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Our group introduced the concept of time-domain holography as the temporal equivalent of the well-known process of spatial-domain holography, a feat that represents a new milestone within the context of the so-called space-time duality.
Time-domain holography involves two main steps, respectively equivalent to the signal recording stage and the signal retrieval stage Fig. In the signal recording stage, an interferogram is created by inserting the time-domain information signal and a reference monochromatic wave CW signal in a heterodyne detection configuration using a single photodector.
Alternatively, the modulating interferogram signal can be also computationally designed for generation of a desired, user-defined optical complex waveform using the described single intensity-modulation scheme. In the signal retrieval stage, the optical complex waveform is created by inserting the previously detected temporal hologram or the computationally generated hologram created using an arbitrary waveform generator as a signal modulating the temporal waveform of another CW light source, e. At the output of the modulator, several terms can be identified that are spectrally separated, exactly as in the spatial-domain holography problem.
One of these terms is an exact copy of the information signal, and can be easily filtered in selected using a band-pass optical filter Fig. There is also an additional term that is the temporal complex conjugate of the input signal — if selected through a complementary band-bass optical filtering process, this would enable a simple way of achieving optical phase conjugation of the input signal, a highly desired signal-processing functionality for many interesting operations.
This novel concept has been experimentally demonstrated through the generation and subsequent retrieval of user-defined, complex optical temporal waveforms using simple schemes based on time-domain equivalents of holographic concepts. In particular, Fig. Fernandez, M. Li, J.
Basics of waveguide selection - TvTechnology
Express, vol. A time lens is the temporal equivalent of a spatial thin lens, typically implemented through quadratic temporal phase modulation of the waveform under analysis. Related with this concept, a temporal zone plate enables the compression of CW light into short optical pulses through a two-step process, involving temporal modulation e. Temporal zone plates do not exhibit the limiting trade-off between temporal aperture and frequency bandwidth temporal resolution of conventional linear electro-optic time lenses, enabling compression of CW light over a much longer temporal period time aperture.
The latest is of critical importance to achieve higher energy pulses. There are two kinds of temporal zone plates — temporal intensity and phase zone plates, which can be realized by temporal intensity and phase modulation, respectively. As an example, temporal phase zone plates, which are the time-domain analog of spatial phase zone plates, are illustrated in Fig.
To demonstrate the introduced temporal zone plate concept, we set up a linear optical pulse compression experiment, in which 1st-order, 2nd-order, and 3rd-order temporal phase zone plates are used. The electronic waveforms, which are used to drive the electro-optic phase modulator, are shown in Fig. The temporal apertures for order 1, 2, and 3, which equal to the temporal duration of the electronic waveforms, are 1. The corresponding compressed pulse waveforms are shown in Fig. There is a good agreement between numerical simulation in which the experimental limitation is considered so that it is slightly deviated from the ideal profile and experiment.
Thus the time-bandwidth products ratio of temporal aperture to resolution for these three experiments are 50, , and , respectively, significantly surpassing the capabilities of conventional time lenses. For further advancements in optimized temporal zone plate designs, see  below. Space-time duality.