Research Of Negative Refraction In Photonic Crystal And Mode Characteristics Of Anisotropic Cylindrical Optical Microcavity

As a carrier of information and energy, photon has a high speed, huge capability, and low power, and is interference-free. Therefore people intend to make a kind of integrated optics circuit to control the photons. Photonic crystals and optical microcavtity, which are the basis elements of integrated optics circuit, are proposed to meet this need, and have attracted an increasing interest of scientists.Photonic crystal is a kind of optical media whose refractive index is periodically modulated. Due to its unique properties, such as photonic band-gap and photonic localization, photonic crystal has received a lot of attention since it was proposed in 1980s. Today their theoretical basis is almost consummate, and the research focus is designing of photonic crystals devices with special function.Optical microcavity is those cavities with dimension of optical wavelength in one direction at least. They have important potential in many field including quantum computing, sensor, low-threshold narrow-line-width laser and full optical communication filter. Now the researchers are trying to design microcavities with high quality factor, a small mode-volume, directional emission, no mode degeneracy and tunability.In the above background, this thesis studies the negative refraction in two-dimensional photonic crystals, and the mode character of cylindrical microcavity made of electric anisotropic medium. The primary research and achievement are as follows:1. The influence of radius-error and position-error of dielectric-rod on the properties of beam splitter, which is based on positive-negative refraction within a single band in a two dimensional photonic crystal, were both investigated by the frequency-difference time-domain method, respectively. This study is instructive to fabricate the photonic crystal devices experimentally.2. In order to solve the drawbacks of beam splitter based on positive-negative refraction within a single band in a photonic crystal, positive-negative refraction based on overlapping bands in a two dimensional photonic crystal is proposed and studied by the plane-wave expansion method, the equifrequency contours method and the finite-difference time-domain method. In the later positive-negative refraction effect, the transmittance is improved in respect that there is only one reflected beam in traditional reflective direction at both input interface and output interface. Either positive or negative refracted beam launching onto the output interface will excite only one transmitted beam in air. Therefore it will be more convenient to receive these transmitted beams or couple them into the next optical devices. Since negative and positive refraction is induced by the second and third band, respectively and separately, the beam splitter based on this effect has a flexible incident angle to operate properly, and its splitting effect can be manipulated by adjusting the incident angle. In addition, this thought provides a novel mechanism to control light propagation by overlapping bands in photonic crystals.3. A complete numerical simulation system to deal with microcavity made of electric anisotropic medium is explored, including deduced iterative formula of the 2D finite-difference time domain method for electric anisotropic medium in its principal axis coordinate system, and introducing a volume-average effective permittivity approximation to deal with the microcavity boundary, transferring the time-domain signal to accurate spectrum by Pade approximation with Baker's algorithm. The validity of these numerical methods in solving the microcavity problem is demonstrated by the consistency of the analytical solution with the numerical solution for isotropic cylindrical microcavity.4. Cylindrical microcavity made of electric anisotropic medium is proposed, and its mode characters, such as spectrum control, directional emission, and suppression to higher radial number mode, are studied. For this anisotropic cylindrical microcavity, the following conclusions is reached:the resonant frequency for different whispering-gallery modes has a similar shift in direct proportion to the relative difference of two principal refractive indices; The axial symmetry as cylinder geometry configuration have destroyed by anisotropy and thus results to a significant directional emission from the microcavity; The quality factors decay exponentially due to increasing directional emission when the anisotropy increases; The anisotropic microcavity can efficiently suppress those modes with larger radial mode number and thus operates conveniently in single-mode. This novel tuning characteristic of anisotropic cylindrical microcavity will play an important role in many areas, such as low threshold microlaser with tunable wavelength, tunable filter and sensitive sensor.