Study On Dirac Points Of Plasmonic Photonic Superlattices And Optical Properties Of Graphene Quantum Dot

Periodic photonic nanostructures based on surface plasmon polaritons(SPPs)have important applications to sub-wavelength concentration of light and optical nanodevices,as the photonic bands are controllable and the SPPs can be confined to nanoscale beyond the diffraction limit.In addition,the existence of photonic Dirac points(DPs)in the bandstructure can enrich the physical properties of plasmonic superlattices.In graphene,its electronic DPs are the origins of many remarkable properties,such as quantum Hall effect,Zitterbewegung effect.Introducing these remarkable properties associated with electronic DPs to optical systems has important future applications for active photonic nanodevices.One of the work of this thesis is to perform a systematic and in-depth study on the DPs of one-dimensional plasmonic superlattices involving with the physical properties,tunability and robustness.Compared with the surface plamons in metals,graphene plasmons are much more confined and lowerloss.In addition,the conductivity of graphene plasmons can be tuned by chemical doping or gate voltages.Consequently,graphene plasmons are emerging as a promising alternative to metal plasmons.However,the classical description of the optical response of nanometer-sized graphene is invalid,as quantum finite-size effects can not be neglected.Another work of this thesis is to mainly study on the optical and plasmonic properties of graphene nano-flakes(GNFs)based on first-principles calculations.The research contents and achievements of this thesis are listed as follows:By inserting graphene sheets into periodic metallodielectric structures,we propose a versatile platform for electrical and all-optical control of photonic beams with deep-subwavelength accuracy.We study the tunability of the photonic Dirac point(DP)and Zitterbewegung effect.Specifically,by tuning the graphene permittivity via gate voltages,chemical doping or the optical Kerr effect,one can control the creation or elimination of a DP,and induce a spectral variation of the DP exceeding 30 nm,as well as vary the amplitude and frequency of Zitterbewegung.We perform a comparative study of the Anderson localization of light beams in disordered layered photonic nanostructures that,in the limit of periodic layer distribution,possess either a DP or a Bragg gap in the spectrum of the wavevectors.In particular,we demonstrate that the localization length of the Anderson modes increases when the width of the Bragg gap decreases,such that in the vanishingly small bandgap limit,namely when a Dirac point is formed,the photonic modes of the disordered lattices located near DPs remain delocalized even when the strength of disorder is as high as 80%.The robustness of the DP also manifests itself in the fact that the inversely proportional dependence of the transmission on the lattice length near the DP remains unchanged under strong disorder.The DP of one dimensional plasmonic superlattices appears when the spatial average permittivity of supperlttices(??)is zero.We find that the DP is associated with the topological origin of SPPs.By calculating the Zak phase,we reveal that the topology of plasmonic lattices is determined by the sign of ??.As such the topology and their associated interfacial states are extremely robust against structural disorder.These topologically protected interfacial modes can be viewed as the generalization of the conventional SPPs existing at metallic-dielectric interfaces.The choice of the building block is crucial to design quantum metamaterials with desired properties and GNFs are promising candidates as they inherit the remarkable properties from the extended graphene sheet,and can be grown either by bottomup chemical synthesis or top-down electron beam patterning in various shapes and sizes.We propose a rigorous full quantum-mechanical approach to study the linear and nonlinear optical response of GNFs with different shapes and sizes.We find that the optical response of GNFs significantly depends on their shape and size.Specifically,increasing the size of nano-flakes,the quantum plasmons shift to lower frequency.By introducing the cavity into the structure,one can tune the optical response of GNFs.We also investigate the optical response of GNFs dimers.