where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Recent advancements in computational inverse-design approaches — algorithmic techniques for discovering optical structures based on desired functional characteristics — have begun to reshape the landscape of structures available to nanophotonics. Here, we outline a cross-section of key developments in this emerging field of photonic optimization: moving from a recap of foundational results to motivation of applications in nonlinear, topological, near-field and on-chip optics. Starting with a desired optical output it is possible to use computational algorithms to inverse design devices. The approach is reviewed here with an emphasis on nanophotonics.

Inverse design in nanophotonics

Ultrathin dielectric gaps between metals can trap plasmonic optical modes with surprisingly low loss and with volumes below 1 nm3. We review the origin and subtle properties of these modes, and show how they can be well accounted for by simple models. Particularly important is the mixing between radiating antennas and confined nanogap modes, which is extremely sensitive to precise nanogeometry, right down to the single-atom level. Coupling nanogap plasmons to electronic and vibronic transitions yields a host of phenomena including single-molecule strong coupling and molecular optomechanics, opening access to atomic-scale chemistry and materials science, as well as quantum metamaterials. Ultimate low-energy devices such as robust bottom-up assembled single-atom switches are thus in prospect.

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Extreme nanophotonics from ultrathin metallic gaps

Innovative approaches and tools play an important role in shaping design, characterization and optimization for the field of photonics. As a subset of machine learning that learns multilevel abstraction of data using hierarchically structured layers, deep learning offers an efficient means to design photonic structures, spawning data-driven approaches complementary to conventional physics- and rule-based methods. Here, we review recent progress in deep-learning-based photonic design by providing the historical background, algorithm fundamentals and key applications, with the emphasis on various model architectures for specific photonic tasks. We also comment on the challenges and perspectives of this emerging research direction. The application of deep learning to the design of photonic structures and devices is reviewed, including algorithm fundamentals.

Deep learning for the design of photonic structures

Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields: moving from a recap of foundational results to motivation of emerging applications in nonlinear, topological, near-field and on-chip optics.

Outlook for inverse design in nanophotonics

An absorptive metasurface based on film-coupled colloidal silver nanocubes is demonstrated. The metasurfaces are fabricated using simple dip-coating methods and can be deposited over large areas and on arbitrarily shaped objects. The surfaces show nearly complete absorption, good off-angle performance, and the resonance can be tuned from the visible to the near-infrared.

Large-Area Metasurface Perfect Absorbers from Visible to Near-Infrared.

A major difficulty in applying computational design methods to nanophotonic devices is ensuring that the resulting designs are fabricable. Here, we describe a general inverse design algorithm for nanophotonic devices that directly incorporates fabrication constraints. To demonstrate the capabilities of our method, we designed a spatial-mode demultiplexer, wavelength demultiplexer, and directional coupler. We also designed and experimentally demonstrated a compact, broadband 1 × 3 power splitter on a silicon photonics platform. The splitter has a footprint of only 3.8 × 2.5 μm, and is well within the design rules of a typical silicon photonics process, with a minimum radius of curvature of 100 nm. Averaged over the designed wavelength range of 1400–1700 nm, our splitter has a measured insertion loss of 0.642 ± 0.057 dB and power uniformity of 0.641 ± 0.054 dB.

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Fabrication-constrained nanophotonic inverse design.

In wavelength division multiplexing schemes, splitters must be used to combine and separate different wavelengths. Conventional splitters are fairly large with footprints in hundreds to thousands of square microns, and experimentally demonstrated multimode-interference-based and inverse-designed ultracompact splitters operate with only two channels and large channel spacing (>100 nm). Here we inverse design and experimentally demonstrate a three-channel wavelength demultiplexer with 40 nm spacing (1500, 1540, and 1580 nm) with a footprint of 24.75 μm2. The splitter has a simulated peak insertion loss of −1.55 dB with under −15 dB crosstalk and a measured peak insertion loss of −2.29 dB with under −10.7 dB crosstalk.

Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer

Particle accelerators represent an indispensable tool in science and industry. However, the size and cost of conventional radio-frequency accelerators limit the utility and reach of this technology. Dielectric laser accelerators (DLAs) provide a compact and cost-effective solution to this problem by driving accelerator nanostructures with visible or near-infrared pulsed lasers, resulting in a 104 reduction of scale. Current implementations of DLAs rely on free-space lasers directly incident on the accelerating structures, limiting the scalability and integrability of this technology. We present an experimental demonstration of a waveguide-integrated DLA that was designed using a photonic inverse-design approach. By comparing the measured electron energy spectra with particle-tracking simulations, we infer a maximum energy gain of 0.915 kilo-electron volts over 30 micrometers, corresponding to an acceleration gradient of 30.5 mega-electron volts per meter. On-chip acceleration provides the possibility for a completely integrated mega-electron volt-scale DLA.

On-chip integrated laser-driven particle accelerator.

We present a gradient-based algorithm to design general 1D grating couplers without any human input from start to finish, including a choice of initial condition. We show that we can reliably design efficient couplers to have multiple functionalities in different geometries, including conventional couplers for single-polarization and single-wavelength operation, polarization-insensitive couplers, and wavelength-demultiplexing couplers. In particular, we design a fiber-to-chip blazed grating with under 0.2 dB insertion loss that requires a single etch to fabricate and no back-reflector.

Logan Su

Papers

Large-Area Metasurface Perfect Absorbers from Visible to Near-Infrared.

Fabrication-constrained nanophotonic inverse design.

Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer

On-chip integrated laser-driven particle accelerator.

Fully-automated optimization of grating couplers.