every port has been derived. Then the coupling relation of between the symmetrical resonant cavity and waveguide has been analyzed. According to transmission coefficient expression, the photonic crystal parameter relationship has been obtained when the transmission coefficient is the biggest. According to theoretical analysis results, a square crystal lattice photonic crystal symmetrical four channel filter has been designed. And we have carried on the simulation computation using the FDTD method. According to the analysis conclusion in third chapter, and suitable selection parameters, the filter efficiency of four channels can achieve 96%. The merits of square crystal lattice photonic crystal symmetrical filter are the structure symmetry, simply design and highly filter efficiency. The demerits are that many crystal lattices are need and the structure is big. This design method may be used to manufacture integration photonic crystal multi-channel filter.4. According to the theoretical analysis, we have designed a triangle crystal lattice highly efficient photonic crystal four-channel optical filter, and have carried on the simulation analysis using FDTD method. Looking from the simulation process, it not only needs that the parameter must match with the theoretical analysis, but also needs that we should be flexible selection parameter, defect rod size and position based on the theory to design the highly effective photonic crystal optical filter. Looking from the simulation results, the filter efficiency of multi-channel filters are over 90%. According to the problem in designing, we analyzed the reason of influence filter efficiency, and provide the methods to improve filter efficiency. The merits of this design method are structure simple, manufacture convenient, medium material simple and filter efficiency high. The method provides a very good reference for design and manufacture highly efficient multi-channel photonic crystal filter.The innovations of the dissertation are given below: 1,Through many times simulation, we find that the suitable adjustment the dielectric rod radius between defect waveguide and resonant cavity can be greatly improved the efficiency of coupling. Appling the method to multi-channel filter design, we find that the filter efficiency can improve about 50% when the dielectric rod radius is proportion with ransonant cavity dielectric rod radius. The law has high reference value for design multi-channel photonic crystal filter.2,According to coupled mode theory, we obtained the parameters conditions of high coupling efficiency between waveguide and symmetric resonant cavity. We design a square lattice photonic crystal symmetry resonant cavity four-channel optical filter, the filter efficiency of every channel is high than 96%. The relationship between the channel wavelength and crytal constant is given, and the central wavelength of every channel is around 1550nm when crystal constant is 570nm.The interval of adjacent channel is less than 20nm. A good reference is provided for the design of high efficiency photonic crystal filter.3,According to coupled mode theory, the transmission coefficient expression of between reflective Waveguide and resonant cavity is calculated, and the parameters condition of high coupling efficiency is given. We design a triangle lattice photonic crystal reflective resonant cavity four-channel optical filter, and the filter efficiency of every channel is high than 90%. The central wavelength of every channel is around 1550nm when crystal constant is 550nm.The interval of adjacent channel is less than 20nm. Compared with square lattice photonic crystal filters, the merits of triangle lattice photonic crystal filter have small volume, facility to design and easy to integrated.In summary, this article has not only analyzed the primary factor of influence photonic crystal filter efficiency, and given the design method of improving the filter efficiency, but also designed the square crystal lattice photonic crystal four channel filter and the triangle crystal lattice photonic crystal reflection type four channel filter. The filter efficiency of every channel is over 90%, and the relationship expression of crystal constant and channels wavelength has also given. The article has the very high reference value for design and manufacture highly efficient photonic crystal multi-channel optical filter.