When waves impinge on the interface between different materials, light is partially reflected, propagating back towards the incident side (Fig. 1a). The temporal dual of this phenomenon is a time-interface: this occurs when the optical properties of a medium are abruptly changed at one instant in time and uniformly in space, as illustrated in Fig. 1b. At such an event, a portion of the wave is instantaneously time-reflected. The phenomena associated with time-reflection are intriguingly different from conventional reflection at a spatial interface. Conventional spatial reflection (e.g., an echo) that we are familiar with reproduces the same temporal sequence as an input signal. This is depicted in Fig. 1a: the image of a cat reflecting off a spatial interface appears as the cat turns around, similar to the image we are used to seeing in a mirror. The reflected signal oscillates at the same frequency as the emitted one, but it is reversed in terms of spatial momentum. In the case of visible light, this means that the image preserves its color, e.g., blue in Fig. 1a, for sound it preserves its pitch.
On the contrary, at a time-interface the reflected signals are time-reversed and frequency-shifted. In this scenario, the time-reflected cat image appears to be walking in reverse towards its source, and at a different frequency (the cat color switches to red in Fig. 1b) as the properties of the material have changed. Notice that the spatial length of the cat image remains the same, but its temporal content is stretched. This is due to the conservation of momentum at the time-interface, which stems from the spatial homogeneity of the material change, in a dual fashion to the conservation of frequency at a conventional spatial interface. This effect was theoretically predicted over 65 years ago , but never been observed so far for electromagnetic waves.
In our recent paper in Nature Physics , we report a breakthrough experiment leading to the first observation of this phenomenon for electromagnetic waves in a tailored metamaterial. Broadband signals are sent into a meandered strip of metal about 6 meters long, loaded by a dense array of electronic switches connected to reservoir capacitors that can be abruptly added or subtracted to the medium carrying the signal through the switches (Fig. 2a). We then trigger the switches all at the same time, suddenly doubling the wave impedance as experienced by the signals traveling along the line. This change is made uniform across the entire line by carefully synchronizing the switches, hence producing the requirements to realize a temporal interface. As shown in Fig. 2b, the measured time-reflected signal faithfully carries a time-reversed copy (purple, then a yellow marker in V1 right after the switch logic on) of the incoming signal (yellow marker followed by a purple one before the switching). Both the time-reflected signal registered at the input port and the time-refracted one (the residual forward wave) recorded in V2 are stretched in time because of the frequency conversion caused by the time interface.
We have also been able to combine multiple time interfaces to realize constructive or destructive interference between multiple time-reflected signals, which produces the temporal dual of a Fabry-Pérot cavity. This form of the temporal resonator can be used to realize active frequency filters and tailor the incoming signals. As observed in our experiments, the spectrum of a broadband input signal is indeed translated in frequency by the temporal slab (Fig. 3). In our experiments, we observed two time-reflected signals, as shown in Fig. 3a, whose separation is proportional to the duration of the temporal slab. By taking the Fourier transform of these signals, we clearly observe the result of interference in Fig. 3b, achieving a filtering phenomenon dual to the one of a spatial quarter-wave plate.
In retrospect, key challenges that hinder the realization of electromagnetic time-interfaces have been the large energy requirements needed to abruptly change the bulk properties of a material, and the contrast in electromagnetic properties that can be achieved at fast speeds. To address these challenges, we engineered switched transmission-line metamaterials, rather than altering the bulk reactance using external sources, to overcome these challenges, making time reflections accessible for experimentation in photonics.
The demonstrated time-interfaces induce broadband frequency translation and instantaneous phase-conjugation with low energy and memory cost, of great interest for many photonic applications by offering new degrees of freedom for extreme wave control . Meanwhile, the introduced metamaterial platform can powerfully combine multiple ad-hoc time interfaces, enabling electromagnetic time-crystals, and time-metamaterials . Combined with tailored spatial interfaces, this discovery offers the potential to open totally new directions for photonic technologies and wave-matter interactions, paving the way for exciting applications in wireless communications, such as time-reversal imaging , and for the development of compact, low-energy optical computers.
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- Engheta, N. Metamaterials with high degrees of freedom: Space, time, and more. Nanophotonics 10, 639–642 (2021).
- Yin, S., Galiffi, E. & Alù, A. Floquet metamaterials. eLight 2, 8 (2022).
- Mosk, A. P., Lagendijk, A., Lerosey, G., & Fink, M. (2012). Controlling waves in space and time for imaging and focusing in complex media. Nature photonics, 6(5), 283-292.
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