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Thanks to their high quality factor, combined to the smallest modal volume, defect-cavities in photonic crystal slabs represent a promising, versatile tool for fundamental studies and applications in photonics. In paricular, the L3, H0 and H1 defects are the most popular and widespread cavity designs, due to their compactness, simplicity and small mode volume. For these cavities, the current best optimal designs still result in Q -values of a few times 10 5 only, namely one order of magnitude below the bound set by fabrication imperfections and material absorption in silicon. Here, we use a genetic algorithm to find a global maximum of the quality factor of these designs, by varying the positions of few neighbouring holes. We consistently find Q -values above one million – one order of magnitude higher than previous designs. Furthermore, we study the effect of disorder on the optimal designs and conclude that a similar improvement is also expected experimentally in state-of-the-art systems.

Conventional topological insulators support boundary states with dimension one lower than that of the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insulators have been proposed as a way of realizing topological states with dimensions two or more lower than that of the bulk due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here, we construct photonic higher-order topological insulators (PHOTIs) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacent coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a fourth-order hexadecapole (16-pole) insulator supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.Opening new dimensions for topological insulatorsA theoretical structure that provides extra dimensions to topological insulators could enable novel quantum states to be manipulated. The usual definition of topological insulators is that they act as insulators on the three-dimensional inner bulk, but are highly conductive on their two-dimensional surfaces. However, when photonic topological insulators are constructed, other non-spatial dimensions can be harnessed related to frequency, orbital angular momentum or spin. Shanhui Fan and co-workers at Stanford University, USA, designed photonic higher-dimensional topological insulators made from arrays of ring-shaped resonators. The team showed that each pair of rings acts like a ‘photonic molecule’, generating complex isolated quantum states that could be switched on and off. Their work suggests that these synthetic dimensions could be used to explore exotic new phases of matter, with applications such as quantum computing.

Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology. Photonic processors that can perform arbitrary tasks are in demand for many applications. Here, the authors present a photonic architecture using waveguide and resonator couplings to perform arbitrary linear transformations, by taking advantage of the frequency synthetic dimension.

In the presence of an external magnetic field, the surface plasmon polariton that exists at the metal-dielectric interface is believed to support a unidirectional frequency range near the surface plasmon frequency, where the surface plasmon polariton propagates along one but not the opposite direction. Recent works have pointed to some of the paradoxical consequences of such a unidirectional range, including in particular the violation of the time-bandwidth product constraint that should otherwise apply in general in static systems. Here we show that such a unidirectional frequency range is nonphysical using both a general thermodynamic argument and a detailed calculation based on a nonlocal hydrodynamic Drude model for the metal permittivity. Our calculation reveals that the surface plasmon-polariton at metal-dielectric interfaces remains bidirectional for all frequencies. The local Drude model predicts that, under certain conditions, surface plasmon polaritons at a metal-dielectric surface have a frequency range where only unidirectional propagation is supported. Here, the authors show that in more realistic non-local models surface plasmon polaritons exhibit bidirectional propagation for all frequencies.

There has been significant recent interest in synthetic dimensions, where internal degrees of freedom of a particle are coupled to form higher-dimensional lattices in lower-dimensional physical structures. For these systems, the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide a direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a resonator at frequencies commensurate with its mode spacing, we create a periodically driven lattice of coupled modes in the frequency dimension. The strength and range of couplings can be dynamically reconfigured by changing the modulation amplitude and frequency. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system provide a direct readout of its band structure. We also realize long-range coupling, gauge potentials and nonreciprocal bands by simply incorporating additional frequency drives, enabling great flexibility in band structure engineering. Internal degrees of freedom allow to expand the effective dimensionality of a system along “synthetic” dimensions. Here, the authors demonstrate this by modulating a ring resonator at frequencies commensurate with its mode spacing, and are able to directly measure its synthetic band structure.

