Polarization states and far-field optical properties in dielectric photonic crystal slabs.

We study the role of topological singularities like Bound States in a Continuum (BICs) or Circularly Polarized States (CPSs) in determining ellipticity of the far-field polarization in dielectric metasurfaces. Using finite-difference time-domain as well as rigorous coupled-wave analysis simulations, we determine the behavior of the Stokes parameter S3 in the whole k space above the light cone, with special regard to the region close to the singularities. Moreover, we clarify the relation between the topological singularities and the circular dichroism in reflectivity.

Experimentally realized in situ backpropagation for deep learning in photonic neural networks.

Integrated photonic neural networks provide a promising platform for energy-efficient, high-throughput machine learning with extensive scientific and commercial applications. Photonic neural networks efficiently transform optically encoded inputs using Mach-Zehnder interferometer mesh networks interleaved with nonlinearities. We experimentally trained a three-layer, four-port silicon photonic neural network with programmable phase shifters and optical power monitoring to solve classification tasks using "in situ backpropagation," a photonic analog of the most popular method to train conventional neural networks. We measured backpropagated gradients for phase-shifter voltages by interfering forward- and backward-propagating light and simulated in situ backpropagation for 64-port photonic neural networks trained on MNIST image recognition given errors. All experiments performed comparably to digital simulations ([Formula: see text]94% test accuracy), and energy scaling analysis indicated a route to scalable machine learning.

Theory for Twisted Bilayer Photonic Crystal Slabs.

We analyze scattering properties of twisted bilayer photonic crystal slabs through a high-dimensional plane wave expansion method. The method is applicable for arbitrary twist angles and does not suffer from the limitations of the commonly used supercell approximation. We show strongly tunable resonance properties of this system which can be accounted for semianalytically from a correspondence relation to a simpler structure. We also observe strongly tunable resonant chiral behavior in this system. Our work provides the theoretical foundation for predicting and understanding the rich optical physics of twisted multilayer photonic crystal systems.

Arbitrary linear transformations for photons in the frequency synthetic dimension.

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.

Doubly-Resonant Photonic Crystal Cavities for Efficient Second-Harmonic Generation in III-V Semiconductors.

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.

PT-Symmetric Topological Edge-Gain Effect.

We demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped subsystems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.

Higher-order topological insulators in synthetic dimensions.

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.

Experimental realization of arbitrary activation functions for optical neural networks.

We experimentally demonstrate an on-chip electro-optic circuit for realizing arbitrary nonlinear activation functions for optical neural networks (ONNs). The circuit operates by converting a small portion of the input optical signal into an electrical signal and modulating the intensity of the remaining optical signal. Electrical signal processing allows the activation function circuit to realize any optical-to-optical nonlinearity that does not require amplification. Such line shapes are not constrained to those of conventional optical nonlinearities. Through numerical simulations, we demonstrate that the activation function improves the performance of an ONN on the MNIST image classification task. Moreover, the activation circuit allows for the realization of nonlinearities with far lower optical signal attenuation, paving the way for much deeper ONNs.

Absence of unidirectionally propagating surface plasmon-polaritons at nonreciprocal metal-dielectric interfaces.

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.

A single photonic cavity with two independent physical synthetic dimensions.

The concept of synthetic dimensions has generated interest in many branches of science, ranging from ultracold atomic physics to photonics, as it provides a versatile platform for realizing effective gauge potentials and topological physics. Previous experiments have augmented the real-space dimensionality by one additional physical synthetic dimension. In this study, we endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We observe a wide variety of physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and signatures of topological chiral one-way edge currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.

Experimental band structure spectroscopy along a synthetic dimension.

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.

Wave physics as an analog recurrent neural network.

Analog machine learning hardware platforms promise to be faster and more energy efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for time-varying signals. Here, we identify a mapping between the dynamics of wave physics and the computation in recurrent neural networks. This mapping indicates that physical wave systems can be trained to learn complex features in temporal data, using standard training techniques for neural networks. As a demonstration, we show that an inverse-designed inhomogeneous medium can perform vowel classification on raw audio signals as their waveforms scatter and propagate through it, achieving performance comparable to a standard digital implementation of a recurrent neural network. These findings pave the way for a new class of analog machine learning platforms, capable of fast and efficient processing of information in its native domain.

