We study the nonlinear process of second harmonic generation in photonic time-crystals, materials with refractive index that varies abruptly and periodically in time, and obtain the phase matching condition for this process. We find conditions for which the second harmonic generation is highly enhanced even in the absence of phase matching, governed by the exponential growth of the modes residing in the momentum gap of the photonic time crystal. Additionally, under these conditions, a cascade of higher order harmonics is generated at growing exponential rates. The process is robust, with no requirement for phase-matching, the presence of a resonance or a threshold, drawing energy from the modulation.

We predict the existence of surface plasmon polaritons at the interface between a metal and a periodically modulated dielectric medium, and find an unusual multi-branched dispersion curve of surface and bulk modes. The branches are separated by momentum gaps indicating intense amplification of modes, and display high and low group velocity ranging from zero to infinity at short wavelengths. We simulate how these SPP modes are formed by launching a properly engineered laser beam onto the metallic interface and examine their space-time evolution. The amplification of the surface plasmons at the interface of a photonic time-crystal offers a path to overcome plasmonic losses, which have been a major challenge in plasmonics.

Photonic quantum computing has been rapidly advancing over the past decade, with measurement-based approaches emerging as particularly promising. A crucial requirement for these approaches is the generation of large-scale cluster states. In this work, we present a method to create cluster states using Photonic Time-Crystals (PTCs) — dielectric materials with their refractive index rapidly modulated in time. PTCs effectively function as a set of optical parametric oscillators and beam-splitters, producing simultaneous two-mode squeezing for many pairs of photonic modes with opposite wavevectors. We utilize this capability to propose a method for generating two-dimensional cluster states, offering important advantages over existing protocols.

Photonic time crystals (PTCs) are materials whose dielectric permittivity is strongly modulated periodically in time at rates comparable to a single cycle of the waves propagating within. Such modulations can have a large impact on the propagation of waves in the medium. For example, all waves with wave vectors associated with the momentum gap are exponentially amplified, which in turn can lead to enhanced light-matter interaction. Here, we study the emission of radiation in a PTC and show that the power of the spontaneous radiation depends on the initial state of the field, and can be controlled through the turn-on process of the PTC. Specifically, if the PTC starts abruptly, the spontaneous emission rate grows monotonically towards the momentum gap, whereas if the PTC is turned on gradually the rate decreases towards the gap. This finding implies that the spontaneous emission rate can be designed and controlled by shaping the temporal modulation of the refractive index, a feature having major consequences for radiation generated in PTCs, such as PTC lasers and antennas.

We study surface plasmons at the interface between a metal and a photonic time crystal. We find momentum bands separated by gaps facilitating intense amplification and high group velocity at extremely short wavelengths.

We demonstrate time-reflection of optical wavepackets propagating in time-modulated synthetic lattice based on coupled optical fiber loops. Time-reflection arises from a temporal boundary created by an abrupt change in the lattice parameters.

We present a method to protect the entanglement of a Bell-state encoded on a single photon performing a two-dimensional discrete-time quantum walk. We find an edge-state at the boundary of two distinct quantum walk domains.

We study the process of second harmonic generation in photonic time-crystals. We find the phase matching condition of the process and show it can be tailored by the photonic time-crystal band structure.

We show that Photonic Time-Crystals generate two-mode squeezing for photonic modes with opposite momentum. Based on this property we propose a three-step algorithm for generation of cluster states for measurement-based quantum computing.

We show that Photonic Time-Crystals (PTCs) produce two-mode squeezing for pairs of photonic modes. We propose an algorithm for generating a cluster state in PTC for a measurement-based quantum computing in a simple three-step process.

We present the concept of temporal Bound States in the Continuum (BIC): bound states in the time dimension embedded in the spatial frequency continuum. These BICs are analytic solutions to Maxwell's equations in time-varying media.

We propose a method for chirality selection of edge modes in topological laser arrays by applying two-stage turn-on. Symmetry breaking is based on the nonlinearity of gain saturation which is always present in lasers.

