Research on Optical Property of 1D Photonic Crystal Containing Negative Index Materials

Photonic crystals (PC) are artificially composed of two or more dielectrics arrangedperiodically. The basic characteristic for photonic crystals is its photonic band gap.Consequently, it provides a good way to manipulate the propagation of photons whichis analogous to the case of electrons in the semiconductor. Since Photonic crystalshave many novel physical properties, it have many potential applications infabricating new type of optical devices.In recent years, a complicated artificial material with negative refraction index hasattracted much attention theoretically and experimentally. If we consider photoniccrystals containing negative refraction index, we will get many new transportationphenomena. Much attention has been attracted to the photonic crystals with left-handmaterials. In this thesis, we make theoretical research on the behavior of light propagation inone dimensional photonic crystals containing negative refraction materials. Manyunique features of light propgation are expected in this structure.We consider one-dimensional photonic crystal coupled-resonator containing defectlayers with negative refractive index. By using the condition that the tangentialcomponents of electromagnetic field and its first derivative are continuous across theinterface, we can get the transfer matrix for normal photonic crystal. We let negativematerials to be defect layers,then obtain the new form of transfer matrix. According totransfer matrix, the recursion relations of the transfer matrix elements are derived tocalculate the transmission of our model. By numerical simulation, we find that whenthe refractive index of defects is changed, the coupling effect between the defectmodes is varied, which results in the change of the impurity band. Some sharptransmission peaks and a wide pass band appear at the same time in the forbiddenband when the refractive index of defects is appopriate.Except the research above, The optical properties of 1D photonic crystals with anepsilon-negative (ENG) material and a mu-negative (MNG) material was investigatedby the transfermatrix theory. With suit parameters of defect layers, the transmittance isindependent of the thickness of defect layers, The reason is the transfermatrix of thepair defect is an unit matrix. The electromagnetic field inside defect layers hasenhanced exponentially by increasing the thickness of defect layers. It is much morestrongly localized than that in the vacuum.Then, we consider the model with normal materials and dispersive materials. Bynumerical simulation, we find there are two band gaps, (?)=0 band gap and Bragggap. Comparing with the Bragg gap, the new band gap is less sensitive to the incidentangle and the polarization. So we also call this (?)=0 band gap omni-directionalband gap. Since we change the incident angle, a new type of band gap forms. It hasnew optical properties, being different from (?)=0 band gap. With the increasing ofthe incident angle, the band gap widen to both sides of the freqencey (?)≌1.Based on the research above, we discuss the dispersive material instead of thenegative medium by using Drude mode. We also get the transfer matrix and theexpression of transmission. For dispersive materials, its permittivity and permeabilityis modulated. With suit parameters of defect layers, the transmittance is alsoindependent of the thickness of defect layers. The electromagnetic field inside defectlayers has enhanced exponentially by increasing the thickness of defect layers too. Then,the transmission and the field distributions of 1D photonic heterostructureswith single negative material was investigated by the transfermatrix theory. With suitparameters, the average permittivity and the average permeability is zero. A completetransmission peak exist in theforbidden gap. The electromagnetic field has enhancedstrongly at the interface. And the peak doesn’t move when the incident anglechanges.The reason is the transfermatrix of the is an unit matrix on the zero averagepermittivity and the zero average permeability conditions.