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Abstract Silicon photonics is an emerging technology which, enabling nanoscale manipulation of light on chips, impacts areas as diverse as communications, computing, and sensing. Wavelength division multiplexing is commonly used to maximize throughput over a single optical channel by modulating multiple data streams on different wavelengths concurrently. Traditionally, wavelength (de)multiplexers are implemented as monolithic devices, separate from the grating coupler, used to couple light into the chip. This paper describes the design and measurement of a grating coupler demultiplexer—a single device which combines both light coupling and demultiplexing capabilities. The device was designed by means of a custom inverse design algorithm which leverages boundary integral Maxwell solvers of extremely rapid convergence as the mesh is refined. To the best of our knowledge, the fabricated device enjoys the lowest insertion loss reported for grating demultiplexers, small size, high splitting ratio, and low coupling-efficiency imbalance between ports, while meeting the fabricability constraints of a standard UV lithography process. 

An accurate assessment of seismic hazard requires a combination of earthquake physics and statistical analysis. Because of the limitations in the investigation of the seismogenic sources and of the short temporal intervals covered by earthquake catalogs, laboratory experiments have played a crucial role in improving our understanding of earthquake phenomena. However, differences exist between acoustic emissions in the lab, events in small, regulated systems (e.g., mines) and natural seismicity. One of the most pressing issues concerns the role of mechanical parameters and how they affect seismic activity across boundary conditions and spatial-temporal scales. Here, we focus on fault friction. There is evidence inferred from geodesy, computational simulations and seismological investigations that most large faults are weak and characterized by very low static friction coefficients which are inconsistent with those of smaller faults and laboratory experiments. We support the hypothesis that static friction decreases with fault size due to the presence of fabrics, roughness, structural asperities and network geometry. We also model its scaling behavior as dependent on a few physical properties (e.g., fault fractal dimension). Conversely, dynamic coefficients are not affected by the spatial scale. Mathematical derivations are based on the hypothesis that earthquake onset results from fracture instability controlled by the extremes of fault shear strength. We validate this using a simple model for earthquake occurrence rooted in fracture mechanics, which reproduces key features of major seismicity (i.e., interevent time distribution, clustering and frequency-size relationship). 

We present a family of numerical methods for the solution of Maxwell’s equations, with application to simulation, optimization, and design. In particular, a novel rectangular-polar integral equation solver is mentioned which can produce solutions to the time harmonic Maxwell’s equations, with high order accuracy, for general 2D and 3D structures, with an extension to time domain problems on the basis of a time re-centering synthesis technique. An effective integral equation acceleration method, the IFGF method (Interpolated Factored Green Function), is used, which evaluates the action of Green function-based integral operators for an 𝑁𝑁-point surface discretization at a computational cost of 𝑂(𝑁log𝑁) operations without recourse to the FFT—thus, lending itself to effective distributed memory parallelization. Computational illustrations include applications to photonic optimization and design. 

We present a frequency/time hybrid integral-equation method for the time-dependent wave equation in two and three-dimensional spatial domains, possibly including closed cavities. 

We present a frequency/time hybrid integral-equation method for the time-dependent wave equation in two and three-dimensional spatial domains, possibly including closed cavities. 

We present a frequency/time hybrid integral-equation method for the time-dependent wave equation in two and three-dimensional spatial domains, possibly including closed cavities. 

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities. The method relies on a hybrid direct/iterative combination of 1)~A differential volumetric formulation (which is based on the use of appropriate Chebyshev differentiation matrices enacting the Laplace operator) and, 2)~A second-kind boundary integral formulation (which, once again, utilizes Chebyshev discretization, but, in this case, in the boundary-integral context). The approach enjoys low dispersion and high-order accuracy for smooth refractivities, as well as second-order accuracy (while maintaining low dispersion) in the discontinuous refractivity case. The solution approach proceeds by application of Impedance-to-Impedance (ItI) maps to couple the volumetric and boundary discretizations. The volumetric linear algebra solutions are obtained by means of a multifrontal solver, and the coupling with the boundary integral formulation is achieved via an application of the iterative linear-algebra solver GMRES. In particular, the existence and uniqueness theory presented in the present paper provides an affirmative answer to an open question concerning the existence of a uniquely solvable second-kind ItI-based formulation for the overall scattering problem under consideration. Relying on a modestly-demanding scatterer-dependent precomputation stage (requiring in practice a computing cost of the order of $$O(N^{\alpha})$$ operations, with $$\alpha \approx 1.07$$, for an $$N$$-point discretization \textcolor{black}{and for the relevant Chebyshev accuracy orders $$q$$ used)}, together with fast ($O(N)$-cost) single-core runs for each incident field considered, the proposed algorithm can effectively solve scattering problems for large and complex objects possibly containing discontinuities and strong refractivity contrasts. 

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensionalinterior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a giveninteriortime-domain problem into a sequence oflimited-durationtime-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence ofHelmholtz frequency-domain problems; (2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point (1); (3) A smooth“Time-windowing and recentering”methodology that enables both treatment of incident signals of long duration and long time simulation; and, (4) A Fourier transform algorithm that delivers numerically dispersionless,spectrally-accurate time evolutionfor given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem—which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology.