Research On The Temporal Talbot Effect And Its Applications

The spatial self-imaging effect is a result of near-field diffraction,that is,when a plane wave propagates through a periodic grating,the same pattern as the grating will appear at a certain distance from the grating.To commemorate its discoverer H.F.Talbot,the spatial self-imaging effect is also called the Talbot effect.According to the time-space duality,T.Jannson found that there is a corresponding Talbot effect in the time domain.A periodic optical pulse sequence is transmits through a dispersive device.According to the relationship between the first-order dispersion and the period of the optical pulse sequence,the temporal Talbot effect can be divided into integer Talbot effect and fractional Talbot effect.Among them,the integer temporal Talbot effect can generate the same signal as the input periodic light pulse sequence.The fractional temporal Talbot effect can be applied to generate light pulse sequences with high repetition rates.When the reciprocal of the duty cycle of the input pulse sequence is greater than the multiplication factor of the output signal,the characteristics of a single pulse can be kept unchanged.So far,based on the characteristics of the effect of small noise fluctuations and high energy utilization,the temporal Talbot effect has shown good application prospects in the fields of passive amplification of signal strength,generation of high-repetition rate pulse signals,and real-time spectrum analysis of analog signals.This thesis investigates the temporal Talbot effect and its application,we designed a discrete Fourier transform system based on the inverse temporal Talbot effect,and designed an arbitrary waveform generation system based on the temporal Talbot effect.Complete theoretical analysis and formula derivation of the above systems were carried out respectively,and the accuracy and effectiveness of the theoretical results of the two systems were further proved through simulation research.And the potential applications of the proposed system in optical signal analysis and processing were discussed.The main research contents and results of this thesis are as follows:1.Based on the inverse Talbot effect,a new scheme to realize the discrete Fourier transform is proposed,which can obtain the output of complex values.Combined with theoretical analysis,the relationship between the input data sequence and the output amplitude of the system is obtained,which satisfies the discrete Fourier transform.At the same time,the problem of phase information loss after the discrete Fourier transform of the data sequence in the existing scheme is solved.And the repetition frequency of input and output pulse remains unchanged.Finally,through numerical simulation,a light pulse sequence with a repetition period of 0.03 ns is transmitted through a dispersive medium with a dispersion amount that satisfies the inverse temporal Talbot effect,which verifies the effectiveness of the system;2.Based on the real-time Fourier transform characteristics in the temporal Talbot effect,we proposed a new high-speed arbitrary waveform generation scheme.A complete theoretical derivation is given to demonstrate the relationship between the input radio frequency signal and the output of the system.An arbitrary temporal waveform is obtained by setting the frequency component of the input signal.Finally,through numerical simulation,the analog signal is sampled using a light pulse sequence with a repetition period of 205 ps,and then the dispersion medium whose dispersion amount satisfies the integer temporal Talbot effect,that is,the first-order dispersion amount is 6738 ps~2,is verified to be correct.This scheme is expected to become a potential solution for high-speed reconfigurable arbitrary waveform generation.