Pith. sign in

REVIEW 3 major objections 4 minor 71 references

Synthetic crystal rotation with spacetime metamaterials

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A spatiotemporally modulated crystal that mimics rotation about the z-axis preserves a combined time-translation/rotation symmetry, conserving $H-\Omega J_{S,z}$, and scatters light into frequency–spin-locked sidebands at…

desk verdict The symmetry argument is clean and the negative-frequency sideband regime is genuinely new; the caveat is the physical realization at optical rotation frequencies. read the letter →

arxiv 2506.02495 v1 pith:UL676UVD submitted 2025-06-03 physics.optics cond-mat.mes-hallquant-ph

Iñigo Liberal , Alejandro Manjavacas This is my paper
classification physics.opticscond-mat.mes-hallquant-ph
keywords syntheticrotationspacetimemetamaterialstime-varyingmediaspinangularmomentumfrequency-SAMlockingnegativefrequencytransitionsopticalKerreffectspatiotemporallightfields
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

The paper argues that a material whose optical axis is turned in time, without any physical motion, changes the symmetry structure of light scattering: time translation and rotation are each broken, but their combination remains a symmetry. Using Noether's theorem, the authors show that this residual symmetry makes the quantity $H-\Omega J_{S,z}$ (energy minus the rotation frequency times spin angular momentum) conserved, locking field amplification to spin generation. Solving a thin-film boundary-value problem, they find that a narrowband input at $\omega_0$ produces sidebands at $\omega_0\pm2\Omega$ carrying opposite circular polarizations, and that when $\Omega$ reaches $\omega_0/2$ the low-frequency sidebands merge at zero frequency and then move to negative frequencies with reversed spin sign. This matters because mechanically rotating bodies are limited to GHz rotation rates, whereas synthetic rotation could in principle reach optical frequencies, opening light-matter interaction regimes that physical rotation cannot enter.

What carries the argument

The load-bearing object is the spatiotemporal rotation symmetry encoded by the identity $\partial_t\varepsilon=\Omega[\mathbb{d}R,\varepsilon]$, meaning that the time derivative of the permittivity equals the rotation generator acting by commutation. Under this symmetry the Lagrangian supports a Noether charge that is a linear combination of total energy $H$ and total spin angular momentum $J_{S,z}$, namely $H-\Omega J_{S,z}$; the continuity equations for energy and SAM carry source terms that cancel precisely when combined with weight $\Omega$. The scattering calculation then rests on the thin-film boundary condition $\mathbf{E}(0,t)=\alpha^{-1}(t)\mathbf{p}(t)=\mathbf{E}_0(0,t)-\frac{Z_0}{2}\partial_t\mathbf{p}(t)$, whose iterative solution produces the $\omega_0\pm2\Omega$ sidebands with opposite circular polarizations.

What would settle it

Drive a thin Kerr-nonlinear film with a circularly polarized pump while sending a weak probe at $\omega_0$ through it, sweeping the pump's rotation rate $\Omega$ from below to above $\omega_0/2$, and measure the reflected spectrum and the circular handedness of each sideband. If the synthetic-rotation picture is right, sidebands appear at $\omega_0\pm2\Omega$ with opposite handedness, merge at $\omega=0$ when $\Omega=\omega_0/2$, and the erstwhile low-frequency sideband re-emerges at positive frequencies with reversed handedness for $\Omega>\omega_0/2$; observing sidebands that stay at positive frequencies with unchanged handedness, or any deviation from the $\pm2\Omega$ spacing, would refute the frequency–SAM locking prediction.

Watch

Extended reading notes

Core claim

The central claim is that a permittivity modulation of the form $\varepsilon(z,t)=R(\Omega t)\varepsilon_S(z)R^{-1}(\Omega t)$ — a static anisotropic profile whose axes are continuously rotated — leaves the wave equation invariant under a combined infinitesimal time translation and axis rotation. This spatiotemporal rotation symmetry enforces conservation of $H-\Omega J_{S,z}$, a linear combination of total energy and total spin angular momentum. Scattering from a thin film implementing this modulation yields, to first order in the anisotropy, a linearly polarized component plus sidebands at $\omega_0\pm2\Omega$ with opposite circular polarization, a frequency–SAM locking that reproduces the spectrum of physically rotating anisotropic particles. For $\Omega\ge\omega_0/2$ the low-frequency sideband pair collapses at $\omega=0$ and then passes into negative frequencies with reversed SAM sign, producing single-sideband and same-sign sideband regimes. The authors propose that a Kerr-nonlinear crystal pumped by a circularly polarized beam realizes this synthetic rotation, since the effective susceptibility takes the form $R(\Omega t)\chi_S R^{-1}(\Omega t)$.

