Electromagnetic Field Eigenvalue Problem. Fdtd Method Applied Research

Based on the introduction of the principle and development of the finite difference time domain (FDTD) method, the application of FDTD method in the electromagnetic eigenvalue problem is investigated theoretically and numerically. The brief researches are as follows:The reason of mode missing in FDTD computation, which is analyzed by the electromagnetic field modal distribution theory, is that the positions of excitation sources and recording points are located at the null field points. As examples, the null field points of rectangular and cylindrical cavities are given. To avoid that the excitation source and recording points are located at null field points in arbitrary resonator, a new method that the multi-excitation and multi-recording points should be randomly set in the FDTD computational field domain is proposed, and the validity has been demonstrated by the numerical examples.As the method that FDTD combines with the fast Fourier transformation (FFT)\Pade approximation is sensitive to inputting data, and hardly obtains the accurate results, a new method based on Grubbs criterion and Gaussian distribution theory is proposed to avoid the default, and the proposed method has been validated by numerical examples.The formula of the full-wave analysis of fin-line by the FDTD method has been deduced. With the help of the deduced formula, one can finish the full-wave analysis of fin-line from the cut-off frequencies of unloaded and dielectric-loaded fine-line, and numerical examples, unilateral and bilateral fin-line, are given to validate the proposed method.A new two-dimensional (2-D) FDTD method is proposed for analyzing the three-dimensional (3-D) dielectric loaded cavity that is uniform in z-direction and has an arbitrary cross-section in x-y plane, the 2-D FDTD formulas have been derived from the Maxwell's curl equations, and the processing method of effective dielectric parameter is also given. As a validation, the resonant frequency and quality factors of three dielectric-loaded cavities have been computed, and the before and after processing dielectric distributions are compared in the pictures.By assuming the dielectric tensor, an uniaxial anisotropic absorbing boundary (UPML) corresponding to 2-D FDTD is derived from the Maxwell's curl equations. An auxiliary differential equation approach is used to obtain an efficient formulation, which can divide assuming tensor and real dielectric parameters to different equations. Then, the 3-D unbounded problem can be simulated by the proposed 2-D FDTD combining with the UPML. To validate the proposed method, the resonant frequencies of three parallel-plate dielectric resonators have been given to show the accuracy and flexibility.