We give a general family of electromagnetic boundary conditions applicable to arbitrary space–time interfaces between electromagnetic media, which include the known space–only and time–only boundary conditions as special cases. These boundary conditions describe a broad class of electromagnetic interfaces, including surfaces in arbitrary motion, ultra-thin (metasurface) media, and cases where the media on one or both sides of the boundary can be both spatially and temporally dispersive. Our approach utilizes 4-dimensional spacetime and addresses the question of how, and in what ways, an electromagnetic field may be connected across a 3-dimensional hypersurface. We show that our proposed boundary conditions are the most general conditions consistent with causality and linearity.

Gravitational waves dynamically modulate the local refractive index of a manifold, whence emerges a moving scaffold that facilitates interactions with lightwaves in relative motion. Conservation of energy and momentum mandates the appearance of sidebands in the spectrum of forward-propagating subluminal light-an effect that is intrinsically directional yet imposes no coherence requirements on the interacting fields. Its kinship with synthetic traveling-wave modulations engineered in meta-optics suggests that such index perturbations could emulate spacetime ripples. In this Letter, we propose a fully covariant, all-optical analog framework for mimicking Brillouin-like forward scattering of light in a plasma by spacetime distortions in laboratory settings.

Co-propagating gravitational and electromagnetic waves in a plasma can generate sidebands on the forward-scattered light, thereby offering an avenue for detection of gravitational radiation. Employing a covariant coupled-wave approach, we model gravitational waves as dynamic, phase-insensitive "luminal moving gratings." Derived phase-matching conditions elucidate how these waves interact with lightwaves whilst simultaneously conserving energy and momentum. Although detecting low-frequency gravitational waves is hindered by the requirement for long interaction lengths, advances in laser technology are set to enable high-frequency detection, with the potential of unlocking insights into the primordial fabric of spacetime.

We demonstrate analytically that gravitational waves, upon interacting with copropagating electromagnetic radiation in a plasma, induce distinctive sidebands on the modulated light, thereby providing a detectable signature of their presence. Employing a fully covariant coupled-wave framework, we envision gravitational waves as phase-insensitive luminal moving gratings and derive explicit phase-matching conditions that articulate such an interaction while conserving both energy and momentum. Beyond preserving the directional signature of gravitational waves, the coupling mechanism imposes no coherence requirements on the photon-by-graviton scattering, hence enabling possibilities for exploiting cosmic microwave background radiation. Although detection at low frequencies is constrained by the requirement of long interaction lengths, advances in laser technology are poised to enable high-frequency gravitational wave detection, potentially unveiling insights into the primordial spacetime ripples that have been traversing the cosmos since the inflationary epoch.

We outline a fully covariant framework for electromagnetic wave propagation in time-varying optical media, where synthetic traveling-wave modulations emulate spacetime perturbations from gravitational waves. This leads to curvaturelike terms in the wave equation for the electromagnetic fourpotential, directly paralleling the metric perturbations of linearized gravity. Such a correspondence establishes a clear analogy between optical modulation and gravitational interactions, hence enabling an all-optical analog of Brillouin-like forward scattering by gravitational waves. This paradigm offers a platform for simulating gravitational waves in laboratory-scale optical systems.

Optical analog computing enables powerful functionalities, including spatial differentiation, image processing, and ultrafast linear operations. Yet, most existing approaches rely on resonant or periodic structures, whose performance is strongly wavelength-dependent, imposing bandwidth limitations and demanding stringent fabrication tolerances. Here, to address some of these challenges, we introduce a highly tunable platform for optical processing, composed of two cascaded uniform slabs exhibiting both circular and linear birefringence, whose response exhibits features relevant to optical processing without relying on resonances. Specifically, using a coupled-wave theory framework we show that sharp reflection minima, referred to as spectral holes, emerge from destructive interference between counter-propagating circularly polarized waves in uniform birefringent slabs, and can be engineered solely through parameter tuning without requiring any spatial periodicity. When operated in the negative-refraction regime enabled by giant chirality, the interference response acquires a highly parabolic form around the reflection minimum, giving rise to a polarization-selective Laplacian-like operator that performs accurate spatial differentiation over a broad spatial-frequency range. This functionality is demonstrated through an edge-detection proof of concept. The required material parameters align closely with recent experimental demonstrations of giant, tunable chirality via meta-optics, presenting a promising pathway towards compact and reconfigurable platforms for all-optical pattern recognition and image restoration.

