Research on Temporal Self-Imaging Effect and Its Applications in Microwave Photonics （Invited）

The temporal Talbot effect represents the time domain counterpart to the classical spatial self-imaging phenomenon， strictly governed by the fundamental physical principle of space-time duality. This coherent interference effect occurs when a periodic optical pulse train propagates through a dispersive medium， such as a standard single mode optical fiber or a chirped Bragg grating， where the group velocity dispersion acts as a quadratic phase filter on the optical signal. Depending on the precise relationship between the pulse repetition period and the accumulated dispersion， the system exhibits two primary behaviors： integer order self imaging， where the original waveform is perfectly reproduced， or fractional order self imaging， which results in the generation of pulse trains with multiplied repetition rates. Furthermore， the dispersive propagation inherently functions as a real-time Fourier transform， mapping the frequency spectrum of an imposed modulation directly into its temporal intensity profile at the output. This review systematically explores these mechanisms， emphasizing their utility as passive， linear， and energy efficient tools for high speed signal processing in the field of microwave photonics.A significant portion of this review addresses the manipulation of pulse repetition frequencies. While early approaches relied on fixed dispersion values， recent advancements allow for flexible multiplication factors. We discuss techniques such as phase pre-coding， which modifies the input phase to transition between fractional Talbot orders without energy loss， and binary intensity modulation， which offers a simpler implementation but suffers from optical power loss. A comparative analysis highlights that complex amplitude pre-coding scheme offers a balanced trade-off between energy efficiency and control complexity. By utilizing a Mach-Zehnder modulator to sculpt the spectrum into a flat profile， this method overcomes the bandwidth limitations of arbitrary waveform generators required for phase coding and the high extinction ratio constraints typical of intensity modulation schemes.In contrast to multiplication， the paper examines passive amplification and weak signal recovery via the inverse temporal Talbot effect. By reversing the dispersion process， distributed energy from a continuous wave or a high-rate pulse train can be coherently focused into high peak power pulses. This concept， realized as a temporal Talbot array illuminator， effectively converts continuous wave light into high-quality pulse trains with tunable parameters. Crucially， this enables noiseless amplification where random， non-coherent noise does not sum up constructively， thereby significantly enhancing the signal-to-noise ratio. Experimental results have demonstrated amplification gains exceeding one hundred and ten times， allowing for the recovery of weak signals that are otherwise submerged below the noise floor of the photodetector.The review further details the application of the real time Fourier transform in real-time spectrum analysis. Standard real-time spectrum analysis faces an inherent trade-off between measurement bandwidth and frequency resolution. To address this， the authors introduce a resolution enhanced architecture using the inverse temporal Talbot effect to temporally stretch the output observation window， effectively magnifying the resolution. Conversely， a bandwidth-enhanced architecture utilizing fractional-order multiplication is proposed to increase the effective sampling rate and measurement range. These innovations successfully decouple the resolution bandwidth constraint， enabling gap free analysis of wideband dynamic radio frequency signals. Additionally， the paper explores arbitrary waveform generation and pulse position control. By manipulating the spectral content via multi-tone modulation， complex temporal waveforms can be synthesized through frequency to time mapping. Similarly， precise control over pulse timing is achieved by modulating the carrier with a frequency modulated signal. This technique effectively converts instantaneous frequency shifts into temporal delays. This capability is applied to non-uniform sampling systems， such as the photonic Nyquist folding receiver， to significantly extend signal reception bandwidth beyond the traditional aliasing limits.Finally， the review outlines emerging applications in other domains， such as temporal cloaking which hides events within dispersion induced time gaps， and prime number factorization via Gaussian sum calculation. The paper concludes by identifying critical challenges for future implementation. These include the precise management of high order dispersion to achieve perfect self imaging and the mitigation of Kerr non-linearities at high optical power levels. Furthermore， the review emphasizes the need for on-chip integration， noting the engineering difficulties in realizing sufficient dispersion on photonic integrated circuits while maintaining a compact Size， Weight， Power， and Cost （SWaP-C） footprint. Despite these hurdles， the temporal Talbot effect remains a versatile and promising foundation for next generation all optical signal processing networks.