Time reflection is a uniform inversion of the temporal evolution of a signal, which arises when an abrupt change in the properties of the host material occurs uniformly in space. At such a time interface, a portion of the input signal is time reversed, and its frequency spectrum is homogeneously translated as its momentum is conserved, forming the temporal counterpart of a spatial interface. Combinations of time interfaces, forming time metamaterials and Floquet matter, exploit the interference of multiple time reflections for extreme wave manipulation, leveraging time as an additional degree of freedom. Here we report the observation of photonic time reflection and associated broadband frequency translation in a switched transmission-line metamaterial whose effective capacitance is homogeneously and abruptly changed via a synchronized array of switches. A pair of temporal interfaces are combined to demonstrate time-reflection-induced wave interference, realizing the temporal counterpart of a Fabry–Pérot cavity. Our results establish the foundational building blocks to realize time metamaterials and Floquet photonic crystals, with opportunities for extreme photon manipulation in space and time.
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All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
The codes that support the findings of this study are available from the corresponding author upon reasonable request.
Lustig, E., Segev, M. & Sharabi, Y. Topological aspects of photonic time crystals. Optica 5, 1390–1395 (2018).
Lyubarov, M. et al. Amplified emission and lasing in photonic time crystals. Science 377, 425–428 (2022).
Winn, J. N., Fan, S., Joannopoulos, J. D. & Ippen, E. P. Interband transitions in photonic crystals. Phys. Rev. B 59, 1551–1554 (1999).
Dutt, A. et al. A single photonic cavity with two independent physical synthetic dimensions. Science 367, 59–64 (2020).
Fleury, R., Khanikaev, A. B. & Alù, A. Floquet topological insulators for sound. Nat. Commun. 7, 11744 (2016).
Cartella, A., Nova, T. F., Fechner, M., Merlin, R. & Cavalleri, A. Parametric amplification of optical phonons. Proc. Natl Acad. Sci. USA 115, 12148–12151 (2018).
Shan, J.-Y. et al. Giant modulation of optical nonlinearity by Floquet engineering. Nature 600, 235–239 (2021).
Hayran, Z., Chen, A. & Monticone, F. Spectral causality and the scattering of waves. Optica 8, 1040–1049 (2021).
Morgenthaler, R. Velocity modulation of electromagnetic waves. IRE Trans. Microw. Theory Tech. 6, 167–172 (1958).
Fante, R. L. Transmission of electromagnetic waves into time-varying media. IEEE Trans. Antennas Propag. 19, 417–424 (1971).
Lerosey, G. et al. Time reversal of electromagnetic waves. Phys. Rev. Lett. 92, 193904 (2004).
Fink, M. & Prada, C. Acoustic time-reversal mirrors. Inverse Probl. 17, R1–R38 (2001).
Chumak, A. V. et al. All-linear time reversal by a dynamic artificial crystal. Nat. Commun. 1, 141 (2010).
Vezzoli, S. et al. Optical time reversal from time-dependent epsilon-near-zero media. Phys. Rev. Lett. 120, 43902 (2018).
Lerosey, G., De Rosny, J., Tourin, A. & Fink, M. Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007).
Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photon. 6, 283–292 (2012).
Pacheco-Peña, V. & Engheta, N. Antireflection temporal coatings. Optica 7, 323–331 (2020).
Akbarzadeh, A., Chamanara, N. & Caloz, C. Inverse prism based on temporal discontinuity and spatial dispersion. Opt. Lett. 43, 3297–3300 (2018).
Pacheco-Peña, V. & Engheta, N. Temporal aiming. Light Sci. Appl. 9, 129 (2020).
Rizza, C., Castaldi, G. & Galdi, V. Short-pulsed metamaterials. Phys. Rev. Lett. 128, 257402 (2022).
Vázquez-Lozano, J. E. & Liberal, I. Shaping the quantum vacuum with anisotropic temporal boundaries. Nanophotonics (2022).
Bacot, V., Labousse, M., Eddi, A., Fink, M. & Fort, E. Time reversal and holography with spacetime transformations. Nat. Phys. 12, 972–977 (2016).
Hayran, Z., Khurgin, J. B. & Monticone, F. ℏω versus ℏk: dispersion and energy constraints on time-varying photonic materials and time crystals. Opt. Mater. Express 12, 3904–3917 (2022).
