Advanced Photonics, Volume. 4, Issue 1, 014002(2022)
Photonics of time-varying media
Fig. 1. Scattering at (a) a spatial discontinuity, generating transmitted and reflected waves propagating in different media with refractive indices
Fig. 2. (a) Schematic of the antireflection temporal coatings proposed in Ref. 39. (b) Numerical results for the field distribution before and after the temporal scattering, showing the incident and transmitted waves, with minimized reflection due to the temporal coating shown in (a). (c) Spectra of the incident, forward, and backward waves. (d) Schematic of TPT symmetric structures proposed in Ref. 40. (e) and (f) The time evolution of the normalized energy (solid curves) and its two constitutions (circle symbols for interferences and the dashed curves for another). (e) Maximum total power and (f) minimum total power. Insets are the field distributions in simulations before, during, and after the TPT slabs. Figures adapted from Refs. 39 and 40.
Fig. 3. (a) A conventional prism decomposing white light into its frequency components in different directions. (b) An inverse prism that maps the light with different momentum into different frequencies. (c) Implementation of the inverse prism proposed in Ref. 28. (d) Temporal aiming proposed in Ref. 43. (e) The conventional Brewster angle. (f) Temporal Brewster angle described in Ref. 44. Figures adapted with permission from Refs. 28, 43, and 44.
Fig. 4. (a) Temporal reflection of graphene plasmons reported in Ref. 54. (b) Impedance matching using a time-switched transmission line.56 (c) Time-switched thin absorber in Ref. 57. (d) Unitary excitation transfer between two coupled circuit resonators.58 (e) Temporal deflection caused by isotropic-to-anisotropic switching on meta-atoms.59 (f) Temporal switching of structural dispersion for ultrafast frequency-shifts, proposed in Ref. 60. (g) Corresponding frequency spectra for the switching in (f). Figures adapted from Refs. 54, 56, 57, 58, 59, and 60.
Fig. 5. (a), (b) Example of a (finite) layered (a) PSC and (b) PTC, and corresponding wave behaviour within the respective band gaps. (c) Band structure of a PTC, showing
Fig. 6. (a) The resonant modes of a structure form a lattice in the frequency dimension. (b) Hopping through its sites can be enabled by time modulation, which can couple their different frequencies. (c) The resulting Hamiltonian is analogous to that of electrons in a periodic ionic potential. (d) A ring resonator combined with a modulator can reproduce such a model, (e) enabling hopping between its equally spaced resonant modes.77 (f)–(h) A synthetic dimension may be constructed in a tight-binding model by introducing long-term coupling between the elements of a chain. In the time-domain, this can be realized by modulating the system at multiple frequencies.78 (i), (j) A spatially 1D chain of ring resonators can be combined with temporal modulation to form a synthetic 2D lattice.79 Figures adapted from Refs. 77
Fig. 7. (a) Two resonators coupled via a combination of constant (
Fig. 8. (a) Light scattered from a flat, time-varying metasurface can access a locus of states that form a hyperbola in phase space, as opposed to an ellipse in spatial metasurfaces. (b) Implementation of a time-modulated metasurface at GHz frequencies. (c) A 1-MHz modulation performs efficient frequency conversion through time-modulation.102 (d) Illustration of surface-wave excitation via the Wood anomalies using (e) spatial and (f) temporal modulation of (g) a surface. (h) Example of the Wood anomaly observed in transmission, the surface-wave excitation is explicitly shown in (i) from a finite-element-time-domain simulation.101 Figures adapted from Refs. 102 and 101.
Fig. 9. (a) Space–time diagram of a space–time crystal with alternating refractive indices
Fig. 10. (a)–(c) Angular momentum biasing: a directional modulation along a ring resonator splits the degeneracy between clockwise and anticlockwise traveling states (a),138 in analogy with the Zeeman splitting of electronic states in a magnetic field (b),138 this can be realized by discretizing the elements of the ring, e.g., periodically modulating three strongly coupled resonators, with a phase of 120 deg between them (c).139 (d) Example of operation of a nonreciprocal ring resonator coupled to two waveguides: excitation from the bottom (top) of the channel waveguide (on the right of the ring) excites a counterclockwise (clockwise) mode, whose resonant frequency has been offset from the one of the clockwise (counterclockwise) mode, so (e) the direction of excitation determines the efficiency of the coupling to the resonator, and hence of the transmission to the output port of the channel waveguide.138 (f), (g) Theoretical and (h) experimental performance of an RF circulator made with angular-momentum biased resonators: (f) and (g) the reciprocal response in the absence (f) and presence (g) of angular biasing, and (h) the performance of the experimental implementation of the circulator.139 Figures adapted from Refs. 138 and 139.
Fig. 11. (a)–(c) A synthetic space–time-modulated crystal (a) is formally equivalent to a fictitious moving bianisotropic time-invariant crystal (b) when
Fig. 12. (a) Time dependence of the electric field intensity at the output port transmitted through different thicknesses (blue to red)
Fig. 13. Examples of applications of space–time metasurfaces. (a) An isolator based on the unidirectional excitation of evanescent modes. (b) Waves scattering off an STM experience a nonreciprocal phase shift. (c) An STM-based circulator.104 (d) Illustration of an experimentally realized space–time coding metasurface, consisting of a square array of individual voltage-controlled elements with binary impedance values, enabling encoding and imprinting of arbitrary phase and amplitude modulation onto different scattered harmonics for (e) beam-steering and shaping.114 (f) Illustration of wave power combining using STMs: incoming waves with frequency
Fig. 14. (a), (b) Concept of photocarrier excitation and time-refraction in ITO:215 (a) A pump pulse transfers energy to the electrons in the conduction band, leading to a temporal variation in the refractive index. (b) As the probe experiences different indices at different delays, its spectral content will be shifted (redshift for negative delay, blueshift for positive). (c)–(f) Measured time-refraction, phase conjugation, and negative refraction signals from a 500-nm-thick AZO slab pumped by 105 fs pulses, at an energy of
Fig. 15. (a) Schematic of a Si metasurface engineered to support collective high-Q Fano resonances.235 (b) Schematic of the self-induced blueshift of harmonics in the resulting Si nanoantenna cavity:235 photons in the antenna will undergo a blueshift due to the rapidly changing permittivity of the medium before being upconverted via third-harmonic generation. (c) Measured spectral evolution for an 80-fs pump pulse length in a GaAs high-
Get Citation
Copy Citation Text
Emanuele Galiffi, Romain Tirole, Shixiong Yin, Huanan Li, Stefano Vezzoli, Paloma A. Huidobro, Mário G. Silveirinha, Riccardo Sapienza, Andrea Alù, J. B. Pendry, "Photonics of time-varying media," Adv. Photon. 4, 014002 (2022)
Category: Reviews
Received: Nov. 15, 2021
Accepted: Dec. 8, 2021
Posted: Dec. 8, 2021
Published Online: Feb. 15, 2022
The Author Email: Galiffi Emanuele (egaliffi@gc.cuny.edu)