Isotropic wavevector domain image filters by a photonic crystal slab device.

We show that several types of isotropic image filters in the wavevector domain can be implemented with a single photonic crystal slab device. Such a slab is designed so that the guided resonance near the Γ point exhibits an isotropic band structure. Depending on the light frequency and the choice of transmission or reflection mode, the device realizes isotropic high-pass, low-pass, band-reject, and band-pass filtering in wavevector space. These filter functions are important for various image processing tasks, including edge detection, smoothing, white noise suppression, and suppression or extraction of periodic noises. We numerically demonstrate these filter functionalities by simulations of a slab structure that is designed to operate in the visible wavelength range. Our work expands the application of nanophotonics-based optical analog computing for image processing.

Ultra-wide-band structural slow light.

The ability of using integrated photonics to scale multiple optical components on a single monolithic chip offers key advantages to create miniature light-controlling chips. Numerous scaled optical components have been already demonstrated. However, present integrated photonic circuits are still rudimentary compared to the complexity of today's electronic circuits. Slow light propagation in nanostructured materials is a key component for realizing chip-integrated photonic devices controlling the relative phase of light and enhancing optical nonlinearities. We present an experimental record high group-index-bandwidth product (GBP) of 0.47 over a 17.7 nm bandwidth in genetically optimized coupled-cavity-waveguides (CCWs) formed by L3 photonic crystal cavities. Our structures were realized in silicon-on-insulator slabs integrating up to 800 coupled cavities, and characterized by transmission, Fourier-space imaging of mode dispersion, and Mach-Zehnder interferometry.

Zero-Index Bound States in the Continuum.

Metamaterials with an effective zero refractive index associated with their electromagnetic response are sought for a number of applications in communications and nonlinear optics. A promising way that this can be achieved in all-dielectric photonic crystals is through the design of a Dirac cone at zero Bloch wave vector in the photonic band structure. In the optical frequency range, the natural way to implement this design is through the use of a photonic crystal slab. In the existing implementation, however, the zero-index photonic modes also radiate strongly into the environment due to intrinsic symmetry properties. This has resulted in large losses in recent experimental realizations of this zero-index paradigm. Here, we propose a photonic crystal slab with zero-index modes which are also symmetry-protected bound states in the continuum. Our approach thus eliminates the associated radiation loss. This could enable, for the first time, large-scale integration of zero-index materials in photonic devices.

Automated optimization of photonic crystal slab cavities.

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.

Statistics of the disorder-induced losses of high-Q photonic crystal cavities.

We analyze and compare the effect of fabrication disorder on the quality factor of six well-known high-index photonic crystal cavity designs. The theoretical quality factors for the different nominal structures span more than three orders of magnitude, ranging from 5.4 × 10(4) to 7.5 × 10(7), and the defect responsible for confining light is introduced in a different way for each structure. Nevertheless, among the different designs we observe similar behavior of the statistics of the disorder-induced light losses. In particular, we show that for high enough disorder, such that the quality factor is mainly determined by the disorder-induced losses, the measured quality factors differ marginally - not only on average as commonly acknowledged, but also in their full statistical distributions. This notably shows that optimizing the theoretical quality factor brings little practical improvement if its value is already much larger than what is typically measured, and if this is the case, there is no way to choose an alternative design more robust to disorder.

Effect of hole-shape irregularities on photonic crystal waveguides.

The effect of irregular hole shape on the spectrum and radiation losses of a photonic crystal waveguide is studied using Bloch-mode expansion. Deviations from a circular hole are characterized by a radius fluctuation amplitude and correlation angle. It is found that the parameter that determines the magnitude of the effect of disorder is the standard deviation of the hole areas. Hence, for a fixed amplitude of the radius fluctuation around the hole, those effects are strongly dependent on the correlation angle of the irregular shape, which suggests how to potentially improve the quality of photonic crystal structures.