Research On Band Structure Of Photonic Crystal With Lossy And Dispersive Materials

Band structure is the basis of photonic crystal for theoretical research and practical application. The most important property of photonic crystal is photonic band gap. Electromagnetic wave can’t propagate when its frequency is among the range of photonic band gap. With the study of photonic crystal, some progress has been made on research about photonic crystal with constant permittivity material. However, most of the materials are lossy and dispersive materials. Hence, effectively solving the band structure of photonic crystal with lossy and dispersive materials is urgent needs to solve. In this thesis, we get the photonic crystal equation of TE mode and TM mode from the Maxwell equations, and we solve the band structure of photonic crystal with lossy and dispersive materials along the irreducible brillouin zone by using Finite Element Method which the eigenvalue is the Bloch wavevector k. The numerical results show that our method is effective. Compared with other methods, the proposed method can calculate the band structure and eigenmode of photonic crystal with lossy and dispersive materials more effectively.Specifically, main contents of this thesis are as follows:The finite element method is introduced to calculate the band structure of lossy and dispersive photonic crystals. By using this method, the calculation of band structure is reduced to a quadratic eigenvalue problem which the eigenvalue is the Bloch wavevector k. Firstly, the calculation of band structure of photonic crystals with dielectric material with square lattice and triangular lattice demonstrated the accuracy of the method. Secondly, the calculation of band structure of dielectric photonic crystals and nine-scatterer photonic crystal show the application of the method. Finally, the dispersion relation of the lossy and lossless photonic crystals is also obtained by the proposed method. The surface plasmon polarizations of dispersive material effects on the band structure and on the field distribution are analyzed. The results provide theoretical basis and reference for studying the lossy photonic crystals and surface plasmon polarizations.