Self-imaging And Effective Electric Field Control Of Light Pulse In Synthetic Temporal Lattice

The regularly arranged atoms in the solid form a stable lattice structure.Electrons under the periodic potential of the lattice have energy bands.Through changing the band structure or introducing external electric and magnetic fields,the movement of electrons can be flexibly controlled in the crystal lattice.Similar to the solid crystal lattice,with the aid of the periodic distribution of the refractive index,a photonic lattice or crystal can be constructed to generate a photonic band structure.By introducing effective electric or magnetic field,many novel optical phenomena are realized,including discrete diffraction,discrete Talbot self-imaging effect,Bloch oscillations and dynamic localization.These phenomena have great applications in high-resolution imaging,optical communication and all-optical information processing.The concept of photonic lattice can also be extended to synthetic dimensions,such as time,frequency,mode and orbital angular momentum.For example,a dynamically modulated optical waveguide can be used to construct a frequency photonic lattice,where the frequency of light wave is distributed in a discrete period.A temporal photonic lattice can be realized with the help of dual-fiber loops with slightly different lengths,and the timing distribution of light wave pulses is also periodic.The construction of synthetic dimensional photonic lattices breaks through the constraints of spatial geometric dimensions on system dimensions,allowing researchers to investigate high-dimensional physics in a low-dimensional spatial structure that is easy to implement.In addition,photon control in the synthetic dimension is more convenient to implement.Control methods that are difficult to achieve in the spatial structure can be introduced,such as dynamically changing gain,loss and potential field.The application of time-varying modulation to the temporal photonic lattice can open up a new way for pulse manipulation.This paper is devoted to the study of the propagation and manipulation of light pulses in the temporal photonic lattice.The Talbot self-imaging effect of a periodic pulse train is studied in the passive temporal lattice.By using the dynamically changing gain/loss,the parity-time symmetry is introduced,which has the regulation effect on the Talbot self-imaging process.Moreover,with the aid of time-varying phase modulation,the time-varying effective vector potential field and electric field are realized.The effective vector potential and electric field are used to manipulate the wavepacket evolution.The main research results are as follows:Firstly,the Talbot self-imaging of the periodic pulse train is studied theoretically in the synthetic temporal photonic lattice.Only when the period of the incident periodic pulse sequence is 1,2 or 4 times of the loop delay difference,the Talbot self-imaging effect of the pulse sequence can be observed.The corresponding Talbot distances are 8,8 and 24 times of the average loop delay.By adjusting the splitting ratio of coupler or imposing linear phase modulation on the incident pulse sequence,the Talbot distance can be manipulated.Furthermore,by injecting several pulse trains into the temporal photonic lattice,the allowed incidence period is extended to the fractional times of the original period.The Talbot effect in the temporal photonic lattice provides novel possibilities for realizing the self-imaging of pulse train.This study has broad application in the fields of high-repetition optical clock signal generation,temporal cloaking and passive optical amplification.Secondly,gain and loss are introduced to construct the parity-time symmetric temporal photonic lattice.The Talbot self-imaging of the periodic pulse train is theoretically studied at the exact and broken phases.Only when the period of the incident pulse sequence is 2 or4 times of the loop delay difference,the Talbot self-imaging effect occurs.By controlling the gain and loss or applying the linear phase modulation on the incident pulse sequence,the Talbot distance can be tuned.In addition,we study the power oscillation phenomenon in the parity-time symmetric Talbot effect.This phenomenon may find applications in tunable optical amplifiers.Thirdly,we construct artificial AC electric field through time-varying phase modulation.The effect of effective AC and DC electric fields on the wavepacket evolution is discussed.Introducing the time-varying phase modulation of opposite magnitude in the two fiber loops can simulate the non-reciprocal phase obtained by the electron in the vector potential field,and then can construct the time-varying effective vector potential and electric field.Under an AC electric field,the wavepacket can propagate in a specific direction without diffraction.By changing the electric field amplitude,we equivalently realize the control of the band structure,thereby controlling the direction of wavepacket propagation.Then the first-to fifth-order dynamic localization effects under AC electric field can be observed.It was found that the higher-order dynamic localization has stronger localization strength and robustness.Then,we construct both AC and DC electric fields.When the DC electric field is an integer multiple of the angular frequency of the AC electric field,the non-diffraction propagation and dynamic localization of the wave packet can also be observed.Moreover,the direction of diffraction-free propagation is extended.As a small amount of detuning is introduced into the DC electric field,we can realize super-Bloch oscillations.It is found that the amplitude and period of its oscillation are inversely proportional to the amount of detuning.The construction of the AC electric field provides new possibilities for pulse control and has potential applications in the field of adjustable optical delay lines.Finally,the Landau-Zener tunneling effect is discussed under the artificial electric field.We found that multiple Landau-Zener tunneling occurs in a single alternating period,and the locations of the tunneling are non-uniformly distributed.By increasing the amplitude of AC electric field,not only the number of tunneling in a single period can be increased,but also the tunneling probability of each tunneling can be increased.Under the artificial AC electric field,the occurrence of Landau-Zener tunneling has a threshold.The threshold is related to initial Bloch momentum.We then construct AC and DC electric fields.By changing the amplitude and phase of the AC electric field,we can manipulate the tunneling probability without changing the wavepacket trajectory.This study has applications in the field of adjustable beam splitters.