Study On Two Dimensional Photonic Crystals And Left-Handed Materials

Presently, photonic crystals (PCs) and left-handed materials (LHMs) are hot research interests for they have intensively potential applications in the fields of optics and microwave. Two dimensional photonic crystals are paid more attention for its easy fabrication, wide applications and various defects that can be incorporated in contrast with three dimensional photonic crystals. However, the study on the theory and application of photonic crystals and left-handed materials is at its initial stage. Great efforts should be put into the research on the theoretical analysis, numerical methods and actual applications of photonic crystals and left handed materials. In this thesis, a new method named T-matrix method is introduced, the negative refraction of photonic crystals and left handed materials is studied, and the application of photonic crystals on slotted waveguide array is explored. The work of the author is mainly focused on:1. The author learns and masters the plane wave method and the finite difference time domain method to calculate the band structure and transmission coefficients of the photonic crystals.2. The T-matrix method is successfully applied to the analysis of two dimensional crystals. The T-matrix method can be used to analyze the scattering of PCs made of periodic arrays of perfectly electric conductor cylinders and dielectric cylinders. It can also be applied to the analysis of photonic crystals embedded in a dielectric slab and finite photonic crystals with or without defects. The T-matrix method is firstly introduced to the analysis of photonic crystals made of gyrotropic cylinders by the author and can be extended to the analysis of photonic crystals made of other anisotropic cylinders.3. The analysis method of a Gaussian beam impinging on a photonic crystal is presented. The method combined with the T-matrix method can be used to analyze the scattering of many types of two dimensional photonic crystals. This analysis method can also be extended to other beams incident on photonic crystals.4. It is interpreted that a wave undergoes negative refraction at the interface of a right-handed material and a left-handed material only by using the boundary conditions and the physical meaning. The reflection and refraction coefficients of the reflected and refracted wave are derived. The theory shows that the wave obeys the Snell's law and the Fresnel's law with a negative index of refraction.5. The negative refraction of photonic crystals is discussed. It is pointed out that one can define an effective refractive index of the photonic crystal when the equal frequency surface approaches circular. The effective refraction index of the photonic crystal can be less than unity or negative. However, it is found that possessing a negative effective index of refraction is not a prerequisite for negative refraction of a photonic crystal.6. The application of photonic crystals to slotted phased waveguide array is explored. The high impedance electromagnetic surface is adopted in our research. The design method of the high impedance electromagnetic surface and the edge-slotted phased guide array is shown. The experimental results are given and from which we draw some useful conclusions.