Designing Photonic Crystal With Large Absolute Band Gap And Superlens Imaging Of Planar Photonic Crystal

As a carrier of energy and information, photons have the performance of huge capacity, high speed, interference-free, low power and so on. Thus people intend to make a kind of integrated optics circuit to control the photons. Photonic crystals, which express the basis elements of integrated optics circuit, are proposed to meet this need, and have attracted great interest.Photonic crystals are a kind of optical material whose refractive index is periodically modulated. Due to their unique properties, such as photonic localization and photonic band-gap, photonic crystal has attracted much attention since they were proposed in1980s. Now their theoretical basis is almost consummate, so that the researches focus on designing of photonic crystals devices for special applications.In the background, the thesis researches the achievement of large complete band gap of photonic crystal and the negative refraction in two-dimensional photonic crystals. And the primary research and achievement are as follows:1. A novel two-dimensional complex photonic crystal with dielectric rods and veins in square and honeycomb lattice is presented to achieve large complete band gaps. The rods with different symmetries, shapes, orientations, and sizes are investigated numerically. The sizes of gaps are intensively affected by these geometric parameters. Extremely large gaps are realized by the parameter optimization with gallium arsenide material. The scattering of veins is more dominant than that of rods which demonstrates the validity of the complex photonic crystal structures. Furthermore, an excellent wide region of dielectric rods and veins, where the sizes of gaps are universally large, is found in square and honeycomb lattice, respectively.2. A two-dimensional anisotropic annular photonic crystal slab structure composed of circular air holes and dielectric rods with finite thickness in a triangular lattice is presented to achieve an absolute photonic band gap. Positive uniaxial crystal Tellurium is introduced to the structure with the extraordinary axis parallel to the extension direction of rods. The role of each geometric parameter is investigated by employing the conjugate-gradient method. A large mid-gap ratio is realized by the parameter optimization. A flat band called as anomalous group velocity within two large gaps is discovered and can be widely applied in many fields. A hybrid structure with GaAs slab and Te rods is designed to achieve a large gap and demonstrates that the annular structure can improve the gap effectively.3. The left-handed behavior of a photonic crystal flat lens with graded-index in honeycomb lattice is proposed and theoretically studied. The performance of flat superlens imaging of this structure has been demonstrated by the FDTD simulations. The FWHM of image decreases to62%comparing to that of the image of PC slab without graded-index. The evanescent waves can be amplified and propagate to far field range. The image is not limited besides the interface. The canalization effect of this structure is analyzed and the tolerance of edge cut of the graded-index structure is pretty well.4. The resolution of imaging is limited by the missing of high-frequencies information. The superlens employing negative refraction can compensate these components. But for the Directional coupling of Bloch waves and the low coupling efficiency of large-angle waves, the resolution of sub-wavelength imaging is not satisfactory. However, the sub-wavelength metallic grating can produce high-order diffracted waves carrying a lot of high-frequencies information. Therefore, this structure is used to inhibit the0-order diffraction and enhance the high-order diffraction to achieve super-resolution.5. The resolution of imaging is limited by the missing of high-frequencies information. However, these information can be amplified by the metamaterial or surface plasmon polaritons. A silver film having sub-wavelength slit sandwiched between a front grating similar to Fresnel zone plate and back grating, are proposed to realize super-resolution imaging. We choose a wavelength in which the surface plasmon polaritons can be excited and negative refraction imaging can be implemented synchronously. By the numerical simulations, a fine image can be actualized within several wavelengths distance from the silver film.6. A fast algorithm for chirp Z-transforms is improved form chirp Z transforms, which is developed by using two fast Fourier transforms(FFT) and an analytical Gaussian kernel. Its computational complexity is better than a fast convolution algorithm. The algorithm can unify the numerical calculations of the responses of many physical systems such as Fresnel transforms and fractional Fourier transforms. Besides, we can freely choose the sampling numbers in both x space (signal domain) and v space (response domain) under the restriction of the Nyquist theorem, so it can zoom in on any portion of the data of interest or study the fine structures of some chirp systems, for example, near-field diffraction. However, there are some problems when the algorithm is implemented, such as the discarding of the data, the smallness of the response domain, the bigness of the computational complexity and so on. To avoid the problem mentioned formerly, we make a change on the implementing of the algorithm in this paper. Then we compared the numerical results of some chirp systems with the analytical ones. The accuracy of Fourier transforms of Gauss function is higher than the order10-15for most cases, and the accuracy of Fourier transforms of rectangle function is about the order10-3which is essentially limited by the accuracy of the fast Fourier transforms. At the last, this algorithm is used to calculate some typical systems of scalar diffraction and fractional-order Fourier transforms, and the results are in good agreement with other literatures.