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REVIEW 2 major objections 4 minor 77 references

Space-Time Event Scattering and Extension Method (STESEM): A Universal Framework for Scattering in Space-Time Metamaterials

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that scattering of any waveform at any moving space-time interface follows from one local boundary event plus an extension along invariant traveling-wave coordinates, computed with no coordinate transformations.

desk verdict STESEM is a solid tutorial that repackages the group's earlier event-tracing ideas into a single framework; the derivations check out, but the 'arbitrary trajectory' claim is constrained by an unstated injectivity condition. read the letter →

arxiv 2608.03333 v1 pith:3HHIH5XE submitted 2026-08-04 physics.optics

Klaas De Kinder , Amir Bahrami , Christophe Caloz This is my paper
classification physics.optics
keywords space-timemetamaterialsmovingboundarieselectromagneticscatteringDopplershiftfrequencychirpingtraveling-wavecoordinatesacceleratedinterfaceslaboratory-frameformulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This tutorial paper introduces the space-time event scattering and extension method (STESEM) and claims it as a universal scheme for scattering at a moving space-time interface — the elementary building block out of which space-time metamaterials are assembled. Scattering is decomposed into a local event, where the wave trajectory meets the moving boundary and the moving boundary conditions fix the scattered waveform values, and an extension, in which those values ride unchanged along the invariant traveling-wave coordinates of the scattered waves. Because everything is computed directly in the laboratory frame, the method sidesteps the Lorentz- or Rindler-frame transformations that earlier treatments required and that break down for accelerated or multi-velocity configurations. If the claim is right, amplitudes, frequency conversions and phase offsets all emerge from a single expression per scattered wave, for any incident waveform. The six canonical boundaries analyzed — stationary, instantaneous, corner, constant-velocity, wedge, and accelerated — are presented as variants of the same two-step procedure.

What carries the argument

The central object is the traveling-wave coordinate $\tau^\pm_i = n_i z/c \mp t$, which labels each point of a waveform and stays constant along the wave's trajectory in a nondispersive medium. STESEM rests on that invariance: each observation point is traced back to the scattering event where its wave trajectory crosses the boundary $z[t]$; the moving boundary conditions, Eqs. (3)–(4), are enforced there and the values slide unchanged along those coordinates. For accelerated interfaces the event is located through the auxiliary functions $f^\pm_i[t_\star] = n_i z[t_\star]/c \mp t_\star$ and their inverses $(f^\pm_i)^{-1}$, evaluated numerically when no closed form exists.

What would settle it

Run a 1+1D Maxwell solver on a Gaussian pulse at an oscillating boundary, $z[t] = A\sin(\Omega t)$, using the paper's parameters $(n_1,\eta_1)=(1,1)$, $(n_2,\eta_2)=(2,0.5)$. Where a wave trajectory crosses the boundary twice, the inverse $(f^\pm_i)^{-1}(\tau^\pm_i)$ gives two candidate scattering times and Eq. (14) has no single value, while the simulation shows a coherent sum of all crossings. For a monotone accelerated boundary, instead, matching the predicted chirp $\omega^\pm_i/\omega_i = (n_1 v_m[t_\star]/c - 1)/(n_i v_m[t_\star]/c \mp 1)$ against the spectrogram would confirm the method

Watch

Extended reading notes

Core claim

Scattering of any incident waveform at any space-time interface is claimed to be set by two laboratory-frame steps: at the scattering event, where the wave trajectory from an observation point meets the boundary trajectory $z[t]$, the moving boundary conditions fix the scattered waveform values; those values then extend to every other point because $\tau^\pm_i = n_i z/c \mp t$ is invariant along propagation. One scheme yields Fresnel coefficients, $n_1/n_2$ time-interface scaling, cascaded corner events, moving-interface Doppler shifts, the wedge's infinite series, and accelerated-interface chirping, with events located by inverting $f^\pm_i[t_\star] = n_i z[t_\star]/c \mp t_\star$.

Load-bearing premise

The method assumes that every observation point corresponds to one and only one scattering event on the boundary — the one-to-one correspondence asserted in Sec. III and used through the inverse mappings $(f^\pm_i)^{-1}$ in Eqs. (14) and (A53) — which fails when an interface trajectory winds back so that a wave trajectory crosses it more than once.

Editorial extensions

If this is right

  • One expression per scattered wave delivers the full response — amplitude, frequency transition, and phase offset — for an arbitrary incident waveform, so pulse-shape transformation is obtained directly rather than through separate amplitude and phase derivations.
  • Configurations with no common comoving frame, such as two interfaces moving at different velocities, become tractable: the wedge solution is an infinite geometric series of elementary moving-interface events with closed-form coefficients.
  • Complex structures assemble modularly from known events: the space-time corner is a stationary-interface event plus a temporal-interface event plus one secondary scattering of the later-backward wave.
  • Accelerated boundaries produce a continuously varying instantaneous Doppler scaling — frequency chirping — with the local scaling set by the interface velocity at each portion of the waveform's own scattering event.
  • For arbitrary interface trajectories the method reduces to a numerical recipe: build the auxiliary functions $f^\pm_i$ from the trajectory, invert them over the traveling-wave coordinate arrays, and evaluate the scattering formulas.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: where a wave trajectory crosses an oscillating or self-retracing boundary several times, the paper's unique-event premise fails; a natural extension, not stated in the paper, is a coherent event-history sum over all crossings, each weighted by its own local boundary coefficients.
  • Beyond the paper: because the scattered waveform's argument is written as a composition of the interface trajectory through $z[t_\star]$, the framework implies a design route the authors leave implicit — prescribe a target output waveform and solve for the interface trajectory that produces it, with the single-crossing condition as the solvability constraint.
  • Beyond the paper: the event-plus-extension decomposition should transfer to 2+1D and 3+1D, with the invariant coordinate replaced by a phase coordinate on the wave cone and the event becoming a curve or surface of intersection, generalizing the corner and wedge results to space-time edges and prisms.
  • Beyond the paper: adding material dispersion is a substantive extension rather than a corollary, because the traveling-wave coordinate is no longer invariant for every spectral component once the medium disperses; the extension step itself would then need to become spectral propagation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper introduces STESEM, a two-step procedure for scattering at a 1+1D space-time interface: first enforce moving boundary conditions at the scattering event on the interface trajectory, then extend the resulting waveforms away from the interface using invariance of the traveling-wave coordinates. The method is applied to stationary, instantaneous, space-time corner, uniformly moving, wedge, and accelerated interfaces, with full derivations in the appendix. The paper claims that this provides a universal framework for arbitrary incident waveforms and arbitrary interface trajectories directly in the laboratory frame, without coordinate transformations, yielding scattering amplitudes, frequency transitions, and phase transformations in one formulation.

Significance. If the stated universality is made precise, the paper is a valuable unifying tutorial. The derivations are careful and self-contained: no parameters are fitted, all coefficients follow from the moving boundary conditions, the stationary- and constant-velocity limits reduce to the familiar Fresnel and Doppler results, and the appendix contains the full algebra for every canonical case. The modular decomposition into a local event plus an invariant-coordinate extension is elegant and likely to be pedagogically useful. However, the advertised universality for arbitrary interface trajectories is not established by the derivation as written; the reader's stress-test concern about the injectivity of the auxiliary mappings lands, and this directly affects the central claim rather than a peripheral detail.

major comments (2)
  1. [Sec. III; Sec. V.F; Appendix A.8, Eqs. (13)-(14), (A51)-(A54)] The central claim that every observation point maps to a unique scattering event, so that (f_i^±)^{-1} is single-valued, is not true for arbitrary accelerated trajectories. Differentiating f_1^- = n_1 z[t]/c + t and f_2^+ = n_2 z[t]/c - t gives df_1^-/dt = n_1 v_m/c + 1 and df_2^+/dt = n_2 v_m/c - 1. These are strictly monotone only for -c/n_1 < v_m(t) < c/n_2 for all t. The text restricts to 'accelerated subluminal' without defining the bound (Sec. V.F), while Secs. III and V.G claim 'arbitrary' and 'fully general' trajectories. If v_m drops below -c/n_1 (possible with |v_m|<c when n_1>n_2), f_1^- becomes non-injective, Eq. (14) has multiple t* values, and re-scattering is omitted. Please state the needed velocity window, restrict the universality claim accordingly, or extend the construction to multivalued branch handling.
  2. [Appendix A.8, Eqs. (A47)-(A48)] The accelerated-interface ansatz contains only ψ_1^- and ψ_2^+, and the coefficients in Eq. (A48) become singular at v_m = -c/n_1 (reflection denominator) and at v_m = c/n_2 (transmission denominator). For n_1 ≠ n_2 these velocities are subluminal, so the stated 'subluminal' restriction does not exclude them. The paper does not discuss the physical meaning of these singularities or whether the scattered-wave ansatz must be changed (e.g., by including later-backward/later-forward waves) when the trajectory crosses these thresholds. Since Sec. V.F claims to treat arbitrary accelerated subluminal interfaces, this is a load-bearing gap.
minor comments (4)
  1. [Appendix A.5, Eq. (A19d)] The argument of ψ_i in ψ_2^{+T} and in the associated Heaviside factor is written with τ_2^-; it should be τ_2^+ to match Eq. (A14b) and the definition of the forward-scattered wave.
  2. [Appendix A.7, Eq. (A42b)] There appears to be a missing '+' sign between the two terms on the right-hand side; as printed the expression reads as a product. Also, the constant in the first term is written as τ'_0 while Eq. (A45b) defines it as Δτ'_0.
  3. [Footnote [53]] The footnote contains unresolved '[?]' placeholders for the spatial and temporal transition-region references; these should be completed before publication.
  4. [Sec. V.F] The numerical procedure in step (v) instructs the reader to use a standard inversion routine, but for non-monotonic f_i^± such a routine silently selects one branch. This should at least be flagged in the text, given the injectivity restriction discussed in the major comments.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: STESEM derives the scattering response from standard moving boundary conditions and an independent characteristic extension; the unstated injectivity condition on the inverse mapping is a correctness limitation, not an input-output circularity.

full rationale

The paper's derivation chain is self-contained. The starting point is the general traveling-wave representation (Eqs. (1)-(2)) and the electromagnetic moving boundary conditions (Eqs. (3)-(4)), which are standard results cited to Pauli, Kong, and the spacetime-metamaterial literature, not derived from the target answers. For each canonical structure, the scattering amplitudes at the interface are obtained by algebraically solving these boundary conditions (e.g., Eqs. (6), (11), (12), (A48)), and the extension to arbitrary observation points uses only the invariance of the traveling-wave coordinate tau_i^± along scattered-wave trajectories (Eqs. (7)-(9), (A49)-(A54)). No parameter is fitted to a subset of data and then renamed a prediction; the moving boundary conditions are independent inputs, and the known Fresnel and temporal-interface results are reproduced as special cases, providing external benchmarks. The citations to the authors' prior work on accelerated interfaces [43], wedges [49], retarded-argument imposition [51], and related chirping/pulse-shaping [44,45] are contextual and do not carry the derivation: the accelerated-interface formulas (A47)-(A54) are derived in-line from the same boundary conditions and characteristic extension, not imported from those references. The one real caveat is a validity-domain gap: the claim that Eq. (A53) 'maps every observation point onto its unique scattering event for an arbitrary accelerated interface' requires the auxiliary functions f_i^±[t*] = n_i z[t*]/c ∓ t* to be injective, which in turn requires the instantaneous velocity to be restricted (e.g., -c/n_1 < v_m < c/n_2 for the reflected/transmitted wave pair). For trajectories violating this, the inverse mapping is multi-valued and re-scattering is omitted. This is an unstated assumption about the allowed interface trajectories and hence a correctness risk, but it is not circular: the predicted scattered field is not assumed in the input equations. The overall derivation is therefore free of self-definitional, fitted-input, or self-citation load-bearing circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The framework introduces no new physical entities and fits no free parameters. It rests on standard wave solutions, imported moving boundary conditions, and an unstated uniqueness assumption about the scattering-event correspondence. The central 'arbitrary trajectory' claim is therefore weaker than the assumptions actually used.

assumptions (3)
  • standard math The traveling-wave ansatz E_i^± = ψ_i^±(n_i z/c ∓ t), with H, D, B linked through η_i and n_i, spans all solutions of Maxwell's equations in 1+1D isotropic, linear, nondispersive media.
    Sec. II, Eqs. (1)-(2). This is the standard d'Alembert solution of the 1D wave equation.
  • domain assumption The moving boundary conditions E_1 - v_m B_1 = E_2 - v_m B_2 and H_1 - v_m D_1 = H_2 - v_m D_2 are valid for arbitrary interface velocity, including accelerated motion.
    Sec. III, Eqs. (3), cited to [30, 56, 57]. The paper applies this at every instant without deriving or justifying it for accelerated interfaces.
  • ad hoc to paper Every observation point maps to exactly one scattering event; the auxiliary functions f_i^±[t*] are invertible and single-valued.
    Sec. III asserts one-to-one correspondence; Sec. V.F and Appendix A.8 use (f_i^±)^{-1} in Eqs. (14) and (A53). This fails for non-monotonic interface trajectories, so the method's 'arbitrary trajectory' claim depends on an unstated condition.

