High-performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design.

We present a photonics topology optimization (TO) package capable of addressing a wide range of practical photonics design problems, incorporating robustness and manufacturing constraints, which can scale to large devices and massive parallelism. We employ a hybrid algorithm that builds on a mature time-domain (FDTD) package Meep to simultaneously solve multiple frequency-domain TO problems over a broad bandwidth. This time/frequency-domain approach is enhanced by new filter-design sources for the gradient calculation and new material-interpolation methods for optimizing dispersive media, as well as by multiple forms of computational parallelism. The package is available as free/open-source software with extensive tutorials and multi-platform support.

Photonic topology optimization with semiconductor-foundry design-rule constraints.

We present a unified density-based topology-optimization framework that yields integrated photonic designs optimized for manufacturing constraints including all those of commercial semiconductor foundries. We introduce a new method to impose minimum-area and minimum-enclosed-area constraints, and simultaneously adapt previous techniques for minimum linewidth, linespacing, and curvature, all of which are implemented without any additional re-parameterizations. Furthermore, we show how differentiable morphological transforms can be used to produce devices that are robust to over/under-etching while also satisfying manufacturing constraints. We demonstrate our methodology by designing three broadband silicon-photonics devices for nine different foundry-constraint combinations.

Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides.

We investigate the design of taper structures for coupling to slow-light modes of various photonic-crystal waveguides while taking into account parameter uncertainties inherent in practical fabrication. Our short-length (11 periods) robust tapers designed for ? = 1.55?m and a slow-light group velocity of c/34 have a total loss of < 20 dB even in the presence of nanometer-scale surface roughness, which outperform the corresponding non-robust designs by an order of magnitude. We discover a posteriori that the robust designs have smooth profiles that can be parameterized by a few-term (intrinsically smooth) sine series which helps the optimization to further boost the performance slightly. We ground these numerical results in an analytical foundation by deriving the scaling relationships between taper length, taper smoothness, and group velocity with the help of an exact equivalence with Fourier analysis.

Tailoring repulsive optical forces in nanophotonic waveguides.

We describe a mechanism and propose design strategies to selectively tailor repulsive-gradient-optical forces between parallel, nanophotonic waveguides via morphology augmented by slow-light band-edge modes. We show that at small separation lengths, the repulsive force can be made nearly 2 orders of magnitude larger than that of standard dielectric waveguides with a square cross section. The increased coupling interactions should enable a wider dynamic range of optomechanical functionality for potential applications in sensing, switching, and nanoelectromechanical systems.

Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.

Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.

Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures.

We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers.

Zero-group-velocity modes in chalcogenide holey photonic-crystal fibers.

We demonstrate that a holey photonic-crystal fiber with chalcogenide-glass index contrast can be designed to have a complete gap at a propagation constant beta = 0 that also extends into the non-zero beta region. This type of bandgap (previously identified only at index contrasts unattainable in glasses) opens up a regime for guiding zero-group-velocity modes not possible in holey fibers with the more common finger-like gaps originating from beta-->infinity. Such modes could be used to enhance nonlinear and other material interactions, such as for hollow-core fibers in gas-sensor applications.

The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers.

Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).