Load-bearing premise

The calculation assumes the material's optical response tracks the rotating axis instantly and locally, with the permittivity exactly equal to $R(\Omega t)\varepsilon_S R^{-1}(\Omega t)$ at every instant and a thin-film polarization $\mathbf{P}=\mathbf{p}\,\delta(z)$ with $\mathbf{p}=\alpha(t)\mathbf{E}(0,t)$; real Kerr or free-carrier media respond with finite speed and dispersion, and that lag is not modeled when the rotation approaches the light frequency.

Editorial extensions

If this is right

  • At low rotation frequencies, synthetic rotation reproduces the spectral fingerprints of mechanically rotating anisotropic particles, so rotating-body experiments could be mimicked in stationary setups.
  • Rotation frequencies comparable to the carrier frequency become accessible, enabling sideband collapse at $\omega=0$, negative-frequency sidebands, and SAM sign reversal — regimes mechanical rotation cannot reach.
  • Pulses scattered by a synthetically rotating film become spatiotemporal light fields whose polarization changes within the pulse, offering continuously varying optical torque or coherent control of several polarized transitions in a single pulse.
  • Because $H-\Omega J_{S,z}$ is conserved, any net energy change of the field is accompanied by a proportional change in spin angular momentum, locking amplification to spin generation.
  • At $\Omega\ge\omega_0$, the SAM spectrum consists of two high-frequency sidebands of the same sign, a regime that could modify vacuum friction, Casimir torques, and rotation-induced entanglement.

Reading between the lines

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

  • The symmetry argument is formulated at the level of the wave equation, not the thin-film approximation, so the same conservation law $H-\Omega J_{S,z}$ should hold for bulk, multilayer, and metasurface geometries; testing a thick slab would separate the symmetry prediction from boundary-specific artifacts.
  • The instantaneous-response assumption is the fragile point as $\Omega$ approaches material resonances; a dispersive model should predict additional shifts or extra sidebands beyond the $\omega_0\pm2\Omega$ pattern, giving an experimental handle on how fast synthetic rotation can actually be driven.
  • The predicted opposite circular polarization of the two sidebands suggests a direct route to frequency-polarization entanglement: detecting a photon at $\omega_0+2\Omega$ and one at $\omega_0-2\Omega$ should reveal correlated polarizations if the scheme is operated quantum mechanically.
  • Any modulation mechanism that reproduces the rotating form $R(\Omega t)\varepsilon_S R^{-1}(\Omega t)$ — acoustic, electronic, free-carrier, or nonlinear — should exhibit the same universal sideband structure, since only the symmetry and not the microscopic mechanism enters the conservation law.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies a medium whose permittivity is a continuously rotating anisotropic tensor, ε(z,t)=R(Ωt)ε_S(z)R^{-1}(Ωt), modeling a synthetic crystal rotation. The authors show that this spatiotemporal modulation preserves a combined time-translation and rotation symmetry, and they use Noether's theorem to derive the conserved quantity H−ΩJ_{S,z}, a linear combination of electromagnetic energy and spin angular momentum (SAM). They also derive continuity equations for energy and SAM and verify the cancellation of the sources/sinks. For a thin-film realization, they analyze the transient scattering of pulses, finding spatiotemporal light with intra-pulse SAM variations and an exact correlation ΔH=ΩΔJ_{S,z}. In the frequency domain, a first-order perturbative solution predicts sidebands at ω0±2Ω with opposite circular polarizations (frequency–SAM locking), with special degenerate regimes at Ω=ω0/2 and sign reversals for Ω>ω0/2. The authors propose an implementation based on the optical Kerr effect with a circularly polarized pump, and they discuss how the synthetic rotation can access rotation frequencies comparable to or exceeding the optical frequency, which is impossible for mechanical rotation.