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Cite this review

Pith. "Pith review of Space-Time Event Scattering and Extension Method (STESEM): A Universal Framework for Scattering in Space-Time Metamaterials." pith.science (2026). https://pith.science/paper/3HHIH5XE

@misc{pith2026260803333,
  author       = {Pith},
  title        = {Pith review of: Space-Time Event Scattering and Extension Method (STESEM): A Universal Framework for Scattering in Space-Time Metamaterials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3HHIH5XE}},
  note         = {Machine review of arXiv:2608.03333}
}
read the original abstract

Space-time metamaterials offer unprecedented control over electromagnetic waves by enabling simultaneous manipulation of spatial and temporal degrees of freedom. However, analytical descriptions of their scattering processes remain fragmented, with existing approaches typically requiring configuration-specific derivations or transformations to specialized reference frames that become impractical for accelerated or multi-interface structures. In this tutorial, we introduce the space-time event scattering and extension method (STESEM), a universal framework for electromagnetic scattering at arbitrary space-time interfaces. By decomposing the scattering process into a local interaction event and a subsequent extension along invariant traveling-wave coordinates, STESEM formulates space-time scattering directly in the laboratory frame without requiring coordinate transformations. The method provides a unified description of scattering amplitudes, frequency transitions and phase transformations for arbitrary incident waveforms and interface trajectories. We demonstrate the framework by deriving the complete scattering responses of canonical space-time structures, including stationary and instantaneous interfaces, space-time corners, uniformly moving interfaces, wedges and accelerated boundaries. Beyond providing analytical solutions, STESEM reveals the physical principles underlying these distinct phenomena and shows that complex space-time scattering processes can be constructed from elementary moving-interface interactions. This framework establishes a systematic foundation for analyzing and designing advanced space-time metamaterials, enabling extensions toward dispersive, bianisotropic and higher-dimensional systems.

Figures

Figures reproduced from arXiv: 2608.03333 by the authors.

Figure 1
Figure 1. FIG. 1. Overview of a space-time metamaterial structure and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Canonical space-time interfaces [30, 58]. Top row: space-time trajectory diagrams in the direct space-time domain, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Scattering results obtained by STESEM for the canonical space-time structures in Fig. 2 with parameters ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Works this paper leans on

77 extracted references · 76 canonical work pages

  1. [51]

    De Kinder, A

    K. De Kinder, A. Bahrami, and C. Caloz, Scattering and chirping at accelerated interfaces, Phys. Rev. Appl.25, 014077 (2026)

    work page 2026

  2. [1]

    The two media are characterized by refractive indicesn i and impedancesη i, wherei= 1,2 denotes the medium

    Problem Statement We consider a one-dimensional electromagnetic sys- tem consisting of a moving abrupt interface separat- ing two isotropic, linear and nondispersive media. The two media are characterized by refractive indicesn i and impedancesη i, wherei= 1,2 denotes the medium. The interface moves along thez-direction and is de- scribed by the trajector...

    work page

  3. [2]

    General Boundary Conditions The electromagnetic moving boundary conditions at the interface,z[t], are given by [30, 56] E± 1 −v m[t⋆]B± 1 z=z[t ⋆] =E ± 2 −v m[t⋆]B± 2 z=z[t ⋆] , (A3a) H ± 1 −v m[t⋆]D± 1 z=z[t ⋆] =H ± 2 −v m[t⋆]D± 2 z=z[t ⋆] , (A3b) wheret ⋆ represents the scattering time at the interface (Fig. 1d). Substituting Eqs. (A1) into Eqs. (A3) wi...

    work page

  4. [3]

