Wave Localization Properties At The Dirac Frequency In 2D And Quasi-2D Photonic Crystals

2D materials have attracted a great deal of researchers' interests due to their unique properties,one of the most fascinating features is the Dirac point in the electronic band structure of graphene which has a conical singularity with linearly vanishing density of states and linear dispersion in its vicinity.In recent years,more and more people have investigated the Dirac points in photonic crystals due to their unusual dispersion relations,including Klein tunneling,Zitterbewegung,and pseudo-diffusive transmission.Meanwhile,a new kind of light confinement and guided mechanism at the Dirac frequency comes into being,which is quite different from the traditional photonic bandgap or total internal reflection theory.Moreover,these Dirac localized/guided modes can exhibit unique algebraic profiles,as a new quasi-quantum effect in photonic crystals,which will add new capabilities and more flexibility to the design techniques of novel photonic components,photonic chips and optical sensors.In this thesis,by means of theoretical analysis,numerical calculations and microwave experiment,the properties of Dirac cones,localized modes and related features at the Dirac frequency in different wavebands,different lattice types,dispersive/non-dispersive materials,2D/quasi-2D photonic crystals are studied in depth,which enriches the diversity of the theory.The main research works and results are summarized as follows:1)Numerical simulations and experimental analysis of localized Dirac mode in dielectric photonic crystals.A novel kind of localized Dirac mode in a TE polarized triangular photonic crystal is introduced which has high quality factor,slow decay rate with an algebraic form and stable standing wave properties.The small refractive index difference approximation method is performed on a TM polarized triangular lattice photonic crystal to analyze the degeneracy of the corner points of the Brillouin zone and the dispersion properties around these points.It's derived to get that the TM mode of the triangular lattice photonic crystal with defects is completely similar with that of the TE mode,which supports localization features at the Dirac frequency.By using numerical methods to calculate the TM localized Dirac modes and verify their features,it can be found that the related simulation results and theoretical analysis are consistent.The localized Dirac modes in complex lattice photonic crystals such as honeycomb lattice,Kagome lattice and A7 lattice are also discussed,which enrich the diversity of the theory and provide a variety of choices for the fabrication of new guiding wave devices with excellent performance.2)Microwave measurement of the localized Dirac mode in a photonic crystal resonator.A 2D microwave photonic crystal with a defect in the center is designed,and its cavity mode at the the Dirac frequency is calculated.The unique properties of this mode are explained.The experiment is handled to measure the transmission spectrum with and without defects.It is found that a resonant peak occurs at the Dirac frequency only when a defect is introduced.The frequency of the peak does not shift when the incident wave changes direction.Due to this testing configuration will not excite any edge modes,the experiment validates the existence of a localized mode,namely the localized Dirac modes.Although the experiment is carried out in the microwave frequency range,the conclusion can be extended to other electromagnetic bands according to the proportional scaling characteristics of photonic crystals.3)Numerical simulations and theoretical analysis of localized Dirac mode in metallic photonic crystals.The bandstructure calculation method of a metallic(dispersive medium)photonic crystal containing loss is derived,which can be extended to various simplified models such as photonic crystals without loss or containing non-dispersive materials.The small refractive index difference approximation method is performed on a TM polarized triangular lattice metallic photonic crystal to analyze the degeneracy of the corner points of the Brillouin zone and the dispersion properties around these points.The TM polarization Dirac frequency localization characteristics of triangular lattice metallic photonic crystals with defects in optical band and TE/TM Dirac localization characteristics of metallic photonic crystals with various types of defects in microwave band are derived.All of the theoretical predictions are verified by numerical simulations,and have a good fit with each other.The tunable localized Dirac mode in frequency is realized by filling plasma into the background of metallic cylinder-type photonic crystal.Although the dielectric functions of metals,the dispersive media,depend on the electromagnetic wave frequency,it is found that the photonic crystal resonator composed of metallic media can also support localized Dirac modes,showing the same properties with dielectric photonic crystal cavities.It will provide helps to extend the applications of new optical devices.4)Numerical simulations and theoretical analysis of localized Dirac mode in photonic crystal slabs.The relationship between the slab modes and ordinary 2D photonic crystal modes is studied.The small refractive index difference approximation method is performed on a triangular lattice photonic crystal slab to analyze the degeneracy of the corner points of the Brillouin zone and the dispersion properties around these points.It is shown that TE-like Dirac cone can be found in a photonic crystal slab,and the Dirac cone can be obtained by lifting the frequency of the Dirac cone of the corresponding 2D photonic crystal.The localization characteristics at the Dirac frequency are analyzed and the influence of slab thickness of the localized Dirac mode is discussed.Because the photonic crystal slab has more practical significance in the actual design,processing and application,it will provide favorable supports to the utilization of this novel device.