Yin, S., Galiffi, E. & Alù, A. Floquet metamaterials. eLight 2, 8 (2022).
Engheta, N. Metamaterials with high degrees of freedom: space, time, and more. Nanophotonics 10, 639–642 (2021).
Galiffi, E. et al. Photonics of time-varying media. Adv. Photonics 4, 014002 (2022).
Galiffi, E., Yin, S. & Alú, A. Tapered photonic switching. Nanophotonics 11, 3575–3581 (2022).
Mendonça, J. T., Martins, A. M. & Guerreiro, A. Temporal beam splitter and temporal interference. Phys. Rev. A 68, 043801 (2003).
Caloz, C. & Deck-Leger, Z.-L. Spacetime metamaterials—part II: theory and applications. IEEE Trans. Antennas Propag. 68, 1583–1598 (2020).
Caloz, C. & Deck-Leger, Z.-L. Spacetime metamaterials—part I: general concepts. IEEE Trans. Antennas Propag. 68, 1569–1582 (2020).
Pendry, J. B. Time reversal and negative refraction. Science 322, 71–73 (2008).
Bruno, V. et al. Negative refraction in time-varying strongly coupled plasmonic-antenna–epsilon-near-zero systems. Phys. Rev. Lett. 124, 43902 (2020).
Miyamaru, F. et al. Ultrafast frequency-shift dynamics at temporal boundary induced by structural-dispersion switching of waveguides. Phys. Rev. Lett. 127, 053902 (2021).
Li, H., Yin, S., Galiffi, E. & Alù, A. Temporal parity-time symmetry for extreme energy transformations. Phys. Rev. Lett. 127, 153903 (2021).
Carminati, R., Chen, H., Pierrat, R. & Shapiro, B. Universal statistics of waves in a random time-varying medium. Phys. Rev. Lett. 127, 94101 (2021).
Ono, M. et al. Ultrafast and energy-efficient all-optical switching with graphene-loaded deep-subwavelength plasmonic waveguides. Nat. Photon. 14, 37–43 (2020).
Nishida, A. et al. Experimental observation of frequency up-conversion by flash ionization. Appl. Phys. Lett. 101, 161118 (2012).
This work was supported by the Air Force Office of Scientific Research MURI program with grant no. FA9550-18-1-0379, the Simons Collaboration on Extreme Wave Phenomena and a Vannevar Bush Faculty Fellowship. A.A. acknowledges support from the Army/ARL via the Collaborative for Hierarchical Agile and Responsive Materials (CHARM) under cooperative agreement W911NF-19-2-0119. E.G. was supported by the Simons Foundation through a Junior Fellowship of the Simons Society of Fellows (855344).
The authors declare no competing interests.
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Extended Data Fig. 1 Design and analysis of the TLM.
(a) Equivalent T-network for one unit cell of our TLM when the switches are closed. Here, d is the physical length of the unit cell (0.2080 m) and jb=j2.753 is the normalized load susceptance at 100 MHz. (b) Normalized dispersion relation and (c) normalized Bloch impedance of our transmission line, assuming a unit-cell electrical length of θ=kd=72°, and an normalized load susceptance of b=2.753, both evaluated at 100 MHz. The blue lines and the red lines correspond to the unloaded and the loaded lines respectively. In order to identify the optimal unit-cell electrical length θ and cutoff frequency of the first band gap ωc, which is related to the load susceptance b, two dimensional parametric studies were done to generate maps of (d) the temporal reflection coefficient and (e) the frequency translation ratio. The red line in panel (a) corresponds to the combination of (θ,ωc) that yields the largest reflection coefficient. The white boxes with dotted borders in both panels denote regions in which the load susceptance become inductive (that is, negative).
Extended Data Fig. 2 Practical circuit layout and measurement setup.
(a) Layout for the unit cell. The descriptions of the components can be found in Supplementary Table 1. (b) Schematic for the complete TLM, showing how the unit cells are connected. (c) Simplified schematic of the experimental set up for time domain measurements. Power supply for the switches and a separate function generator for switch control are not shown.
Extended Data Fig. 3 Circuit model of time-switched transmission-line (TL).
Panels (a) and (b) correspond to the loading and removal of a shunt capacitor respectively. C1(C2) denotes the value of effective distributed capacitance of the TL before (after) closing or opening the switch. Panel (c) demonstrates the time variation of voltages and charges on each capacitor, as well as their total values sensed by the TL, corresponding to a numerical example of panel (a) with C2=4C1. Panel (d) shows the same quantities for a numerical example of Panel B with C2=C1/4.