    Space (Stationary) Interface For a space interface, the scattered waves areψ − 1 (re- flection) andψ + 2 (transmission), see Fig. 2a. Since the interface does not move, its velocity is zero (v m = 0) and hence, the interface trajectory is simply described byz=z 0. Consequently, the boundary conditions re- duce to the continuity ofE ± i andH ± i [Eq. (A3)]...

    work page

  5. [4]

    Time (Instantaneous) Interface At a time interface, the scattered waves areψ − 2 (later- backward) andψ + 2 (later-forward), as shown in Fig. 2b. The interface occurs instantaneously throughout space and is therefore described byt=t 0, corresponding to the limiting casev m → ∞. Consequently, the scattering event is identified by its spatial positionz ⋆, r...

    work page

  6. [5]

    A 3) and the time interface (Sec

    Space-time Corner The space-time corner combines the space interface (Sec. A 3) and the time interface (Sec. A 4), as illustrated in Fig. 2c. Unlike the previous canonical structures, a space-time corner cannot be described by a single scat- tering event. Instead, the interaction proceeds through two successive scattering events. The first scattering even...

    work page

  7. [6]

    Constant-V elocity T raveling Interface At a constant-velocity traveling interface in the sub- luminal regime (|v m|< c/n 2) [69], the scattered waves areψ − 1 (reflection) andψ + 2 (transmission), see Fig. 2d. The interface is described byz=v mt+z 0. In this case, Eqs. (A4) result in 1−n 1 vm c ψi h − 1−n 1 vm c t⋆ +n 1 z0 c i + 1 +n 1 vm c ψ− 1 h 1 +n 1...

    work page

  8. [7]

    Space-Time W edges This canonical space-time structure example consists of two interfaces moving at different constant veloci- ties, see Fig. 2e [49]. The interfaces are parametrized asz=v m,it+z i, wherev m,i denotes the modulation ve- locity andz i the initial position of interfacei= 1,2. The waves inside the wedge are denoted byψ + 2 andψ − 2 , rep- re...

    work page

Show all 77 references
  1. [8]

    Accelerated Interface At an accelerated subluminal interface, the scattered waves areψ − 1 andψ + 2 , see Fig. 2f [43]. The interface is 17 parametrized in a general form asz=z[t]. Application of Eqs. (A4) for an accelerated interface yields 1−n 1 vm[t⋆] c ψi n1 z[t⋆] c −t ⋆ +...

  2. [9]

    R. M. Walser, Electromagnetic metamaterials, Proc. SPIE4467, 1 (2001)

    2001

  3. [10]

    Tretyakov, On the history of complex-media electro- magnetics and metamaterials research, Opt

    S. Tretyakov, On the history of complex-media electro- magnetics and metamaterials research, Opt. Mater. Ex- press16, 2453 (2026)

    2026

  4. [11]

    T. J. Cui, S. Zhang, A. Al` u, M. Wegener, S. J. Pendry, J. Luo, Y. Lai, Z. Wang, X. Lin, H. Chen,et al., Roadmap on electromagnetic metamaterials and metasurfaces, J. Phys. Photonics6, 032502 (2024)

    2024

  5. [12]

    V. G. Veselago, The electrodynamics of substances with simultaneously negative values ofϵandµ, Phys.-Uspekhi 10, 509 (1968)

    1968

  6. [13]

    J. B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett.85, 3966 (2000)

    2000

  7. [14]

    Shurig, J

    D. Shurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Metamaterial elec- tromagnetic cloak at microwave frequencies, Science314, 977 (2006)

    2006

  8. [15]

    D. R. Smith and D. Schurig, Electromagnetic wave prop- agation in media with indefinite permittivity and perme- ability tensors, Phys. Rev. Lett.90, 077405 (2003)

    2003

  9. [16]

    Linden, C

    S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Magnetic response of metamaterials at 100 terahertz, Science306, 1351 (2004)

    2004

  10. [17]

    Caloz, Metamaterial dispersion engineering concepts and applications, Proc

    C. Caloz, Metamaterial dispersion engineering concepts and applications, Proc. IEEE99, 1711 (2011)

    2011

  11. [18]

    W. T. Chen, A. Y. Zhu, and F. Capasso, Flat optics with dispersion-engineered metasurfaces, Nat. Rev. Mater.5, 604 (2020)

    2020

  12. [19]

    M. G. Silveirinha, Nonlocal homogenization model for a periodic array ofϵ-negative rods, Phys. Rev. E73, 046612 (2006)

    2006

  13. [20]