Harnessing the full complexity of optical fields requires the complete control of all degrees of freedom within a region of space and time—an open goal for present-day spatial light modulators, active metasurfaces and optical phased arrays. Here, we resolve this challenge with a programmable photonic crystal cavity array enabled by four key advances: (1) near-unity vertical coupling to high-finesse microcavities through inverse design; (2) scalable fabrication by optimized 300 mm full-wafer processing; (3) picometre-precision resonance alignment using automated, closed-loop ‘holographic trimming’; and (4) out-of-plane cavity control via a high-speed μLED array. Combining each, we demonstrate the near-complete spatiotemporal control of a 64 resonator, two-dimensional spatial light modulator with nanosecond- and femtojoule-order switching. Simultaneously operating wavelength-scale modes near the space–bandwidth and time–bandwidth limits, this work opens a new regime of programmability at the fundamental limits of multimode optical control.Panuski et al. demonstrate a programmable photonic crystal cavity array, enabling the spatiotemporal control of a 64 resonator, two-dimensional spatial light modulator with nanosecond- and femtojoule-order switching.

With an ultimately thin active region, monolayer transition metal dichalcogenide lasers have the potential of realizing ultralow lasing threshold and power consumption. The flexibility also enables integration possibilities on unconventional substrates. Here, we report a photonic crystal surface emitting laser using monolayer tungsten disulfide as the gain medium. The cavity design utilizes a heterostructure in the photonic crystal lattice to provide lateral confinement for a high quality factor with a compact active region. Room-temperature continuous wave lasing is realized after integrating monolayer tungsten disulfide flakes onto the silicon nitride photonic crystal on a quartz substrate. Highly directional, near surface-normal emission has also been experimentally demonstrated. The work reported here demonstrates that a large-area single-mode directional laser can be realized from a monolayer gain medium, which is critical for laser scaling for on-chip integration in data and sensing applications.

Photonic crystal (PhC) slabs, or patterned multilayer waveguides, are known to support truly guided modes with no losses, as well as quasi-guided modes that lie in the continuum of far-field radiation. In this contribution, we present a guided-mode expansion approach – and the corresponding free software named legume – that allows calculating a number of features of PhC slabs: (a) symmetry properties and the issue of polarization mixing in coupling to far-field radiation; (b) the occurence of bound states in a continuum, which have infinite Q-factor and give rise to topological singularities of the far-field polarization; (c) the description of active two-dimensional layers through a suitably formulated light-matter coupling Hamiltonian, allowing to describe the regime of strong coupling leading to photonic crystal polaritons. Comparison with rigorous coupled-wave analysis, and the insurgence of non-hermitian features in the optical properties, are also addressed.

Second-order nonlinear effects, such as second-harmonic generation, can be strongly enhanced in nanofabricated photonic materials when both fundamental and harmonic frequencies are spatially and temporally confined. Practically designing low-volume and doubly-resonant nanoresonators in conventional semiconductor compounds is challenging owing to their intrinsic refractive index dispersion. In this work we review a recently developed strategy to design doubly-resonant nanocavities with low mode volume and large quality factor via localized defects in a photonic crystal structure. We built on this approach by applying an evolutionary optimization algorithm in connection with Maxwell equations solvers; the proposed design recipe can be applied to any material platform. We explicitly calculated the second-harmonic generation efficiency for doubly-resonant photonic crystal cavity designs in typical III–V semiconductor materials, such as GaN and AlGaAs, while targeting a fundamental harmonic at telecom wavelengths and fully accounting for the tensor nature of the respective nonlinear susceptibilities. These results may stimulate the realization of small footprint photonic nanostructures in leading semiconductor material platforms to achieve unprecedented nonlinear efficiencies.

We theoretically study the relation between polarization singularities and optical properties in dielectric metasurfaces, or photonic crystal slabs. We focus on nondegenerate photonic bands leading to symmetry-protected Bound States in a Continuum (BICs). First, we discuss how BICs lead to polarization singularities in the far field, whose winding numbers – or topological charges – follows from the symmetry of the lattice. Then, we determine the polarization properties via the Stokes parameters, focusing on the conditions for the occurrence of a nonvanishing circular polarization. Finally, we calculate the optical response in reflection and the degree of circular dichroism. The results shed light on the role of polarization singularities and symmetry in determining the optical chirality.