Research On Temporal Imaging And Second-order Temporal Lau Self-imaging

Temporal imaging has crucial value in the fields about signal handling,communication and others.However,the signal distortion will occur when the temporal signal goes through the lens or transmitted in a dispersive medium.The signal distortion will affect the reconstruction of temporal pulse.To solve this problem,based on the space-time duality,this paper studies the temporal imaging of time-lens and second-order temporal Lau self-imaging on the basis of establishing the relationship between impulse response function and transformation matrix.The space-time duality is received from the equations of paraxial diffraction and the pulse dispersion.The connection is built between the ABCD transformation matrix and the impulse response function.And the impulse response functions of some temporal systems are discussed by using relationship.Based on spatial imaging and space-time duality,temporal imaging of lens scheme is designed.Using the above scheme,the impulse response function and light intensity about the time-lens with different aperture are obtained.This paper discusses the size of lens aperture affects the quality of imaging in time domain.It turns out to be that as the aperture gets bigger,the loss of high-frequency information is reduced and the resolution is improved.The results indicate that the temporal imaging of time-lens with aperture is equivalent to the lens imaging with diffraction limited system in the spatial domain.Based on the space-time duality,a second-order Lau self-imaging scheme based on the intensity correlation of the temporal incoherent light source is devised.The intensity fluctuation correlation expressions depicting second-order Lau effect are derived.In addition,the relationship between the distribution of newly established periodic optical pulses and the GDD parameter of the medium is analyzed and depicted.The results,on one hand,show that temporally periodic structures are nonlocally superposed due to the joint dispersion of correlated light pulses.The results,on the other hand,show that when the GDD parameter of dispersion medium between the two gratings is an integral multiple of the Talbot GDD parameter(|?2-?1|=m?T}),the fringes of periodic light pulses are obtained.However,when the GDD parameter of dispersion medium between two gratings is an odd time of half the Talbot GDD parameter(|?2-?1|=(2g+1)?T/2),the periodic pulses are reconstructed with a half period shift.Our results may be useful for the application of light field correlation in temporal optics,especially for remotely transmitting the periodic temporal signals robustly.