Spatial Photonics In Novel Photonic Lattices

Dynamics control of the light in time and space is the eternal pursuit of optics,and it is of importance for both theoretical guide and practical application for achiev-ing various photoelectric device and all-optical devices.The optical control of spatial photonics,including the size of localized state,the wave shape,the direction of prop-agation,and the interaction of optical wave,depends on various optical lattices.This dissertation is focusing on the analysis and simulation of propagation dy-namics of optical waves in some new types of optical lattices,including quasi-periodic lattice,PT-symmetry lattice,longitudinal modulation lattice,and graphene optical lat-tice.We have discussed and studied the Localization-delocalization wavepacket tran-sition in Pythagorean quasi-crystal potentials,the mechanism of PT-symmetry break as the increasing of gain and loss,Diffractionless propagation of subwavelength beams and generation of Subwavelength Plasmonic Nanovortices in longitudinal modulation lattice,and bandgap structure and nonlinear optical solitons in a periodically patterned graphene sheet.The dissertation includes mainly as following parts:(1)We introduce a new type of potential,not belonging to any type of quasi-crystals considered before,that is built as an interference pattern of two identical mutually-rotated periodic sublattices(square or hexagonal).All linear eigenmodes are localized when the control parameter p2 exceed a threshold in the aperiodic potential,whereas all modes are delocalized regardless of p2 as they represent the conventional Bloch states.And in the quasi-periodic lattice,stable soliton solutions can been found in the first finite gap.(2)We study mode properties in multimode optical waveguides with parity-time(PT)symmetry.We find that two guiding modes with successive orders 2m-1 and 2m form a mode pair in the sense that the two components of the pair evolve into the same mode when the loss and gain coefficient increases to some critical values,and they experience PT symmetry breaking simultaneously.For waveguides that in their conservative limit support an odd number of guiding modes,a new mode with a proper order emerges upon the increase of the gain and loss level,so that it pairs with the al-ready existing highest-order mode and then breaks their PT symmetry simultaneously.Depending on the specific realizations of PT-symmetric potentials,higher-order mod-e pairs may experience symmetry breaking earlier or later than the lower-order mode pairs do.(3)We go beyond the paraxial approximation and demonstrate,solving the full set of the Maxwell's equations for the light propagation in deeply subwavelength waveg-uides and periodic lattices with balanced gain and loss,that the PT symmetry may stay unbroken in this setting.Moreover,the PT symmetry in subwavelength guiding structures may be restored after being initially broken upon the increase of gain and loss.(4)we study the applicability of the Kapitza effect to control the propagation of structured subwavelength light beams.We show that a sufficiently deep modula-tion of the dielectric permittivity allows a nearly complete diffraction cancellation of multiple-peak subwavelength beams,and we study how the degree of diffraction can-cellation decreases as the spatial spectrum of the input beam broadens.We also find that subwavelength light beams can be steered by varying the depth of the permittiv-ity modulation.In particular,a sufficiently large permittivity modulation is shown to cause otherwise titled inputs to propagate always along the direction of modulation.(5)We found that tunneling between neighboring waveguides can be suppressed for specific frequencies of the out-of-phase refractive index modulation,affording undistorted propagation of the input subwavelength light spots over hundreds of Rayleigh lengths.Tunneling inhibition turns out to be effective only when the waveg-uide separation in the array is above a critical threshold.Inclusion of a weak focusing nonlinearity is shown to improve localization.(6)We demonstrate that plasmonic helical gratings consisting of metallic nanowires imprinted with helical grooves or ridges can be used efficiently to generate plasmonic vortices with radius much smaller than the operating wavelength.In our pro-posed approach,these helical surface gratings are designed so that plasmon modes with different azimuthal quantum numbers(topological charge)are phase-matched,thus al-lowing one to generate optical plasmonic vortices with arbitrary topological charge.Our analysis,based both on the exact solutions for the electromagnetic field propagat-ing in the helical plasmonic grating and a coupled-mode theory,suggests that even in the presence of metal losses the fundamental mode with topological charge m=0 can be converted to plasmon vortex modes with topological charge m=1 and m=2 with a conversion efficiency as large as 60%.(7)We study linear and nonlinear mode properties in a periodically patterned graphene sheet.We demonstrate that a subwavelength onedimensional photonic lat-tice can be defined across the graphene monolayer,with its modulation depth and cor-respondingly the associated photonic band structures being controlled rapidly,by an external gate voltage.We find the existences of graphene lattice solitons at the deep-subwavelength scales in both dimensions,thanks to the combination of graphene in-trinsic self-focusing nonlinearity and the graphene plasmonic confinement effects.