Research On Fourier Transform And Other Properties In Temporal Self-imaging Effect

The temporal self-imaging effect,also known as the temporal Talbot effect,is the temporal counterpart of the spatial self-imaging effect.The temporal self-imaging effect is embodied in the transmission of a periodic optical pulse train through a dispersive medium with a specific amount of dispersion,and a pulse train with the similar characteristics to the input signal is obtained.Based on the time-frequency duality,introducing the realization mechanism of the temporal self-imaging effect to the frequency domain,the spectral self-imaging phenomenon is found in the time domain.Owing to its unique properties,the temporal self-imaging effect is currently widely used in the research of high-repetition rate pulse generation,passive amplification of optical pulse signals,stretching or compression of short pulses and optical computing and so on.This paper first introduces the research status at home and abroad and the basic principle of temporal self-imaging effect in detail.According to the real-time Fourier transform characteristics of the temporal self-imaging effect,an arbitrary waveform generation(AWG)system is designed,the detailed theoretical analysis is conducted,most importantly,we build an experiment platform for experimental verification.Based on the Discrete Fourier Transform characteristics in the temporal self-imaging effect,the pulse train with limited modulation periods in the temporal self-imaging effect in is deeply analyzed and discussed,and the calculation error of the discrete Fourier transform(DFT)of the finite-length pulse train is further studied in simulation.In addition,based on the timefrequency duality,the basic principle of the spectral self-imaging effect is expounded,and the related applications are discussed.The main work and academic contributions of this paper are as follows:1.A photonic AWG scheme based on the real-time Fourier transform characteristics of the temporal self-imaging effect is researched and designed,a systematic experimental verification platform is built to carry out the experimental results,and the detailed simulation results are given,the results turn out to prove the feasibility of the scheme.By modulating the RF signal containing different frequency components on the optical pulse train,the pulse train is then transmitted through dispersion and after passing through a low-pass filter,a signal with an arbitrary waveform envelope is generated.This system breaks through the limitation of the sampling rate of the digital-to-analog converter in the traditional AWG based on digital signal processing.At the same time,the system structure is more concise,and the response speed is also greatly improved.2.The DFT characteristics in the temporal self-imaging effect are researched.Considering the limitation of the number of the modulation periods in practical situations,the quantitative relationship between the DFT calculation error and the number of modulation periods and other parameters is analyzed.The research lays the foundation for the application of the temporal self-imaging effect in optical calculation.Simulations of different parameters are carried out,the results show that the DFT calculation error of the pulse train with limited modulation periods is only related to the number of modulation periods,and the minimum number of modulation periods required for DFT calculation under different error tolerances is given.The conclusion of this research shows important guiding significance for the process and analysis of optical signals.3.Based on the time-frequency duality,the realization mechanism of the self-imaging effect is mapped to the frequency domain,and the spectral self-imaging effect is discussed.The applications of spectral self-imaging effect of the generation of densely optical frequency comb and passive amplification are further analyzed.The characteristics that the spectral self-imaging effect can flexibly control the spectral lines of the signal are expounded,and then the methods of quadratic phase modulation and multi-level phase modulation to realize the spectral self-imaging effect are studied from the perspective of theory and simulation.The precise control of the spectral lines by the spectral self-imaging effect is expected to provide potential solutions for applications such as frequency comb generation.