Significance. If the central theoretical result is correct, the derivation of a conserved quantity H−ΩJ_{S,z} for a rotating synthetic crystal is a clean and elegant contribution to the symmetry analysis of spacetime metamaterials. The frequency–SAM locking and the continuity-equation formulation provide a useful framework, and the agreement with the rotating-particle theory of Ref. [9] at low Ω is a valuable cross-check. The paper's main advertised significance, however, is access to rotation frequencies comparable to light frequency and the resulting qualitatively new regimes. That claim currently rests on an instantaneous, dispersionless Kerr model that is not physically established at Ω∼ω0. For this reason, the novelty of the work as a route to new optical-frequency phenomena is not yet fully demonstrated, although the conservation law and sideband structure themselves are internally sound and machine-checkable.

major comments (3)
  1. [Practical implementations, Eq. (1)] The central claim of accessing rotation frequencies on the order of the optical frequency relies on the physical realizability of Eq. (1) at such high Ω. The implementation section derives χeff=R(Ωt)χS R^{-1}(Ωt) by substituting EP=E0(bx cosΩt + by sinΩt) into the instantaneous third-order response Pi=χ^(3)_ijkl EjEkEl. This treats the pump as a real vector rotating at Ω with no carrier and assumes a dispersionless, memoryless χ^(3). For Ω∼ω0, the pump field would necessarily contain optical-frequency components, and the relevant χ^(3)(ω_s;ω_s,−ω_p,ω_p) would have finite response times and resonances, so the polarization-sensitive effective permittivity would not reduce to the exact rotation form assumed in Eq. (1). The abstract and conclusions advertise rotation frequencies comparable to light frequency, but the paper does not provide a causal, multi-frequency model or an explicit estimate of the maximum Ω for which the instantaneous approximation is valid. This is a load-bearing gap in the physical-realization story.
  2. [Frequency-domain response, 'To first order'] The sideband spectrum and the qualitative regimes described in Fig. 3 are derived from a first-order perturbative expansion in (αx−αy), as stated in the paragraph containing Eq. (8). The paper uses this first-order result to assert the degeneracy at Ω=ω0/2, the sign reversal for ω0/2<Ω<ω0, and the single-sideband behavior. If higher-order terms become significant at large modulation strength or at the degenerate points, these spectral features could be modified or supplemented by additional sidebands. The manuscript should state the parameter range in which the first-order truncation is quantitatively reliable, especially for the advertised new regimes at Ω∼ω0.
  3. [Transient response, Fig. 2] The transient analysis uses the thin-film boundary condition P=p(t)δ(z) with p=α(t)E(0,t), but the explicit form of α(t) is not given in the main text. It is presumably α(t)=R(Ωt)α_S R^{-1}(Ωt), but the reader cannot verify the numerical implementation or the domain of validity of the thin-film approximation from the main text alone. The paper should define α(t) explicitly and provide the corresponding boundary-value equation in the main text or clearly reference the equation in the Supplementary Material.
minor comments (4)
  1. [Throughout] There are several typographical errors: 'correspodding' in the definition of jS,z, 'of of' in the sentence confirming the conservation of H−ΩJS,z, and 'characterizeed' in the frequency-domain section. These should be corrected.
  2. [Reference [48]] Reference [48] is cited as 'See Supplementary Material', which is not a standard bibliographic entry. The authors should explicitly list the supplementary material with a URL or DOI, as is customary for the journal.
  3. [Practical implementations] The sentence 'calcite is a centrosymmetric trigonal crystal [52] with a high-frequency cut-off that enables third-harmonic generation into the ultraviolet [53,54]' might be more precisely stated as 'a centrosymmetric crystal with trigonal symmetry' to avoid confusion, since calcite is not always described as trigonal in the point-group sense used earlier. This is a minor wording issue.
  4. [Frequency-domain response, Fig. 3] The caption of Fig. 3 states that the SAM is normalized to ((αx−αy)/16|E(0)|)^2, but the exact definition of the normalization factor could be clearer, especially the factor of 16, which appears to depend on the coefficients in Eq. (8). A more explicit definition would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the conservation law and sideband structure follow from the stated modulation ansatz with no fitted parameters, and the optical-frequency realizability concern is a physics assumption, not a circularity.

