Liu, David, Lucas H. Gabrielli, Michal Lipson, and Steven G. Johnson. “Transformation inverse design.” Optics Express 21 (2013): 14223-14243. Abstract
We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap because transformation optics circumvents the need to solve Maxwell's equations at each step. We apply this technique to the design of multimode waveguide bends (realized experimentally in a previous paper) and mode squeezers, in which all modes are transported equally without scattering. In addition to the optimization, a key point is the identification of the correct boundary conditions to ensure reflectionless coupling to untransformed regions while allowing maximum flexibility in the optimization. Many previous authors in transformation optics used a certain kind of quasiconformal map which overconstrained the problem by requiring that the entire boundary shape be specified a priori while at the same time underconstraining the problem by employing "slipping" boundary conditions that permit unwanted interface reflections. (C) 2013 Optical Society of America
Gabrielli, Lucas H., David Liu, Steven G. Johnson, and Michal Lipson. “On-chip transformation optics for multimode waveguide bends.” Nature Communications 3 (2012). Abstract
Current optical communication systems rely almost exclusively on multimode fibres for short- and medium-haul transmissions, and are now expanding into the long-haul arena. Ultra-high bandwidth applications are the main drive for this expansion, based on the ability to spatially multiplex data channels in multimode systems. Integrated photonics, on the other hand, although largely responsible for today's telecommunications, continues to operate almost strictly in the single-mode regime. This is because multimode waveguides cannot be compactly routed on-chip without significant inter-mode coupling, which impairs their data rate and prevents the use of modal multiplexing. Here we propose a platform for on-chip multimode devices with minimal inter-mode coupling, opening up the possibilities for integrated multimode optics. Our work combines a novel theoretical approach-large-scale inverse design of transformation optics to maximize performance within fabrication constraints-with unique grayscale-lithography fabrication of an exemplary device: a low-crosstalk multimode waveguide bend.