Frequency Band Structures Of Metal/Dielectric Photonic Crystals Analyzed By The Method Of Interfacial Operator And The Method Of Homotopy

In this thesis,we apply the method of interfacial operator along with the method of homotopy to study the band structures of the lossy metal/dielectric photonic crystals.The approach consists of two steps:(1)First,consider the(non-lossy)free electron gas model.Solving for the band structures in both TM and TE modes by the method of interfacial operator,we obtain the photonic band structures of the non-lossy metallic photonic crystals.(2)Then,consider the(lossy)Drude model for the metal.The method of homotopy starts from each frequency band obtained for the free-electron model,progressively iterating it to yield the corresponding frequency band of the lossy metal/dielectric photonic crystal.Each frequency is a complex number;the imaginary part of it signifies attenuation.The main content of this thesis contains two parts with a synopsis depicted below:(?)One-dimensional metal/dielectric photonic crystals:(1)The metal dielectric function of free electron gas model.By controlling variables,qualitative and respectively study the influence of metal materials,dielectric constant,metal layer filling rate,photonic crystal's reciprocal lattice vector and propagation constant on the band structures and the dispersion relations.Compared with the photonic band structures and dispersion relations of Ag/air and Cu/air,After the coordinate unit is normalized,the curves of the two structures are the same.It is corresponding by comparing the results of Ag/air and Ag/fused-silicon with the theoretical results,so the frequency of electromagnetic wave in SPPs mode can be controlled by adjusting the dielectric constant.The larger the filling ratio of the metal layer,the greater the cut-off frequency of the band.The larger the propagation constant,the lower the influence of the low frequency band curves.The influence of the reciprocal lattice vector on the dispersion curves is small.(2)The metal dielectric function in the Drude model.The attenuation of electromagnetic wave propagation in Ag/air photonic crystals is calculated by using the homotopy method.For the band gap width and the position of the band gap,because the difference between the imaginary part and the real part of the dielectric function is about 2 orders of magnitude,there are no obvious difference between using the free electron gas model and the Drude model.(?)Two-dimensional metal/dielectric photonic crystals:The TE and TM modes all have the lowest cut-off frequency in the right triangular cylinder structure.For both the square cylinder structure and right triangular cylinder structure,There is a maximum loss at the surface plasmon frequency.When the frequency is higher or lower than the surface plasma frequency,the loss will decrease rapidly.And the loss will be changed by varying the reciprocal lattice vector.For the band gap width or position in free electron gas model and Drude model,there is no obvious difference.It is same as the condition of one dimensional.The interfacial operator approach complemented by the homotopy method has been demonstrated to be a powerful tool for studying the frequency band structures of the lossy metal/dielectric photonic crystals.