    Taravati, B

    S. Taravati, B. A. Khan, S. Gupta, K. Achouri, and C. Caloz, Nonreciprocal nongyrotropic magnetless meta- surface, IEEE Trans. Antennas Propag.65, 3589 (2017)

    2017

  14. [21]

    F. R. Morgenthaler, Velocity modulation of electromag- netic waves, IRE Trans. Microw. Theory Tech.6, 167 (1958)

    1958

  15. [22]

    Weinstein, Linear signal stretching in a time-variant system, IEEE Trans

    H. Weinstein, Linear signal stretching in a time-variant system, IEEE Trans. Circuits Syst.12, 157 (1965)

    1965

  16. [23]

    Elliott and J

    B. Elliott and J. Gunn, Signal processing with a time- varying transmission, in1966 IEEE International Solid- State Circuits Conference. Digest of Technical Papers, Vol. 9 (1966) pp. 20–21

    1966

  17. [24]

    J. T. Mendon¸ ca and P. K. Shukla, Time refraction and time reflection: Two basic concepts, Physica Scripta65, 160 (2002)

    2002

  18. [25]

    Bacot, M

    V. Bacot, M. Labousse, A. Eddi, M. Fink, and E. Fort, Time reversal and holography with spacetime transfor- mations, Nat. Phys.12, 972 (2016)

    2016

  19. [26]

    Shlivinski and Y

    A. Shlivinski and Y. Hadad, Beyond the Bode-Fano bound: Wideband impedance matching for short pulses using temporal switching of transmission-line parame- ters, Phys. Rev. Lett.121, 204301 (2018)

    2018

  20. [27]

    H. Li, A. Mekawy, and A. Al` u, Beyond Chu’s limit with Floquet impedance matching, Phys. Rev. Lett.123, 164102 (2019)

    2019

  21. [28]

    Hayran and F

    Z. Hayran and F. Monticone, Beyond the Rozanov bound on electromagnetic absorption via periodic temporal modulations, Phys. Rev. Appl.21, 044007 (2024)

    2024

  22. [29]

    Akbarzadeh, N

    A. Akbarzadeh, N. Chamanara, and C. Caloz, Inverse prism based on temporal discontinuity and spatial dis- persion, Opt. Express.43, 3297 (2018)

    2018

  23. [30]

    Pacheco-Pe˜ na and N

    V. Pacheco-Pe˜ na and N. Engheta, Temporal aiming, Light Sci. Appl.9, 129 (2020)

    2020

  24. [31]

    Pacheco-Pe˜ na and N

    V. Pacheco-Pe˜ na and N. Engheta, Antireflection tempo- ral coatings, Opt. Mater. Express.7, 323 (2020)

    2020

  25. [32]

    J. T. Mendon¸ ca, A. M. Martins, and A. Guerreiro, Tem- poral beam splitter and temporal interference, Phys. Rev. A68, 043801 (2003)

    2003

  26. [33]

    J. T. Mendon¸ ca, A. Guerreiro, and A. M. Martins, Quan- tum theory of time refraction, Phys. Rev. A62, 033805 (2000)

    2000

  27. [34]

    J. Xu, W. Mai, and H. Werner, Douglas, Complete polar- ization conversion using anisotropic temporal slabs, Opt. Express.46, 1373 (2021)

    2021

  28. [35]

    H. Li, S. Yin, and A. Al` u, Nonreciprocity and Faraday rotation at time interfaces, Phys. Rev. Lett.128, 173901 (2022)

    2022

  29. [36]

    H. He, S. Shang, J. Qi, F. Bo, and H. Li, Faraday rota- tion in nonreciprocal photonic time-crystals, Appl. Phys. Lett.122, 051703 (2023)

    2023

  30. [37]

    Caloz and Z.-L

    C. Caloz and Z.-L. Deck-L´ eger, Spacetime metamaterials—Part I: General concepts, IEEE Trans. Antennas Propag.68, 1569 (2019)

    2019

  31. [38]

    Caloz and Z.-L

    C. Caloz and Z.-L. Deck-L´ eger, Spacetime metamaterials—Part II: Theory and applications, IEEE Trans. Antennas Propag.68, 1583 (2019)

    2019

  32. [39]

