Input And Output Coupling Properties Of Two Deimensional Photonic Crystal Waveguides

With the developments of theory and technology of nano-structures, sub-wavelengthphotonic structures are widely investigated, and a solid foundation for all-optic systemhas been founded. However, with the decreasing of volumes of photonic elements, theinput and out coupling become more and more difficult, which is becoming a bottle-neckof modern nano photonics. In this thesis, using theoretical analysis, and full-vector nu-merical simulation methods, the input and output coupling properties of photonic crystalwaveguides are investigated. We aim to explore high efficient input and directional outputmethods, and provide valuable results to the modern nano-photonics.A highly efficient directional output mechanism based on cascaded photonic crystal(PC) waveguide and self-collimated PC structures is proposed and investigated both the-oretically and numerically using the finite-difference time-domain (FDTD) method. Weanalyze the transmission properties of the PC waveguide, and those of the self-collimationbeams in the cascading PC. Then a frequency matching method is used to find properstructures for directional emission, and highly directional beaming is obtained numeri-cally. Results show that the output efficiency is about 80%, and divergence angle lessthan 6?. We systematically investigate the effects of the structural parameters on thecoupling efficiency, which include the thickness, width of the cascading layers, and alsothe coupling intensity between the WG and the cascading layers. We then introduce anarbitrary curving the cascading layers, and investigate the effect of curvature radius onthe directional beaming. We find that a positive curvature makes the beaming distanceshorter, and highly focused at near field region. However, a minus curvature enlargesthe directional distance. The bandwidth of the directional emission is also investigated,and results show that, for the specific structure investigated in this thesis, within a rela-tive bandwidth of 2.4% near the self-collimation frequency, all the frequencies can realizedirectional emission.The mechanism of multiple directional emission of PC waveguide is investigated.By analyzing the directional emission process of PC waveguide, we find that the distribu-tion of the effective sources on the surface determines the emission profile of the beam.An interference model of multiple coherent point source is developed to describe this phe- nomena, which is verified by numerical results. Two structures of discretely modulatedexit surface, and multiple waveguide branch are investigated in detail to realize multipledirectional emission. Results shows that, using these two structures, one can obtain Nb(Nb = 1, 2,···) directional beams, also Nb, and the divergence angle are predicted ex-actly using the interference model. When coupled with traditional dielectric waveguides,a high efficiency 1 ? Nb power splitter is numerically realized. The emission propertiesof asymmetric structures are also investigated. Results show that the divergence angleis smaller, and the structure is more simple, and also the loss is less than the symmetri-cal ones. Due to the asymmetric property, the signals with different frequencies are alsofiltered in space when directionally emitted from the waveguide.A highly efficient input mechanism based on spherical lens made of negative re-fractive index (NRI) material is proposed and investigated theoretically and numericallyusing FDTD method. Using the SRR (split ring resonator) and rod model of NRI mate-rial, high efficiency input coupling between a wide beam (with a waist width of 16λ0) anda sub-wavelength PC waveguide (with a width of 0.5λ0) is realized (λ0 is the wavelengthin vacuum). The coupling efficiency is more than 93%, and the thickness of the coupleris only (4～6)λ0. Using the Snell’s law of NRI material, we derive a focusing lengthformula, and investigate the changes with incident angle. We find the focusing propertiesof the lens to wide parallel beams, which is difference with the ?at NRI lens. We sys-tematically investigate the effects of incident frequency, de?ection angle, and transverseshift of the beam on the coupling efficiency, and also make a comparison with those of atraditional lens made of positive refraction. Our results show that the advantages of NRIlens coupler lies in the smaller size, and higher efficiency. When the NRI lens coupler ismade of photonic crystal, but not SRR/Rod structure, we investigate the profiles of equalfrequency surface, and effective negative refraction of an designed triangle lattice PCstructure. A NRI lens made of PC is proposed, and the coupling properties is investigatedand compared with those of SRR/Rod model.