Numerical Simulation And Characteristics Analysis Of Photonic Crystal Fibers

Since St. J. Russell proposed the conception of photonic crystal fibers, PCFs, a lot of universities and institutes have been spending great deal of manpower and material resource on the theory and application research for the PCFs. The PCFs are a new kind of optical fibers that employ the structured arrangement of the photonic crystals (PC). The results of theory and experimentation show that the PCFs have many unique optical characteristics, such as endless single mode, manipulable mode areas, flexible dispersions and high non-linear. PCFs are a new developing direction of the optical fiber technology and they would have good application prospects in the special fibers and photonic & electronic devices. Because of the structural character, PCFs guide light using two quit different mechanisms, viz. total internal reflection and photonic band gap effects. The total internal reflection PCFs are analogous to the conventional fibers in mechanisms of guiding light, with a little difference. Photonic band gap PCFs are of a new guidance mechanism, which is unique to the PBG-PCFs'periodic construction medium. When the scale length of the medium is comparative with the wavelength, photonic band gap will be formed in the periodic medium. If a line defection is introduced, certain frequency optical rays will be located in the defection region and transmit along the defection. For the different mechanisms of guiding light, PCFs have many new features referred in the first paragraph. For the different operation mechanism, the analysis methods of PCFs are different from each other, which are more complex compared with the conventional fibers. Since the PCFs'appear, people are looking for simple, rapid and effective methods to deal with the PCFs. In this process lots of methods are presented, such as the effective reflective index approach, plane-wave expansion method, Finite-Difference Time-Domain method (FDTD) and Finite-Element method. In this paper, the orthogonal functions model is employed to modeling PCFs. On the basis of further studying to the theory of electromagnetic wave, we set up the eigenfunctions in form of matrix by the method of expanding electric field and refractive index function in the wave equation, and the detailed steps of solving the eigenfunctions were introduced too. Based on this orthogonal functions model, we analyzed some transmission features of the TIR-PCFs in details, such as the mode features and dispersion characteristics, having achieved some useful conclusions. And the scale property of waveguide dispersion in PCFs was deduced by a mathematic method, which is very important during the process of the PCFs'dispersion designing.