    Caloz, Z.-L

    C. Caloz, Z.-L. Deck-L´ eger, A. Bahrami, O. C. Vicente, and Z. Li, Generalized space-time engineered modulation (GSTEM) metamaterials: A global and extended per- spective, IEEE Antennas Propag. Mag.65, 60 (2022)

    2022

  33. [40]

    Y. Yu, H. Hu, Q. Yang, L. Zou, D. Liu, H. C. Zhang, and Y. Luo, Fundamentals and applications of time-varying media: A review (2026), arXiv:2604.15629

    2026 arXiv

  34. [41]

    E. S. Cassedy and A. A. Oliner, Dispersion relations in time-space periodic media: Part I—Stable interactions, Proc. IEEE51, 1342 (1963)

    1963

  35. [42]

    E. S. Cassedy, Dispersion relations in time-space periodic media: Part II—Unstable interactions, Proc. IEEE55, 1154 (1967)

    1967

  36. [43]

    Deck-L´ eger, A

    Z.-L. Deck-L´ eger, A. Akbarzadeh, and C. Caloz, Wave deflection and shifted refocusing in a medium modulated by a superluminal rectangular pulse, Phys. Rev. B97, 104305 (2018)

    2018

  37. [44]

    P. A. Huidobro, E. Galiffi, S. Guenneau, R. V. Craster, and J. B. Pendry, Fresnel drag in space-time-modulated metamaterials, Proc. Natl. Acad. Sci. USA116, 24943 (2019)

    2019

  38. [45]

    P. A. Huidobro, M. G. Silveirinha, E. Galiffi, and J. B. Pendry, Homogenization theory of space-time metamate- rials, Phys. Rev. Appl.16, 014044 (2021)

    2021

  39. [46]

    L. Xu, G. Xu, J. Huang, and C.-W. Qiu, Diffusive Fizeau drag in spatiotemporal thermal metamaterials, Phys. Rev. Lett.128, 145901 (2022)

    2022

  40. [47]

    Bahrami, Z.-L

    A. Bahrami, Z.-L. Deck-L´ eger, and C. Caloz, Electrody- namics of accelerated-modulation space-time metamate- rials, Phys. Rev. Appl.19, 054044 (2023)

    2023

  41. [48]

    De Kinder, A

    K. De Kinder, A. Bahrami, and C. Caloz, Doppler pulse amplification, Phys. Rev. Appl.24, 044029 (2025)

    2025

  42. [49]

    Taravati and G

    S. Taravati and G. V. Eleftheriades, Generalized space- time-periodic diffraction gratings: Theory and applica- 19 tions, Phys. Rev. Appl.12, 024026 (2019)

    2019

  43. [50]

    J. B. Pendry, Air conditioning for photons, Opt. Mater. Express.14, 407 (2024)

    2024

  44. [52]

    Z. Li, X. Ma, K. De Kinder, A. Bahrami, and C. Christophe, Space-time graded-index interfaces and related chirping, Nanophotonics14, 3211 (2025)

    2025

  45. [53]

    Bahrami, K

    A. Bahrami, K. De Kinder, and C. Caloz, Arbitrary pulse shaping using accelerated interfaces, Small Struct. , e202500340 (2025)

    2025

  46. [54]

    B. E. A. Saleh and M. C. Teich,Fundamentals of Pho- tonics, 3rd ed. (New York: Wiley, 2019)

    2019

  47. [55]

    Deck-L´ eger, N

    Z.-L. Deck-L´ eger, N. Chamanara, M. Skorobogatiy, M. G. Silveirinha, and C. Caloz, Uniform-velocity space- time crystals, Adv. Photonics1, 56002 (2019)

    2019

  48. [56]

    Stefanini, E

    L. Stefanini, E. Galiffi, S. Yin, S. Singh, D. M. Sol ´ ıs, N. Engheta, A. Toscano, D. Ramaccia, F. Bilotti, and A. Al` u, Theory and experimental observation of scatter- ing by a space-time corner, Phys. Rev. Lett.135, 113802 (2025)

    2025

  49. [57]

    Bahrami, K

    A. Bahrami, K. De Kinder, Z. Li, and C. Caloz, Space- time wedges, Nanophotonics14, 3939 (2025)

    2025

  50. [58]

    Lampe, E

    M. Lampe, E. Ott, and J. H. Walker, Interaction of elec- tromagnetic waves with a moving ionization front, Phys. Fluids21, 42 (1978)