full rationale

The central derivation is self-contained. Equation (1) defines the spatiotemporal permittivity; Eq. (3) and Eq. (5) express the residual spatiotemporal rotation symmetry, and the conserved quantity H - Omega*J_{S,z} is obtained through Noether's theorem and independently by explicit continuity equations (Eqs. (6)-(7)), so no input is renamed as a prediction. The frequency-domain sidebands at omega0 +/- 2*Omega with opposite circular polarizations are obtained by an iterative solution of the thin-film boundary problem, not by fitting; the agreement with rotating-particle theory [9] is an external benchmark. The self-citations [39-41] provide context on spatiotemporal symmetries and the Noether formula, but the paper re-derives the needed continuity equations, so they are not load-bearing. The main caveat is physical rather than circular: the practical-implementation section assumes an instantaneous Kerr response with the pump treated as a real rotating vector at frequency Omega, which is not established at Omega ~ omega0; that is a realizability or validity limitation, not a case of the derivation being equivalent to its input.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central symmetry-conservation result is derived from Maxwell's equations and Noether's theorem without fitted parameters. The paper rests on several modeling assumptions: an instantaneous local permittivity that rotates exactly, a thin-film delta-function polarizability, a first-order perturbative frequency-domain solution, and a Kerr-effect implementation with an undepleted circular pump. These are physical assumptions, not fitted parameters, and are not all validated experimentally.

assumptions (5)
  • standard math The Lagrangian density L = ε0/2 ∂tA·ε·∂tA - ε0c^2/2 (∂zA)^2 produces the correct wave equation via Euler-Lagrange, and Noether's theorem applies to the combined time-translation/rotation symmetry.
    Invoked in the 'Spatiotemporal symmetries and conserved quantities' section; standard variational principle for fields in media.
  • domain assumption The permittivity modulation exactly mimics rotation of an anisotropic crystal: ε(z,t)=R(Ωt)ε_S(z)R^{-1}(Ωt), with axes rotating at angular velocity Ω.
    Eq. (1) is the modeling premise; no microscopic derivation of how such a modulation is generated or maintained is given.
  • domain assumption Thin-film approximation: induced polarization is P(z,t)=p(t)δ(z), p=α(t)E(0,t), with boundary value equation E(0,t)=α^{-1}p=E0(0,t)-(Z0/2)∂t p.
    Used for transient and frequency-domain scattering; valid in the limit d<<λ0 but residual effects are not quantified.
  • domain assumption Frequency-domain response is obtained from an iterative solution and truncated at first order; the expression for eP(ω) includes only sidebands at ω0±2Ω.
    The 'first order' truncation is stated but higher-order corrections and convergence are not analyzed.
  • domain assumption A circularly polarized optical pump induces an effective Kerr susceptibility of the form χ_eff=R(Ωt)χ_S R^{-1}(Ωt) for select crystal symmetries.
    Practical implementation section; assumes undepleted pump, instantaneous Kerr nonlinearity, and specific crystal point groups.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Synthetic crystal rotation with spacetime metamaterials." pith.science (2026). https://pith.science/paper/UL676UVD

@misc{pith2026250602495,
  author       = {Pith},
  title        = {Pith review of: Synthetic crystal rotation with spacetime metamaterials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UL676UVD}},
  note         = {Machine review of arXiv:2506.02495}
}
read the original abstract

The interaction of light with rotating bodies has been historically limited to rotation frequencies much smaller than optical frequencies. Here, we investigate synthetic crystal rotations, i.e., spatiotemporal modulations mimicking the rotation of an anisotropic crystal, which grant access to large rotation frequencies. Spatiotemporal modulations change the fundamental symmetries of the electromagnetic field, breaking temporal and rotation symmetries, but preserving a spatiotemporal rotation symmetry that enforces the conservation of a combination of energy and spin angular momentum (SAM). The scattering of optical pulses by synthetically rotating crystals results in spatiotemporal light with intra-pulse SAM changes. The frequency-domain response reveals sidebands with frequency/SAM locking, and negative frequency sideband transitions for large enough rotation frequencies. Our results highlight the qualitatively different light-matter interaction regimes accessed by synthetic rotations.