We introduce topological edge states in photonic space-time crystals. We show that photonic space-time crystals support propagating edge states and find a unique edge state that grows exponentially in energy whilst following the spatio-temporal edge.

Propagating topological edge states have been extensively studied in two-dimensional photonic topological insulators (TIs) [1]. Apart from other photonic TIs in higher dimensions, 3D TIs have recently been implemented with microwaves [2] and acoustic waves [3], the latter inducing topology through a dislocation. Here we report the first experimental demonstration of a three-dimensional topological insulator at optical frequencies and observe the propagation dynamics of its unidirectional edge states in two spatial and one modal dimensions [4]. In our system, the introduction of a screw dislocation into a weak 3DTI serves to establish a closed 3-dimensional path that encircles the 3D structure around the outer parameter and loops back along the axis of the dislocation.

We study light propagation of electromagnetic waves in a medium with a homogeneous refractive index varying quasi-periodically in time. We study two types of time-varying quasi-crystals: Andrey Aubrey and Fibonacci sequence.

The hallmark of topological insulators is the scatter-free propagation of waves in topologically protected edge channels. This transport is strictly chiral on the outer edge of the medium, and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional topological edge states have been demonstrated on several different platforms, and are emerging as a promising tool for robust lasers, quantum devices, and other applications. However, three-dimensional photonic topological insulators, specifically those supporting topologically protected edge states in all 3D, have thus far remained out of experimental reach. Here, we demonstrate a three-dimensional photonic topological insulator with protected topological edge states. The topological protection is enabled by a screw dislocation. For this purpose, we utilize the concept of synthetic dimensions in a 2D photonic waveguide array by introducing an additional modal dimension to transform the system into a 3D photonic topological insulator. The lattice dislocation endows the system with edge states propagating along three-dimensional trajectories, with topological protection akin to strong photonic topological insulators. Our work paves the way for utilizing three-dimensional topology in photonic science and technology.

We experimentally demonstrate three-dimensional photonic topological insulators induced by lattice dislocations. We observe topological protected surface states, as well as light propagating unidirectionally along a screw dislocation.

Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed a growing interest in artificial gauge fields generated either by the geometry or by time-dependent modulation, as they have been enablers of topological phenomena and synthetic dimensions in many physical settings, e.g., photonics, cold atoms, and acoustic waves. Here, we formulate and experimentally demonstrate the generalized laws of refraction and reflection at an interface between two regions with different artificial gauge fields. We use the symmetries in the system to obtain the generalized Snell law for such a gauge interface and solve for reflection and transmission. We identify total internal reflection (TIR) and complete transmission and demonstrate the concept in experiments. In addition, we calculate the artificial magnetic flux at the interface of two regions with different artificial gauge fields and present a method to concatenate several gauge interfaces. As an example, we propose a scheme to make a gauge imaging system-a device that can reconstruct (image) the shape of an arbitrary wavepacket launched from a certain position to a predesigned location.

We demonstrate photonic structures supporting topological edge-states propagating in full 3D. These robust edge-states propagate in a screw motion in a 3D topological insulator with two spatial dimensions and one synthetic dimension.

We propose a system that exploits the fundamental features of topological photonics and synthetic dimensions to force many semiconductor laser resonators to synchronize, mutually lock, and under suitable modulation emit a train of transform-limited mode-locked pulses. These lasers exploit the Floquet topological edge states in a 1D array of ring resonators, which corresponds to a 2D topological system with one spatial dimension and one synthetic frequency dimension. We show that the lasing state of the multielement laser system possesses the distinct characteristics of spatial topological edge states while exhibiting topologically protected transport. The topological synthetic-space edge mode imposes a constant-phase difference between the multifrequency modes on the edges, and together with modulation of the individual elements forces the ensemble of resonators to mode lock and emit short pulses, robust to disorder in the multiresonator system. Our results offer a proof-of-concept mechanism to actively mode lock a laser diode array of many lasing elements, which is otherwise extremely difficult due to the presence of many spatial modes of the array. The topological synthetic-space concepts proposed here offer an avenue to overcome this major technological challenge and open new opportunities in laser physics.