Study And Application Of Fdtd Method In Optical Fiber

In this paper, the application of finite-difference time-domain (FDTD) method modeling to analyze some propagating properties of optical fiber is studied. The development and applications of FDTD method are summarized. Then, the principle of FDTD method in Cartesian coordinate and cylindrical coordinate systems, especially for singularity processing in cylindrical coordinate, is expounded. Further, some practical problems of FDTD computation are studied: the setting of absorbing boundary condition (ABC) and incident wave, numerical dispersion and error analysis. Based on the perfectly matched layer (PML) absorbing boundary condition, a new form of PML absorbing boundary condition in cylindrical coordinate suitable for optical fiber is derived. The key point of this paper made a study of the application of FDTD method to dispersive, nonlinear materials. Two methods are introduced to deal with the relationship between the electric flux density vector and the electric field vector: auxiliary differential equation (ADE) method and Z transform method. The auxiliary differential equation of wave propagation in multiple Lorentz-dispersive and nonlinear media is derived. After the study of the optical pulse propagating in silica optical fiber, the best electric intensities for this material with different length are obtained. Furthermore, The frequency-domain relationship between the electric flux density and the electric field is managed with the Z transform, which is of frequent use for digital filtering and signal processing. The optical pulse propagating in nonlinear and dispersive media is analyzed with Z transform, which is simpler than with auxiliary differential equation method.