Research On The Optical Localization And Talbot Effect In Synthetic Photonic Lattices

The synthetic photonic lattice is composed of a coupler connecting two optical fibers with a length difference,and the optical transmission can be divided into two discrete axes by time multiplexing technology,which is equivalent to the photonic lattice.By adding electro-optical modulators,acousto-optic modulators,and other optical components to the loops,it can be equivalent to the refractive index distribution of the synthetic photonic lattice.This system can flexibly control lattice parameters,so it is used as an experimental platform to study the manipulation of discrete optical transmission,providing a new way to manipulate optical transmission.In recent years,researchers have discovered many valuable optical phenomena in synthetic photonic lattice systems,such as time reversal transmission,Berry curvature effect,Bloch oscillation,Anderson locality,Talbot effect,and so on.Optical localization refers to the optical phenomenon that the beam always maintains the localization during transmission,which has broad application prospects in optical information processing and optical communication.Talbot effect is a traditional optical self-imaging phenomenon,which is widely used in the fields of optics and microscopy.In the synthetic photonic lattice,on the one hand,optical localization can be achieved by introducing randomness,nonlinearity,defects,etc.,and on the other hand,Talbot effect can be realized by changing the gain and loss coefficients or adding linear phase,which further promotes the rapid development of light field regulation.In the thesis,the two-phase modulation synthetic photonic lattice as the research platform,combined with coupling mode,phase circulation,dispersion relationship,and other theories,systematically analyzes the localization phenomenon of light pulses in the synthetic photonic lattice.Combining the principles of Hermitian and non-Hermitian photonics,the Talbot effect in the anti-parity-time symmetry lattice was studied.The specific work content is as follows:1.Taking the synthetic photonic lattice as the platform,the optical phase is changed by the electro-optical modulator in the two loops,and the two-phase modulation synthetic photonic lattice model and its corresponding equivalent synthetic photonic lattice are constructed.According to the phase modulation method,the periodic phase circulation of every four adjacent couplers is obtained.On the one hand,the dispersion relationship is derived by introducing a discrete plane wave solution based on Bloch theory,and the band structure distribution is analyzed by combining the phase circulation difference.On the other hand,the numerical iterative method is used to simulate the optical transmission phenomenon in the photonic lattice of the two-phase modulation synthesis.By analyzing the band structure and optical transmission characteristics,it is concluded that:when the phase modulation period is small,there is a localization-delocalized transition in both moire phase circulation modulation and non-moire phase circulation modulation.During the large phase modulation period,there is a transition of optical localization and oscillation.Finally,we use a statistical chart to visually show the localization distribution of light generated by the dual-phase modulation period.2.In the two-phase synthetic photonic lattice,the electro-optical modulator and acoustic-optic modulator are used to adjust the phase distribution,gain,and loss coefficient respectively,and the anti-PT synthetic photonic lattice is constructed.Based on the physical model,the iterative equation of the coupling mode is listed,the dispersion relationship is derived by combining the discrete plane wave solution,and the band structure is obtained.Then,according to the conditions for the generation of the Talbot effect and the calculation method of the Talbot distance,the conditions for the light pulses to produce the Talbot effect and Talbot distance are theoretically analyzed.Finally,the Talbot self-imaging phenomenon under Hermitian phase modulation and non-Hermitian modulation was simulated and studied.The results show that when the incident pulse period is N=2,4,6,8,there is the Talbot effect in the system;when the initial phase isφ=π/2,the Talbot effect will disappear if the gain and loss coefficients are more than 0.33;other factors being equal,the Talbot phenomenon is same if the initial phase φ=0 and π=π.