Pulse-driven photonic transitions and nonreciprocity in space-time modulated metasurfaces

TL;DR

The paper tackles the challenge of inducing photonic transitions between eigenstates at optical frequencies without sustained periodic modulation. It develops a theoretical framework for traveling spatiotemporal pulse modulations applied to dispersion-engineered metastructures, deriving a Dyson-like evolution and a Fermi’s golden rule–style transition rate that couples initial and final states through the modulation spectrum $\tilde{V}(\Omega_f-\Omega_i)$ while conserving the quantity $\beta = k - \omega/v_m$. The work shows that structured media, via tailored density of states, can channel broadband modulation into selective transitions between discrete states or radiation-continuum channels, even with a single modulation cycle. It demonstrates substantial nonreciprocity in free-space radiation using metasurfaces near leaky modes, achieving 25 dB isolation in the fast-decay regime and up to 61 dB in a slow-decay, front-induced regime, highlighting practical pathways for ultrafast, energy-efficient dynamic photonics with potential for free-space isolation and on-chip photonic processing. The findings establish a practical framework where dispersion engineering and ultrafast modulation enable time-varying photonic functionalities previously limited to continuous modulation, with broad implications for spatio-temporal wavefront control and photonic computing.

Abstract

Time-varying photonic systems open new possibilities for controlling light, enabling photonic time crystals, time reflection and refraction, frequency conversion, synthetic gauge fields, optical nonreciprocity, among others. These effects emerge from the dynamic modulation of optical properties, which can mediate photonic transitions between eigenstates of different frequencies and/or wavevectors. To achieve such transitions, conventional approaches rely on periodic modulation schemes that demand ultrafast modulation rates and continuous energy input, posing significant practical challenges at optical frequencies. Here, we demonstrate that periodic-modulation-driven photonic transitions within the radiation continuum can be effectively mimicked using a single-period ultrafast pulse modulation, eliminating the need for sustained continuous modulation. By leveraging dispersion engineering in metasurfaces to tailor the density of states in the radiation continuum, we achieve controlled frequency transitions and theoretically demonstrate strong nonreciprocity for free-space waves as a key application. Our findings may guide future experimental research on time-varying photonics using materials such as transparent conductive oxides and semiconductors, expanding the possibilities for ultrafast and reconfigurable optical technologies. More broadly, our work may establish a practical and energy-efficient framework for dynamic photonic systems, with potential applications ranging from spatio-temporal wavefront manipulation to photonic computing and ultrafast signal processing.

Figures (4)

• Figure 1: | Controlling photonic transitions under traveling pulse modulation.a, Photonic transitions can be direct (frequency-only) or indirect (involving both frequency and wavevector changes), enabling functionalities such as isolation, frequency conversion, time reversal, light storage, and synthetic gauge fields. b,c, In a homogeneous medium, a traveling periodic modulation couples an input wave at a given $(\omega,k)$ to discrete radiation states. This selectivity comes from the fixed modulation frequency and wavevector. d,e, In contrast, a traveling pulse modulation has a broadband spectrum, so the transition spans many $(\omega,k)$ states. Without guided leaky modes (that is, without spectral regions of high DOS), the incident energy is spread inefficiently across the radiation continuum. f,g, When the medium is structured to support guided leaky modes, the associated spectral regions of high DOS act as channels that the broadband pulse modulation can couple into. This allows efficient transitions without requiring precise tuning of the modulation frequency and wavevector. Unlike periodic modulation, which enforces discrete shifts, pulse modulation can couple into leaky modes even when the dispersions of the initial and final states are not parallel, since different frequency--wavevector offsets are allowed.
• Figure 2: | Photonic transitions in slab and photonic crystal waveguides under traveling pulse modulation.a, Dispersion diagram of a dielectric slab waveguide showing the fundamental guided mode and the diagonal transition induced by a traveling pulse modulation. b, Dispersion of a PhC slab waveguide, obtained by introducing periodic holes, showing band folding and the appearance of a leaky mode inside the light cone (yellow region). The upper-right insets in a and b show the wavevector-resolved DOS at $k_x a / 2\pi = 0.25$; the lower insets illustrate the corresponding structures. c, Frequency-resolved electric field magnitude along the waveguide axis for the homogeneous slab, showing mostly spectral broadening and weak radiation since no true leaky modes are available. d, For the PhC waveguide, the traveling pulse modulation couples the guided mode to the leaky mode inside the light cone (red circle), producing efficient radiation. The leaky mode propagates in the negative $x$-direction, consistent with the negative slope of its dispersion relation. e--g, Far-field intensity distributions for different cases. e, Homogeneous slab with traveling pulse modulation: broad and inefficient radiation over many angles and frequencies, reflecting the continuous radiation continuum. f, Homogeneous slab with periodic traveling-wave modulation: discrete coupling into specific radiation modes at selected $(\omega,k)$ points. g, PhC slab with traveling pulse modulation: efficient coupling into specific frequencies and angles set by the leaky mode dispersion. The far-field amplitude is more than an order of magnitude stronger than in e and comparable to f. The inset shows the case of periodic modulation combined with spatial structuring, where coupling is restricted to a single frequency--angle channel due to the monochromatic modulation spectrum.
• Figure 3: | Metasurface-mediated nonreciprocal photonic transitions under a traveling pulse modulation with fast relaxation.a, Unit cell of the metasurface comprising GaAs, AlGaO, and SiO$_2$, with a traveling pulse modulation applied along the $+x$-direction. b, Dispersion diagram of the metasurface, showing transitions (dashed arrows) between states 1 and 2 induced by the modulation. The inset shows the magnetic field profile of state 1. c, Far-field intensity for the metasurface, demonstrating excitation of state 1 (red circle) and its transition to state 2 (red circle), radiating at a different angle and frequency. d, In the backward direction, excitation of state 2 does not couple back to state 1. Because the modulation enforces diagonal transitions in $(\omega, k_x)$ space, the backward excitation lies on the opposite side of the dispersion (positive $k_x$), and the same diagonal shift cannot reach state 1. As a result, mainly specular reflection occurs (blue circle). e, For a homogeneous slab without metasurface structuring, state 1 couples very weakly to state 2, since the frequency--angle points of state 1 and state 2 do not correspond to any leaky guided mode in the radiation continuum. f, In the homogeneous case, backward excitation at the frequency--angle of state 2 also results mainly in specular reflection, confirming that metasurface structuring is required for strong nonreciprocal transitions.
• Figure 4: | Metasurface-mediated nonreciprocal photonic transitions under a traveling pulse modulation with a slow relaxation.a, Unit cell of the metasurface comprising GaAs, AlGaO, and SiO$_2$, with a traveling pulse modulation applied along the $+x$-direction. b, Dispersion diagram of the metasurface for two GaAs refractive index states ($\Delta n = 0$ and $\Delta n = 0.5$), showing how the slow relaxation produces an effective transition between them. The lower left inset shows the magnetic field profile of state 1. c, Far-field intensity for the metasurface, showing excitation of state 1 (red circle) and its coupling to state 2 (red circle) enabled by the modulation. d, In the backward direction, the excitation begins from the unpumped configuration ($\Delta n = 0$), where the frequency–angle point of state 2 does not lie on any dispersion branch. No coupling back to state 1 occurs and only specular reflection is observed (blue circle). e, For a homogeneous slab without metasurface structuring, state 1 does not couple to state 2, since the frequency–angle point of state 2 does not correspond to any leaky guided mode in the radiation continuum. f, In the homogeneous case, backward excitation at the frequency–angle of state 2 also produces only specular reflection, as no dispersion branch exists there, similar to d.