Figures

Figures reproduced from arXiv: 2506.02495 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

71 extracted references · 59 canonical work pages

  1. [9]

    Asenjo-Garcia, A

    A. Asenjo-Garcia, A. Manjavacas, and F. J. Garc ´ ıa de Abajo, Stimulated light emission and inelastic scattering by a classical linear system of rotating particles, Physical Review Letters 106, 213601 (2011)

    work page 2011

  2. [1]

    P. A. Tipler and G. Mosca, Physics for scientists and engineers (Macmillan, 2007)

    work page 2007

  3. [2]

    potential after the interaction with the thin-film

    (c) Variation in the total energy ∆H = H(t)−H(0) and SAM ∆JS,z = JS,z(t)−JS,z(0), as a function of Ω, normalized to the initial energy H(0). potential after the interaction with the thin-film. A complete video animation and additional examples can be found in [48]. Intuitively, the field consists of re- flected and transmitted pulses, containing cross-pol...

    work page

  4. [3]

    crystals result in the synthetic rotation of an effec- tive anisotropic crystal with nonreciprocal susceptibility χS = {(3bxbx + byby) χxxxx + (bxby − 3 bybx) χxyyy } E2 0 , fur- ther extending the landscape of synthetic rotations (see

    work page

  5. [4]

    S. P. Kish and T. C. Ralph, Quantum effects in rotating reference frames, A VS Quantum Science 4 (2022)

    work page 2022

  6. [5]

    E. J. Post, Sagnac effect, Reviews of Modern Physics 39, 475 (1967)

    work page 1967

  7. [6]

    Schwichtenberg, Physics from symmetry (Springer, 2018)

    J. Schwichtenberg, Physics from symmetry (Springer, 2018)

    work page 2018

  8. [7]

    Frauendiener, Notes on the sagnac effect in general relativity, General Relativity and Gravitation 50, 147 (2018)

    J. Frauendiener, Notes on the sagnac effect in general relativity, General Relativity and Gravitation 50, 147 (2018)

    work page 2018

Show all 71 references
  1. [8]

    G. Li, T. Zentgraf, and S. Zhang, Rotational doppler ef- fect in nonlinear optics, Nature Physics 12, 736 (2016)

    2016

  2. [10]

    Anderson, H

    R. Anderson, H. Bilger, and G. Stedman, Sagnac effect: A century of Earth-rotated interferometers, American Journal of Physics 62, 975 (1994)

    1994

  3. [11]

    Emile and J

    O. Emile and J. Emile, Rotational doppler effect: a re- view, Annalen der Physik 535, 2300250 (2023)

    2023

  4. [12]

    Mazor and B

    Y. Mazor and B. Z. Steinberg, Rest frame interference in rotating structures and metamaterials, Physical Review Letters 123, 243204 (2019)

    2019

  5. [13]

    De Zutter, Scattering by a rotating dielectric sphere, IEEE Transactions on Antennas and Propagation28, 643 (1980)

    D. De Zutter, Scattering by a rotating dielectric sphere, IEEE Transactions on Antennas and Propagation28, 643 (1980)

    1980

  6. [14]

    Shiozawa, Phenomenological and electron-theoretical study of the electrodynamics of rotating systems, Pro- ceedings of the IEEE 61, 1694 (1973)

    T. Shiozawa, Phenomenological and electron-theoretical study of the electrodynamics of rotating systems, Pro- ceedings of the IEEE 61, 1694 (1973)

    1973

  7. [15]

    Y. B. Zel’dovich, L. Rozhanskii, and A. Starobinskii, Ro- tating bodies and electrodynamics in a rotating coordi- nate system, Radiophysics and Quantum Electronics 29, 761 (1986)

    1986

  8. [16]

    Manjavacas and F

    A. Manjavacas and F. J. Garc ´ ıa de Abajo, Thermal and vacuum friction acting on rotating particles, Physical Re- view A 82, 063827 (2010)

    2010

  9. [17]

    Sanders, W

    S. Sanders, W. J. M. Kort-Kamp, D. A. R. Dalvit, and A. Manjavacas, Nanoscale transfer of angular momentum mediated by the casimir torque, Communications Physics 2, 71 (2019)

    2019

  10. [18]

    Lannebere and M

    S. Lannebere and M. G. Silveirinha, Wave instabilities and unidirectional light flow in a cavity with rotating walls, Physical Review A 94, 033810 (2016)

    2016

  11. [19]

    Manjavacas and F

    A. Manjavacas and F. J. Garc ´ ıa de Abajo, Vacuum fric- tion in rotating particles, Physical Review Letters 105, 113601 (2010)

    2010

  12. [20]

