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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.

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.