Manipulations On Light Propagations In Longitudinally Modulated Optical Waveguides And Waveguide Arrays

Controlling the propagation and evolution of light waves is an important topic in optical field.Various optical structures have been proposed to achieve unique control of the propagation behavior of light beams.Especially important structures with periodic changes in refractive index are photonic crystals,photonic lattices,waveguide arrays,etc.Through the energy band engineering,the periodic structures greatly change the spatial dispersion characteristics of light,thus realizing unprecedented control over the spatial evolution of light.Unlike photonic crystal structures,the evolution of light waves in a photonic lattice or waveguide array has a definite propagation direction(longitudinal direction),along which the refractive index of the lattice or array is generally uniform and the modulation of refractive index only occurs in the transverse directions.In recent years,researchers have realized that the longitudinal modulation of refractive index can also be used as a new degree of freedom for unique manipulations on light propagations.This thesis focuses on the longitudinal modulation of waveguides or waveguide arrays,the physics behind the light propagation in such modulated structures have been studied and the unique ways on the light propagation control are revealed.The main contents and achievements of the thesis are listed as follows:(1)Optical localization in the rotating waveguide array.If a longitudinally uniform waveguide array is set to rotate at a constant speed around its center,the beam propagating therein will experience alongitudinal modulation of the refractive index.We study the influence of the array rotation on the optical mode and find that two new types of localized modes appear at two special locations — at the array center and at the array corners.The appearance of the central localized modes is due to the rotation resulting in an increase of the refractive index in the center with respect to its surroundings,while corner localized modes occur due to the inertial centrifugal force from the rotation.We also analyze the effects of self-focusing or self-defocusing nonlinearity on these two new modes.(2)Bloch oscillations in helical waveguide arrays.The optical Bloch oscillation in one-dimensional and two-dimensional helical waveguide arrays is studied.It is found that the amplitude and direction of the Bloch oscillation can be significantly altered by the waveguide spiral.As the helix radius gradually increases from zero,the Bloch oscillation periodically experiences three processes,namely,oscillation weakens,oscillation completely disappears and oscillation reappears with the direction however reversed.The results indicate that the helical waveguide array has potential application in the control of trajectory of the light propagation,and the non-diffracting propagation at the specific helix radius associated with the band collapse provides a new idea to transmit the information such as images.(3)Parity-time(PT)symmetry in twisted multi-core fibers.The tunability of PT symmetry and the propagation dynamics of light in twisted multi-core fibers are studied.It is found that a pair(or pairs)of eigenmodes of the multi-core fiber degenerate at some twist rates,which leads to the breaking of PT symmetry.Therefore,by changing the twist rate,the PT symmetry breaking threshold can be increased or lowered(or even decreased to be zero),which provides a new way to observe the spontaneous PT symmetry breaking.We also study the influence of the self-focusing nonlinearity on the PT symmetry breaking threshold.(4)Optical Rabi oscillation on the sub-wavelength scale.Rabi oscillation is an important concept in quantum mechanics,which meansthat the quantum state is transiting back and forth between two energy levels.In view of the mathematical similarity between the paraxial equation describing the beam propagation and the Schr?dinger equation describing the quantum wavefunction,the Rabi oscillation of the light wave has been extensively studied.However,naturally as an electromagnetic wave,evolution of light actually follows the full vectorial and non-paraxial Maxwell's equations.Then,does the Rabi oscillation still survive in the framework of Maxwell's equations? By rigorously solving the Maxwell equations,we study the propagation of light in sub-wavelength-scaled waveguides whose refractive index is modulated periodically in the longitudinal direction.It is found that Rabi oscillation and efficient mode conversion still occur for the sub-wavelength beams as well as for the surface plasmon polaritons(SPPs)provided that the longitudinal modulation is properly selected.This work indicates that the spatial spot pattern of deep sub-wavelength beams can be controlled by Rabi oscillation.We also analyze the effect of nonlinearity on Rabi oscillation.