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.

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.

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.

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.

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.

Extraordinary wavelength reduction in terahertz graphene-cladded photonic crystal slabs.

Photonic crystal slabs have been widely used in nanophotonics for light confinement, dispersion engineering, nonlinearity enhancement, and other unusual effects arising from their structural periodicity. Sub-micron device sizes and mode volumes are routine for silicon-based photonic crystal slabs, however spectrally they are limited to operate in the near infrared. Here, we show that two single-layer graphene sheets allow silicon photonic crystal slabs with submicron periodicity to operate in the terahertz regime, with an extreme 100× wavelength reduction from graphene's large kinetic inductance. The atomically thin graphene further leads to excellent out-of-plane confinement, and consequently photonic-crystal-slab band structures that closely resemble those of ideal two-dimensional photonic crystals, with broad band gaps even when the slab thickness approaches zero. The overall photonic band structure not only scales with the graphene Fermi level, but more importantly scales to lower frequencies with reduced slab thickness. Just like ideal 2D photonic crystals, graphene-cladded photonic crystal slabs confine light along line defects, forming waveguides with the propagation lengths on the order of tens of lattice constants. The proposed structure opens up the possibility to dramatically reduce the size of terahertz photonic systems by orders of magnitude.

Kinetic inductance driven nanoscale 2D and 3D THz transmission lines.

We examine the unusual dispersion and attenuation of transverse electromagnetic waves in the few-THz regime on nanoscale graphene and copper transmission lines. Conventionally, such propagation has been considered to be highly dispersive, due to the RC time constant-driven voltage diffusion below 1 THz and plasmonic effects at higher optical frequencies. Our numerical modeling across the microwave, THz, and optical frequency ranges reveals that the conductor kinetic inductance creates an ultra-broadband linear-dispersion and constant-attenuation region in the THz regime. This so-called LC region is an ideal characteristic that is known to be absent in macro-scale transmission lines. The kinetic-LC frequency range is dictated by the structural dimensionality and the free-carrier scattering rate of the conductor material. Moreover, up to 40x wavelength reduction is observed in graphene transmission lines.