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Here, we show that isorefractive spacetime crystals with a travelling-wave modulation may mimic rigorously the response of moving material systems. Unlike generic spacetime crystals, which are characterized by a bi-anisotropic coupling in the co-moving frame, isorefractive crystals exhibit an observer-independent response, resulting in isotropic constitutive relations devoid of any bianisotropy. We show how to take advantage of this property in the calculation of the band diagrams of isorefractive spacetime crystals in the laboratory frame and in the study of the synthetic Fresnel drag. Furthermore, we discuss the impact of considering either a Galilean or a Lorentz transformation in the homogenization of spacetime crystals, showing that the effective response is independent of the considered transformation.

Recent studies have shown that low-symmetry conductors under static electric bias offer a pathway to realize chiral gain, where the non-Hermitian optical response of the material is controlled by the spin angular momentum of the wave. In this work, we uncover the topological nature of chiral gain and demonstrate how a static electric bias induces topological bandgaps that support unidirectional edge states at the material boundaries. In our system, these topological edge states consistently exhibit dissipative properties. However, we show that, by operating outside the topological gap, the chiral gain can be leveraged to engineer boundary-confined lasing modes with orbital angular momentum locked to the orientation of the applied electric field. Our results open new possibilities for loss-compensated photonic waveguides, enabling advanced functionalities such as unidirectional, lossless edge-wave propagation and the generation of structured light with intrinsic orbital angular momentum.

Topological photonic systems have recently emerged as an exciting new paradigm to guide light without back-reflections. The Chern topological numbers of a photonic platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green’s function method to determine from first principles the topological invariants of photonic crystals. The proposed formalism does not require the calculation of the photonic band-structure, and can be easily implemented using the operators obtained with a standard plane-wave expansion. Furthermore, it is shown that the theory can be readily applied to the classification of topological phases of non-Hermitian photonic crystals with lossy or gainy materials, e.g., parity-time symmetric photonic crystals. The calculation of the topological invariants of non-Hermitian systems typically relies on the natural modes of the system. Here, an alternative method is presented which does not require the knowledge of the band structure, based on the Green’s function.

Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed-matter systems, as it unveiled that a broken time-reversal symmetry is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo-Tellegen coupling. Here, we use Green’s function method to determine from “first principles” the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo-Tellegen parameter.

Surface plasmons polaritons are collective excitations of an electron gas that occur at an interface between negative- and positive- media. Here, we report the experimental observation of such surface waves using simple waveguide metamaterials filled only with available positive- media at microwave frequencies. In contrast to optical designs, in our setup the propagation length of the surface plasmons can be rather long as low loss conventional dielectrics are chosen to avoid typical losses from negative- media. Plasmonic phenomena have potential applications in enhancing light-matter interactions, implementing nanoscale photonic circuits and integrated photonics.

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with little modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break-down and the Chern topology becomes ill-defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be non-integer notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk-materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large k.

Time-modulated media offer powerful opportunities for controlling light, yet extending such concepts to optical frequencies has remained challenging. Here we propose a different route to photonic spacetime crystals based on modulation of the anomalous velocity in low-symmetry conductors, particularly Weyl semimetals. We show that when driven by a strong optical pump, the anomalous velocity of Bloch electrons induces an ultrafast spacetime modulation that propagates with a superluminal phase velocity relative to the dielectric background. This self-induced modulation enables unidirectional light transport below the optical gap and, near the epsilon-near-zero point, gives rise to collective parametric resonance and stimulated emission of volume plasmons. These findings identify Weyl semimetals as a promising platform for realizing optical spacetime crystals and open a pathway toward active and nonreciprocal photonic systems governed by quantum geometric effects.

In recent years, the confinement of light in open systems with no radiation leakage has raised great interest in the scientific community, both due to its peculiar and intriguing physics and due to its important technological applications. In particular, materials with near-zero permittivity offer a unique opportunity for light localization, as they enable the formation of embedded eigenstates in core-shell systems with suppressed radiation loss. For all the solutions presented thus far in the literature, the exact suppression of the radiation leakage can occur only when the size of the resonator is delicately tuned. Surprisingly, here it is shown that the tuning of the resonator radius may be unnecessary, and that nonlocal metal spherical nanostructures of any size may support multiple embedded eigenstates with a monopole-type symmetry.

Recent studies have shown that non-equilibrium optical systems under static electric fields offer a pathway to realize chiral gain, where the non-Hermitian response of a material is controlled by the spin angular momentum of the wave. In this work, we uncover the topological nature of chiral gain and demonstrate how a static electric bias induces topological bandgaps that support unidirectional edge states at the material boundaries. Curiously, in our system, these topological edge states consistently exhibit dissipative properties. We further show that, by operating outside the topological gap, the chiral gain can be leveraged to engineer boundary-confined lasing modes with orbital angular momentum, locked to the orientation of the applied electric field. Our results open new possibilities for loss-compensated photonic waveguides, enabling advanced functionalities such as unidirectional, lossless edge-wave propagation and the generation of structured light with intrinsic orbital angular momentum.

Here, we investigate the effective response of three-dimensional spacetime crystals formed by spherical scatterers under a travelling-wave modulation. We develop an analytical formalism to homogenize the spacetime crystals that extends the renowned Clausius-Mossotti formula to time-varying platforms. Our formalism shows that travelling-wave spacetime crystals can be used to engineer a wide range of classes of nonreciprocal bianisotropic couplings in the long wavelength limit. In particular, our theory reveals the possibility of realizing a purely isotropic Tellegen response in crystals formed by interlaced sub-lattices of scatterers subjected to different modulation velocities. Furthermore, we introduce a class of generalized Minkowskian crystals that displays invariance under arbitrary Lorentz boosts aligned with a fixed spatial direction. We prove that such systems are formed by pseudo-uniaxial materials with the principal axis aligned parallel to the modulation velocity. The electromagnetic response of such generalized Minkowskian crystals is indistinguishable from that of moving photonic crystals.