Exceptional points of degeneracy are critical junctures wherein eigenvalues and eigenvectors coalesce, resulting in unique dispersion features. In coupled waveguides, they occur via co-directional or contra-directional coupling. The former requires gain-loss modulation, akin to PT-symmetric gratings, whilst the latter relies on negative phase velocity. We illustrate forks in modal dispersion arising due to negative refraction induced by giant chirality. Such an approach circumvents the manufacturing challenges of balancing photon creation and absorption, while not requiring simultaneous negativity of permittivity and permeability. Meta-media with giant and controllable chirality offer exciting opportunities for light manipulation.

Photonic structures and time-crystals, wherein time is incorporated as an additional degree of freedom for light manipulation, have necessitated the development of analytical and semi-analytical tools. However, such tools are currently limited to specific configurations, leaving several unexplored physical phenomena akin to photonic time-crystals elusive. In this communication, using a coupled-wave theory approach, we unveil the occurring light propagation phenomena in a time-periodic bi-isotropic medium whose permittivity, permeability, and chirality parameter are periodic functions of time. Contrary to their static counterparts, we demonstrate that the considered dynamic medium couples only co-handed counter-propagating waves. In cases of non-constant impedance, we prove that two first-order momentum gaps are formed in the Brillouin diagram, resulting in parametric amplification with different amplification factors and corresponding momenta for the right- and left-handed modes, respectively. The presence of chirality plays a major role in manipulating lightwave signals by controlling the center of resonance, the corresponding bandwidth, and the amplification factor in a distinct fashion for each mode. For a finite ``time-slab'' of the medium, we analytically derive the scattering coefficients as functions of time and momentum, discussing how extreme values of optical rotation grant access to the temporal analog of the chirality-induced negative refraction regime. Finally, we demonstrate the mechanism under which elliptical polarizations may change field orientation whilst the electric field propagates in a momentum gap, thus simultaneously showcasing parametric amplification.

We showcase the impact of almost-periodicity on the parametric amplification associated with the first-order momentum gap in photonic time-crystals with time-varying permittivity. Utilizing a vectorial coupled-wave theory approach, we rigorously analyze the scattering by a temporal slab of the considered medium. We pinpoint a critical regime wherein flaws in material tuning paradoxically enhance amplification due to the coupling of fewer, broader modes, resulting in a higher and broader pulselike amplification envelope. Additionally, we demonstrate that the intensity reflectances of time-reversed waves corresponding to secondary "Bragg" resonances achieve remarkably high levels of subharmonic parametric amplification, with the epsilon-near-zero regime serving as a preferred candidate for experimental implementation. Our counterintuitive findings highlight the potential of intentionally leveraging modulation desynchronization and impurities in the temporal unit cell of photonic time-crystals to enhance both the level and the bandwidth of amplification.

Recent claims by Hu and Li (2023 New J. Phys. 25 023007) that isotropic chiral mediums do not exhibit circular birefringence, asserting that both mutually orthogonal circularly polarized states propagate at the same phase velocity, are refuted. We showcase that the analysis is flawed because it incorrectly interprets the eigenstates supported by reciprocal bi-isotropic mediums.

In non-Hermitian systems, particularly those adhering to PT symmetry, exceptional points (EPs) are critical junctures wherein eigenvalues and eigenvectors coalesce. These points induce the convergence of eigenmodes in waveguiding systems, resulting in unique dispersion features and remarkable effects such as slow light. In a configuration comprising two coupled waveguides, EPs can be achieved via mechanisms involving balanced gain-loss modulation or contradirectional modal interference. By leveraging the latter, in homogeneous chirowaveguides without any reliance on periodicity, we demonstrate the signature phase transitions induced by negative refraction due to giant chirality, which does not necessitate the simultaneous negativity of the permittivity and permeability. Our approach offers advantages over traditional PT-symmetric and negativerefractive-index waveguides, as it does not pose the manufacturing difficulties of balancing the creation and absorption of photons while providing opportunities for remarkable light manipulation due to the presence of chirality. Experimental implementations of metamedia with giant and, moreover, controllable chirality indicate that our medium is well within reach of current technology.