    Toroˇ s, M

    M. Toroˇ s, M. Cromb, M. Paternostro, and D. Faccio, Generation of entanglement from mechanical rotation, Physical Review Letters 129, 260401 (2022)

    2022

  13. [21]

    Cromb, S

    M. Cromb, S. Restuccia, G. M. Gibson, M. Toroˇ s, M. J. Padgett, and D. Faccio, Mechanical rotation modifies the manifestation of photon entanglement, Physical Review Research 5, L022005 (2023)

    2023

  14. [22]

    J. R. Deop-Ruano and A. Manjavacas, Control of the ra- diative heat transfer in a pair of rotating nanostructures, Physical Review Letters 130, 133605 (2023)

    2023

  15. [23]

    Manjavacas, F

    A. Manjavacas, F. J. Rodr ´ ıguez-Fortu˜ no, F. J. Garc ´ ıa de Abajo, and A. V. Zayats, Lateral casimir force on a ro- tating particle near a planar surface, Physical Review Letters 118, 133605 (2017)

    2017

  16. [24]

    D. Wang, C. Watkins, and H. Xie, MEMS mirrors for LiDAR: A review, Micromachines 11, 456 (2020)

    2020

  17. [25]

    H. C. Lefevre, The fiber-optic gyroscope (Artech House, 2022)

    2022

  18. [26]

    Silvestri, H

    R. Silvestri, H. Yu, T. Str¨ omberg, C. Hilweg, R. W. Peterson, and P. Walther, Experimental observation of earth’s rotation with quantum entanglement, Science Ad- vances 10, eado0215 (2024)

    2024

  19. [27]

    Li and J

    Y. Li and J. Katz, Laser beam scanning by rotary mir- rors. I. modeling mirror-scanning devices, Applied Optics 34, 6403 (1995)

    1995

  20. [28]

    Reimann, M

    R. Reimann, M. Doderer, E. Hebestreit, R. Diehl, M. Frimmer, D. Windey, F. Tebbenjohanns, and L. Novotny, GHz rotation of an optically trapped nanoparticle in vacuum, Physical Review Letters 121, 033602 (2018)

    2018

  21. [29]

    Galiffi, R

    E. Galiffi, R. Tirole, S. Yin, H. Li, S. Vezzoli, P. A. Huidobro, M. G. Silveirinha, R. Sapienza, A. Al` u, and J. B. Pendry, Photonics of time-varying media, Advanced Photonics 4, 014002 (2022)

    2022

  22. [30]

    Dell’Olio, T

    F. Dell’Olio, T. Natale, Y.-C. Wang, and Y.-J. Hung, Miniaturization of interferometric optical gyroscopes: A review, IEEE Sensors Journal 23, 29948 (2023)

    2023

  23. [31]

    J. Ahn, Z. Xu, J. Bang, Y.-H. Deng, T. M. Hoang, Q. Han, R.-M. Ma, and T. Li, Optically levitated nan- odumbbell torsion balance and GHz nanomechanical ro- tor, Physical Review Letters 121, 033603 (2018)

    2018

  24. [32]

    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 perspec- tive, IEEE Antennas and Propagation Magazine 65, 50 (2022)

    2022

  25. [33]

    Bahrami, Z.-L

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

    2023

  26. [34]

    Engheta, Four-dimensional optics using time-varying metamaterials, Science 379, 1190 (2023)

    N. Engheta, Four-dimensional optics using time-varying metamaterials, Science 379, 1190 (2023)

    2023

  27. [35]

    Caloz and Z.-L

    C. Caloz and Z.-L. Deck-L´ eger, Spacetime metamateri- als—Part I: general concepts, IEEE Transactions on An- 6 tennas and Propagation 68, 1569 (2019)

    2019

  28. [36]

    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, Physical Review B 97, 104305 (2018)

    2018

  29. [37]

    Pendry, E

    J. Pendry, E. Galiffi, and P. Huidobro, Photon conser- vation in trans-luminal metamaterials, Optica 9, 724 (2022)

    2022

  30. [38]

    Mazor and A

    Y. Mazor and A. Al` u, One-way hyperbolic metasurfaces based on synthetic motion, IEEE Transactions on Anten- nas and Propagation 68, 1739 (2019)

    2019

  31. [39]

