Study On The Reflectivity And The Surface States Of Semi-infinite 1D Photonic Crystals Containing Negative Refractive Materials

Photonic crystals are periodically arranged dielectric structures or metal-dielectric structures, whose periodicity is on the scale of the wavelength of the wave involved, and the essential property of the photonic crystals is the photonic bandgaps. The propagation of electromagnetic waves with frequencies in the gap is forbidden, which can be used to control the propagation of photons. The transmission of the photons in photonic crystals is dependent on the properties of the component materials, so the photonic crystals composed of negative refractive materials may bring about a variety of new transmission properties of the photons.Although "infinite" is an ideal model, it is simple and plays an important role in the fundamental theories and applications. If the period arrangement is only along one dimension, the relation between energy and the Bloch wave number can be simply expressed by cosβd = 1/2TrU, where U is the transfer matrix across the elementary unit cell, using the equation we can predict the range of the allowed energy.The wave in the infinite periodic structure is the Bloch-type wave, which has not any allowed mode in the band gaps. But in the semi-infinite structure with a surface, the boundary condition at the surface leads to the solutions with imaginary Bloch wave number, due to the destroy of the exact translational symmetry. Surface states will exist in the photonic band gaps. The electromagnetic(EM) field decays rapidly along the normal direction going away from the surface.Since negative refractive materials possess many unique EM properties, there are a lot of new types of band gaps in the photonic crystals containing metamaterials. Unlike ordinary materials, the surface states are sensitive to the negative refractive materials. They may change positions in the band gaps. All these properties have new applications to control the propagation of photons. In this thesis, based on the Bloch theorem, and by means of numerical stimulations and theoretical analysis, we investigate the reflection on the semi-infinite periodic one-dimensional photonic crystals containing negative refractive materials, and the dispersion behaviour of localized surface states supported in the surface of that. The major contents and important results are given as follows.If the number of the 1D photonic crystal's layer is sufficient large, the reflectivity will rapidly oscillate in the pass band. The oscillation may become smooth for the rough interface, the thickness fluctuation, and the absorption of the medium and so on. The reflectivity measured is different from reflectivity calculated according to the ideal situation. So we give a simple formula to calculate the complex reflection coefficient for the wave incident on a semi-infinite periodic structure. We calculate the reflectivity on the semi-infinite periodic one-dimensional photonic crystals composed of alternate layers of ordinary materials and negative refractive materials. We find that the reflectivity is exactly equal to 1 in the forbidden frequency gap, and in the pass band, it averages out the rapid fluctuation of reflection of the finite structure. When the optical thickness of both ordinary materials and negative refractive materials are in opposite sign, there will be a zero- (n|-) band gap. We analytically proved that the zero- (n|-) band gap is insensitive to incident angle and polarization, and it is also invariant with the scaling of lattice constant. We also analyse its physical mechanisms. In addition, we investigate the property of zero- (n|-) band gap in a quasiperiod Fibonacci semi-infinite structures. It is found that when the Fibonacci sequence is sufficient large, as to be regard as the semi-infinite structures, the zero-(n|-) band gap become stabilized, with fixed gap positions and sizes.Besides, we investigate the dispersion behaviour of localized surface states supported in the surface of a semi-infinite one-dimensional photonic crystals, when the cap layer's optical parameters change. Firstly, when the photonic crystals are adjacent to an dispersive medium background, by increasing the thickness of the cap layer, we find that the surface states are very sensitive to the thickness of the cap layer, under the condition that the average refractive index equals zero. There will be surface states with negative group velocity, when the thickness of the cap layer are at suitable values. We also analyse the dispersion behaviour of localized surface states supported in the surface of a semi-infinite one-dimensional photonic crystals truncated with a thin nonlinear cap layer, which can be regard as aδfunction and satisfys Kerr nonlinearity. We find that the surface states are very sensitive to the nonlinearity of the cap layer on the surface.