Extended Data Fig. 4 A sample of the measurement used to characterize the frequency conversion of our time-interface when the wave impedance reduced.
The left column shows the incident (black), time-reflected (red) and time-refracted (blue) signals. The right column shows their corresponding Fourier transform. A frequency down conversion by about 0.55 is clearly visible through the peak of the frequency spectra.
Extended Data Fig. 5 Circuit simulations for a temporal slab with a fixed ‘ON’ time (τ = 15 ns).
The injected pulses are in the form of Gaussian wave packets with different carrier frequencies and 17.5 MHz spectral FWHM. The simulated circuit consists of 3 cascaded copies of our TLM sample. The left column depicts the time domain waveform of the input pulse, while the middle column shows the total time-reflected output. The right column shows the frequency spectra of the output. All of the spectra exhibit reflection nulls at approximately 38 MHz, which agrees with measured results in Fig. 3d of the main text.
Extended Data Fig. 6 Circuit simulations demonstrating the effect of switch desynchronization.
The black curve corresponds to the simulated voltages at ports 1 and 2 assuming perfect synchronization. The red curve (‘Practical’), which matches the ideal one almost exactly, depicts the simulation of our measurement set up. This shows that despite the finite time delay between adjacent unit cells, our set up can emulate a homogeneous time-interface with very high fidelity.
Extended Data Fig. 7 Investigation on the effect of finite switching time.
(a) Experimental characterization of the circuit switching speed using different types of control signal. Here, a 100 MHz sinusoidal signal is transmitted through a single unit cell sample of the TLM, and the envelope of the output waveform is recorded (black curve). We activate the switch inside the unit cell using different types of control signals Vsw, with drastically different slopes. Both a rectangular control signal (top) and a triangular control signal (bottom) produced identical output envelopes, demonstrating that the rise time of Vsw has very little influence on the switching speed of the circuit. (b) A sample measurement of the control signal used to induce the time-interface. The slew rate of the signal is very low, due to the input reactance of the switches. However as shown in panel (a), simply crossing the activation threshold of the switch (2.3 V according to the datasheet) is sufficient to induce a sharp time-interface. This particular control signal was used to induce the time-interface examined in Fig. 2e of the main text. To further verify the fidelity of the time interface, we perform circuit simulation of the TLM with different 10%-to-90% rise time for the switches, and plot the (c) time domain voltage measured at the input port. The input is a Gaussian wave packet with 50 MHz center frequency and 40 MHz spectral FWHM. The blue curve represents the simulation results when the circuit has the same rise time (3 ns) as our selected RF switches; it is seen to closely match the black curve, which corresponds to the case when the rise time is near zero. As we further increase the rise time to 8 ns (green) and 12 ns (yellow), the amplitude of the time reflection become significantly weaker. (d) Peak amplitude (normalized against the ideal case) of the time reflected wave packet as a function of the switch rise time. The amplitude corresponding to the case of 3 ns rise time was approximately 90% of the ideal amplitude.
Extended Data Fig. 8 Measurement of temporal interference induced by the inverted temporal slab.
(a) Time domain waveform recorded at port 1 for various values of ‘OFF’ duration τ. As τ is increased, so does the separation between the two TR pulses. The second TR pulse is heavily attenuated for larger values of τ, since it experiences increased attenuation. (b) Reflection spectra of inverted temporal slab in the wavenumber (bottom axis) and frequency (top axis) domain. We see distinct reflection minima whose locations are tunable via adjustment of τ.
Extended Data Fig. 9 Compensation of video leakage from the switches.
Top plot shows the uncompensated waveform measured at the input port of the TL, with multiple spurious spikes caused by the rising and falling edges of our control signal. The bottom plot shows the compensated waveform, obtained through subtracting the top plot by a shifted copy of itself. The compensated waveform has much more clearly observable input and TR pulses. A spurious inverted copy of the main signal remains, but can be discarded during analysis.
Supplementary Sections 1–12 and captions for Extended Data Figs. 1–9 and Extended Data Table 1.
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Moussa, H., Xu, G., Yin, S. et al. Observation of temporal reflection and broadband frequency translation at photonic time interfaces. Nat. Phys. (2023). https://doi.org/10.1038/s41567-023-01975-y