    Harwood, S

    A. Harwood, S. Vezzoli, T. Raziman, C. Hooper, R. Tirole, F. Wu, S. Maier, J. Pendry, S. Hors- ley, and R. Sapienza, Super-luminal synthetic motion with a space-time optical metasurface, arXiv preprint arXiv:2407.10809 (2024)

    2024 arXiv

  32. [40]

    Ortega-Gomez, M

    A. Ortega-Gomez, M. Lobet, J. E. V´ azquez-Lozano, and I. Liberal, Tutorial on the conservation of momentum in photonic time-varying media, Optical Materials Express 13, 1598 (2023)

    2023

  33. [41]

    M. M. Jajin, J. E. V´ azquez-Lozano, and I. Liberal, Sym- metries and conservation of spin angular momentum, he- licity, and chirality in photonic time-varying media, Phys- ical Review A 110, 063522 (2024)

    2024

  34. [42]

    Galiffi, P

    E. Galiffi, P. Huidobro, and J. B. Pendry, Broadband nonreciprocal amplification in luminal metamaterials, Physical Review Letters 123, 206101 (2019)

    2019

  35. [43]

    Liberal, A

    I. Liberal, A. Ganfornina-Andrades, and J. E. V´ azquez-Lozano, Spatiotemporal symmetries and energy-momentum conservation in uniform spacetime metamaterials, ACS Photonics 11, 5273 (2024)

    2024

  36. [44]

    J. C. Serra and M. G. Silveirinha, Rotating spacetime modulation: Topological phases and spacetime haldane model, Physical Review B 107, 035133 (2023)

    2023

  37. [45]

    Here, we investigate synthetic crystal rotation, i.e., spatiotemporal modulations that mimic the rotation of an anisotropic crystal (see Fig

    and microwave metasurfaces for orbital angular mo- mentum (OAM) control [46]. Here, we investigate synthetic crystal rotation, i.e., spatiotemporal modulations that mimic the rotation of an anisotropic crystal (see Fig. 1). Specifically, we clarify their fundamental spatiotemp...

    2025 arXiv

  38. [46]

    D. L. Sounas and A. Al` u, Non-reciprocal photonics based on time modulation, Nature Photonics 11, 774 (2017)

    2017

  39. [47]

    Pakniyat and J

    S. Pakniyat and J. S. Gomez-Diaz, Magnet-free elec- tromagnetic nonreciprocity in two-dimensional materials, Journal of Applied Physics 136 (2024)

    2024

  40. [48]

    In general, our results highlight that crystal symmetries and anisotropic nonlinearities can be harnessed to generalize synthetic motion and spatiotem- poral modulation phenomena

    for details). In general, our results highlight that crystal symmetries and anisotropic nonlinearities can be harnessed to generalize synthetic motion and spatiotem- poral modulation phenomena. A centrosymmetric crystal may also be preferred to avoid competition with second-or...

  41. [49]

    Galiffi, P

    E. Galiffi, P. A. Huidobro, and J. Pendry, An archimedes’ screw for light, Nature Communications 13, 2523 (2022)

    2022

  42. [50]

    Moussa and A

    H. Moussa and A. Al` u, Penrose super-radiance in a synthetically rotating metasurface, in 2022 IEEE In- ternational Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI) (IEEE, 2022) pp. 1290–1291

    2022

  43. [51]

    Cohen-Tannoudji, J

    C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-photon interactions: basic processes and applica- tions (John Wiley & Sons, 1998)

    1998

  44. [52]

    See Supplementary Material

  45. [53]

    Y. Shen, Q. Zhan, L. G. Wright, D. N. Christodoulides, F. W. Wise, A. E. Willner, K.-h. Zou, Z. Zhao, M. A. Porras, A. Chong, et al. , Roadmap on spatiotemporal light fields, Journal of Optics 25, 093001 (2023)

    2023

  46. [54]

    Zhan, Spatiotemporal sculpturing of light: a tutorial, Advances in Optics and Photonics 16, 163 (2024)

    Q. Zhan, Spatiotemporal sculpturing of light: a tutorial, Advances in Optics and Photonics 16, 163 (2024)

    2024

  47. [55]

    R. W. Boyd, Nonlinear Optics (Academic Press, 2008)

    2008

  48. [56]

    New, Introduction to nonlinear optics (Cambridge University Press, 2011)

    G. New, Introduction to nonlinear optics (Cambridge University Press, 2011)

    2011

  49. [57]

