Research Of The Beam Propagation In The Periodic Microstructure Materials And Their Applications

With the rapid development of the nanoscale technic and integrated optics, theperiodic structures, utilized as a new type of optical elements, have attractedincreasing interest because some novel merits arise when the devices are reduced tosubwavelength scale. Combined with other devices, the periodic structure in nanosize has made great contributions to the optical networks and photoelectric detectiveequipment. As the most important representation of this category, one-dimensionalphotonic crystal (1D PC) and planar grating have obtained outstanding performancein the application of local electric field enhancement, optical limiting, all-opticalswitch, optical logic gate and optical filters. In this dissertation, considering the wayof modulation from the periodic structure to light beam, we organize the contents byregarding the pattern of interaction between them. Firstly, we focus on the features ofthe light propagating through the linear or nonlinear one-dimensional photonic crystal.Then, the attention is paid to the interaction between the light beam and planardielectric grating. Last, the diffraction theory of the single layer grating will beextended to that of the multiple layers, even the two-dimensional photonic crystalstructure. The details are descripted as follows:(1) By the transfer matrix method, the dependence of the transmittance andphotonic band gap on the parameters of the structure, such as the number of periods,contrast of the refractive indices and optical thickness of the materials is studied. Theimpact of the incident angle and polarization state on the photonic band gap is alsorespectively analyzed. The properties of the1D PC with defect have beeninvestigated, such as the location of the defect mode, the optical enhancement in thedefect layer. It is revealed that the defect mode can move correspondingly towards thelower frequency by increasing the thickness of the defect layer. The opticalenhancement in the photonic crystal is mostly determined by the number of periods.(2) Based on the Z-scan theory of thin film, a novel Z-scan theory forone-dimensional nonlinear photonic crystal is proposed. The dependence of the Z-scan characteristics of the periodic nonlinear1D PC on the optical gain andinduced absorption are analyzed. We discussed the Z-scan characteristics of1D PCwith defect layer. The nonlinear optical effect of the defect is the dominativecontribution to the Z-scan results near the defect mode. The impact of the thicknessand nonlinear coefficient of the defect layer is also analyzed. We presented acomposite optical limiter formed by a1D PC and a thick bulk material. Thetransmission and optical limiting properties of the composite structure are analyzed.(3) Considering the inverse rule for fast Fourier factorization (FFF), anumerically stable and efficient implementation of the rigorous couple-waveapproach (RCWA) of the rectangular grating is presented for both TE mod and TMmode. A triple-layer guided-mode resonance (GMR) Brewster filter consisting of ahomogeneous layer and two identical gratings with their refractive indices equal tothat of the homogeneous layer is presented. The spectral properties of this filter areanalyzed at Brewster angle for a TM-polarized wave, and a narrow reflectance peakcan be obtained near wavelength of800m.(4) We studied the problem of convergence of the nonuniform grating layerunder TM polarization, and the rigorous coupled-wave approach cooperating withdecomposition of electric filed along the grating profile is introduced. The theory isapplied to analyze the diffraction properties of two-dimensional photonic crystal withcylindrical rods as the cell. The photonic band-gap is obtained for both TE and TMpolarizations. The characteristic of photonic band-gap and broad band filter can beoptimized by adjusting the parameters of the structures.