Within the framework of coupled-wave theory, we investigate the propagation of light in a time-periodic chiral medium whose permittivity, permeability, and chirality parameter are periodic functions of time. For non-constant impedance, we show that two first-order momentum gaps emerge in the Brillouin diagram, resulting in parametric amplification with distinct amplification factors and corresponding momenta for right- and left-handed modes. The presence of chirality plays a pivotal role in manipulating lightwave signals, controlling the center of resonance, the corresponding bandgap size, and the amplification factor in a unique manner for each handedness. For a finite "time-slab" of the considered medium, we analytically derive the scattering coefficients as functions of both time and momentum. Additionally, we discuss how extreme values of optical rotation grant access to the temporal analog of the chirality-induced negative refraction regime. Finally, we elucidate the mechanism by which the orientation of the electric field, associated with elliptical polarizations, is altered as the wave propagates within a first-order momentum gap, thereby undergoing simultaneous optical rotation and parametric amplification. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Utilizing coupled-wave theory, we investigate light propagation in a time-periodic bi-isotropic medium. Unlike its static counterpart, the dynamic medium couples co-handed counter-propagating waves, thus forming two momentum gaps in the Brillouin diagram for non-constant impedance. Chirality provides control over the resonance centers, bandwidths, and amplification factors in a distinct fashion for orthogonal polarization states. By deriving simple formulae for the scattering coefficients of a finite “time-slab” of the considered medium, we showcase how extreme optical rotation leads to a negative refraction regime. Even for weak chirality, whereby the chiral scattering coefficients reach a similar level to the corresponding achiral medium, we illustrate how elliptical polarizations can significantly change field orientation, a manifestation of temporal optical activity, while simultaneously being amplified.

We show that a wavelength-independent circular Bragg phenomenon can be exhibited in Faraday chiral media, where the externally applied magnetic field not only relaxes the previously identified matching condition but also offers a degree of freedom for manipulating the location of the chirality-domain resonance and the corresponding bandwidth. Due to uniformity, the phenomenon is necessarily broadband, and applications in highly efficient optical modulation appear within reach of parameters currently achieved in complex meta-media.

We have recently shown that a uniform birefringent medium exhibits a circular Bragg phenomenon that relies solely on resonant tuning of the medium's parameters, rather than on a particular wavelength resonance, thus rendering its electromagnetic response arbitrarily broadband. The resonant condition, however, necessitated a chirality parameter equal to the average refractive index. Here, we demonstrate that non-axial wave propagation in an axially bi-anisotropic uniaxial medium also enacts such a response and, moreover, relaxes the severity of the tuning condition, offering a convenient platform for controlling both the location of the resonance and the cor-responding bandwidth. Anomalous wave propagation at a singular point is additionally identified, in the vicinity of which a remarkably high and intrinsically broadband refractive index can be realized. Recent demonstrations of meta-media with giant and controllable chirality pave the path towards the realistic embodiment of a highly efficient optical modulator.

A new mechanism of Bragg phenomenon is theoretically identified that, remarkably, occurs in a uniform medium and relies on resonant tuning of the medium parameters rather than on wavelength-matching. Due to the uniformity, reflection ensues over a broad wavelength range, much like a metal, but is polarization dependent: one circular state is reflected, whereas the other is transmitted. Such a medium can thus provide a broadband, low-loss polarization divider/combiner. Assessing a realistic embodiment with loss and material dispersion, we discuss practical realizations within range of current meta-media technology at terahertz and optical frequencies.

Recently, scalar coupled-wave theory has been employed to analyze a medium with periodic time-varying permittivity, providing simple expressions and, consequently, straightforward insights into the parametric amplification mechanism. Here, we combine such an approach with the Möbius transformation method to investigate the dispersion and optical response of a finite "time-slab" of the aforementioned medium. We demonstrate the temporal analog of a Bragg grating, discuss the differences with its spatial counterpart, and examine nontrivial scenarios of the permittivity's time-modulation, such as chirping and apodization. Furthermore, we propose a highly selective and, moreover, single-spatial-interface optical sensor, based on phase delineation.

The problem of axial propagation of circularly polarized light in a circularly birefringent structurally chiral medium is exactly solved via full electromagnetic analysis. Underlying symmetries of the system's characteristic matrix reveal interesting insights, which are confirmed by coupled wave theory. For extreme values of chirality, a reverse circular Bragg resonance arises in the negative refraction regime where handedness reversal of counterpart modes occurs. A condition is identified under which circular birefringence precisely offsets structural chirality, rendering the medium simply linearly birefringent. Manufacturing such a medium is feasible via current metamedia and inorganic materials technology and has applications in optics, optoelectronics, and sensing.

A Mobius transformation which conformally maps the unit circle onto itself is applied to the scalar coupled -wave equations, describing electromagnetic wave propagation in Bragg gratings, and reduces them to a first-order nonlinear differential equation of a single real variable. This equation is analytically integrated for linear detuning and numerically for more complicated refractive index modulation scenarios, e.g., chirped and apodized Bragg gratings, offering a platform for identifying both the amplitude and phase of all elements of the transfer matrix of arbitrarily complex cases. A link between coupled-wave theory and coupled oscillators is established, and exploring the transformation's geometrical properties leads to alternative definitions of the photonic band gap.