    M. Shi, R. Li, B. Li, H. Liu, J. Pan, W. Lin, G. Zhang, and N. Ye, Third-order nonlinear optical properties of calcite crystal in UV region, Optik 182, 664 (2019)

    2019

  50. [58]

    Penzkofer, F

    A. Penzkofer, F. Ossig, and P. Qiu, Picosecond third- harmonic light generation in calcite, Applied Physics B 47, 71 (1988)

    1988

  51. [59]

    Adair, L

    R. Adair, L. Chase, and S. A. Payne, Nonlinear refractive index of optical crystals, Physical Review B 39, 3337 (1989)

    1989

  52. [60]

    Y. Zhou, M. Z. Alam, M. Karimi, J. Upham, O. Reshef, C. Liu, A. E. Willner, and R. W. Boyd, Broadband fre- quency translation through time refraction in an epsilon- near-zero material, Nature Communications 11, 2180 (2020)

    2020

  53. [61]

    J. Bohn, T. S. Luk, S. Horsley, and E. Hendry, Spatiotem- poral refraction of light in an epsilon-near-zero indium tin oxide layer: frequency shifting effects arising from inter- faces, Optica 8, 1532 (2021)

    2021

  54. [62]

    Tirole, S

    R. Tirole, S. Vezzoli, E. Galiffi, I. Robertson, D. Maurice, B. Tilmann, S. A. Maier, J. B. Pendry, and R. Sapienza, Double-slit time diffraction at optical frequencies, Nature Physics 19, 999 (2023)

    2023

  55. [63]

    Lustig, O

    E. Lustig, O. Segal, S. Saha, E. Bordo, S. N. Chowdhury, Y. Sharabi, A. Fleischer, A. Boltasseva, O. Cohen, V. M. Shalaev, et al. , Time-refraction optics with single cycle modulation, Nanophotonics 12, 2221 (2023)

    2023

  56. [64]

    Schirato, M

    A. Schirato, M. Maiuri, A. Toma, S. Fugattini, R. Proi- etti Zaccaria, P. Laporta, P. Nordlander, G. Cerullo, A. Alabastri, and G. Della Valle, Transient optical sym- metry breaking for ultrafast broadband dichroism in plas- monic metasurfaces, Nature Photonics 14, 723 (2020)

    2020

  57. [65]

    Crotti, M

    G. Crotti, M. Akturk, A. Schirato, V. Vinel, A. A. Tri- fonov, I. C. Buchvarov, D. N. Neshev, R. Proietti Za- ccaria, P. Laporta, A. Lema ˆ ıtre,et al. , Giant ultrafast dichroism and birefringence with active nonlocal meta- surfaces, Light: Science & Applications 13, 204 (2024)

    2024

  58. [66]

    Duggan, D

    R. Duggan, D. Sounas, and A. Alu, Optically driven ef- fective faraday effect in instantaneous nonlinear media, Optica 6, 1152 (2019)

    2019

  59. [67]

    Duggan, S

    R. Duggan, S. A. Mann, and A. Al` u, Nonreciprocal pho- tonic topological order driven by uniform optical pump- ing, Physical Review B 102, 100303 (2020)

    2020

  60. [68]

    Moussa, G

    H. Moussa, G. Xu, S. Yin, E. Galiffi, Y. Ra’di, and A. Al` u, Observation of temporal reflection and broad- band frequency translation at photonic time interfaces, Nature Physics 19, 863 (2023)

    2023

  61. [69]

    X. Wang, M. S. Mirmoosa, V. S. Asadchy, C. Rock- stuhl, S. Fan, and S. A. Tretyakov, Metasurface-based realization of photonic time crystals, Science Advances 9, eadg7541 (2023)

    2023

  62. [70]

    J. Park, H. Cho, S. Lee, K. Lee, K. Lee, H. C. Park, J.-W. Ryu, N. Park, S. Jeon, and B. Min, Revealing non-hermitian band structure of photonic Floquet me- dia, Science Advances 8, eabo6220 (2022)

    2022

  63. [71]

    Reyes-Ayona and P

    J. Reyes-Ayona and P. Halevi, Observation of genuine wave vector (k or β) gap in a dynamic transmission line and temporal photonic crystals, Applied Physics Letters 107 (2015)

    2015

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.