Study On Light Dynamics In Hermitian And Non-hermitian Synthetic Photonic Lattice

Light controlling refers to the precise regulation of the interaction between optical field and matter,aiming at obtaining new light fields including polarization,phase,frequency,amplitude,and other dimensions,which can be applied to information,chemistry,life,and material fields.In recent years,synthetic photonic lattices have attracted extensive attention as a new class of tools for manipulating light fields due to their simple structure and great compatibility with phase modulators,electro-optic and acousto-optic modulators.The synthetic photonic lattice consists of two fiber loops of different lengths connected by directional couplers.A new periodic discrete optical system is constructed by projecting the field amplitude of the optical pulse onto the multiple of the average length and the length difference of the double fiber loops,which provides a valuable research and application platform for the study of optical wave dynamics in the time and space domains.According to this,a large number of new optical phenomena have been discovered,such as time-reversal optical transmission,topological interface states,the superfluidity of light,etc.Based on the theory of Hermitian and non-Hermitian quantum mechanics,combined with coupled-mode theory,phase circulation,and nonlinear theory,this paper systematically studies the light reflection and transmission phenomena of a single pulse in the synthetic photonic lattice,as well as the nonlinear transmission process,which aims to enrich the theory of synthetic photonic lattices to modulate light fields and reveals the evolution of the optical pulse in the time-space domain.The specific research contents are as follows:In Chapter 1,the basic concepts of Hermitian/non-Hermitian photonics and synthetic photonic lattices are introduced;describes the research progress of synthetic photonic lattices;After that,focuses on the research status of Hermitian/non-Hermitian synthetic photonic lattices,and the research significance of this paper is discussed.In Chapter 2,theoretically constructs the physical model of the Hermitian binary synthetic photonic lattice,analyzes the dynamic equation of the pulse,and solves the system dispersion relation analytically.According to the binary properties of the lattice,the transmittance of the Gaussian beam at the lattice interface is derived.Combined with the physical definition of the group velocity dispersion,the transmission of the optical pulse at the interface is analyzed.Further,the transmission and reflection of light pulses at the interface of binary photonic lattice are simulated.It is found that the optical pulse at the interface can achieve total reflection without diffraction,and the energy in the long and short loops is completely exchanged when the phase distribution and wave vector satisfy certain conditions,that is,the phenomenon of anomalous reflection is achieved.The results provide guidance for the realization of novel optical switches.In Chapter 3,the anti-parity-time symmetry second-order synthetic photonic lattice is innovatively constructed.According to the evolutionary dynamics of pulse in space-time lattices,the band relations are analyzed,and the influence of Kerr self-focusing nonlinearity on light transmission is explored.Then,theoretically and numerically,the double-pulse soliton dynamics in the lattice are systematically studied.It is found that the formation,evolution,and interaction of double-solitons are affected by parameters such as initial relative phase difference,transverse pulse interval,nonlinear effects,and non-Hermitic terms.This work is of great physical significance for grasping the transmission and evolution of multiple optical signals in optical systems,especially for mastering the modulation mechanism of pulses in optical switches and logic gates.In Chapter 4,we make a summary and prospect of the thesis.Firstly,it summarizes the author’s study work at this stage and then discusses the direction and focus of future work.