    1978

  51. [59]

    Bahrami and C

    A. Bahrami and C. Caloz, Retarded argument imposi- tion: A novel approach for solving scattering problems at interfaces formed by space-time modulations, in2025 Nineteenth International Congress on Artificial Materi- als for Novel Wave Phenomena (Metamaterials)(2025) pp. X–021–X–023

    2025

  52. [60]

    1b), with no net transport of matter, theinterfacesare the only entities exhibiting effective translational mo- tion (Fig

    Since the actual atoms and molecules of the structure onlyoscillateunder the external excitation (Fig. 1b), with no net transport of matter, theinterfacesare the only entities exhibiting effective translational mo- tion (Fig. 1c) and may therefore be regarded as the real metaa...

  53. [61]

    In practice, interfaces cannot be perfectly abrupt, nei- ther in space nor in time, and must therefore be smooth. However, if the transition region is much smaller than the wavelength for a spatial interface [?], much shorter than the period for a temporal interface [?] or sat...

  54. [62]

    (1) is arbitrary

    The waveform function,ψ ± i , in Eq. (1) is arbitrary. For instance, for a propagating Gaussian-modulated pulse, it would be written as ψ± i h ni z c ∓t i = exp iω ni z c ∓t exp − (niz/c∓t) 2 σ2 , withωbeing the center frequency andσthe pulse width, reducing to a simple plane ...

  55. [63]

    Van Bladel,Relativity and Engineering, Vol

    J. Van Bladel,Relativity and Engineering, Vol. 15 (Springer Science & Business Media, 2012)

    2012

  56. [64]

    Pauli,Theory of Relativity(Pergamon Press, 1981)

    W. Pauli,Theory of Relativity(Pergamon Press, 1981)

    1981

  57. [65]

    J. A. Kong,Electromagnetic Wave Theory(Wiley, 2008)

    2008

  58. [66]

    Caloz, A

    C. Caloz, A. Bahrami, K. De Kinder, and L. Zhiyu, Space-time engineered modulation (STEM) elements, in2025 Nineteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (2025) pp. X–049–X–051

    2025

  59. [67]

    A. J. Fresnel,M´ emoire sur la loi des modifications que la r´ eflexion imprime ` a la lumi` ere polaris´ ee(De l’Imprimerie De Firmin Didot Fr´ eres, 1834)

  60. [68]

    H. A. Lorentz,Over de theorie der terugkaatsing en brek- ing van het licht(Van der Zande, 1875)

  61. [69]

    D. K. Kalluri, On reflection from a suddenly created plasma half-space: Transient solution, IEEE Trans. Plasma Sci.16, 11 (1988)

    1988

  62. [70]

    M. A. Lampert, Incidence of an electromagnetic wave on a ˇ cerenkov electron gas, Phys. Rev.102, 299 (1956)

    1956

  63. [71]

    M. A. Gaafar, T. Baba, M. Eich, and A. Petrov, Front- induced transitions, Nat. Photonics.13, 737 (2019)

    2019

  64. [72]

    De Kinder and C

    K. De Kinder and C. Caloz, Scattering at space- time interfaces between dispersive media (2026), arXiv:2604.00893

    2026 arXiv

  65. [73]

    II), under which the wavevectorkreduces to the scalar quantityk, linearly related to frequency byk=±nω/c

    The apparent breaking of symmetry between space and time, arising from the restriction of the bottom dia- grams to temporal frequencies, results from the 1+1D and nondispersive-medium assumptions adopted in this paper (Sec. II), under which the wavevectorkreduces to the scalar...

  66. [74]

    J. D. Jackson,Classical Electrodynamics(John Wiley & Sons, 2012)

    2012

  67. [75]

    space-time lens

    L. A. Ostrovskiˇi, A boundary with accelerating motion as a “space-time lens”, Radiophys. Quantum Electron18, 456 (1975)

    1975

  68. [76]

    D’Exelle, K

    C. D’Exelle, K. De Kinder, and C. Caloz, Space-time lensing by accelerated interfaces in dispersive media (2026), arXiv:2607.13780

    2026 arXiv

  69. [77]

    They are treated in [43]

    The other two regimes, the superluminal (|v m|> c/n 1) and interluminal (c/n 2 <|v m|< c/n 1) regime, involve radically different physics. They are treated in [43]

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.