Transformation-optics modeling of 3D-printed freeform waveguides

TL;DR

This paper introduces a transformation-optics-based method to efficiently model 3D-printed freeform waveguides, significantly reducing simulation time while maintaining accuracy, and validates the approach through fabrication and experimental testing.

Contribution

The paper presents a novel transformation-optics technique that simplifies the modeling of complex 3D freeform waveguides, improving computational efficiency and enabling practical design.

Findings

Simulation time reduced by a factor of 3-6.

Good agreement between simulated and experimental transmission.

Method applicable to various freeform waveguide geometries.

Abstract

Multi-photon lithography allows to complement planar photonic integrated circuits (PIC) by in-situ 3D-printed freeform waveguide structures. However, design and optimization of such freeform waveguides using time-domain Maxwell's equations solvers often requires comparatively large computational volumes, within which the structure of interest only occupies a small fraction, thus leading to poor computational efficiency. In this paper, we present a solver-independent transformation-optics-(TO-) based technique that allows to greatly reduce the computational effort related to modeling of 3D freeform waveguides. The concept relies on transforming freeform waveguides with curved trajectories into equivalent waveguide structures with modified material properties but geometrically straight trajectories, that can be efficiently fit into rather small cuboid-shaped computational volumes. We demonstrate the viability of the technique and benchmark its performance using a series of different freeform waveguides, achieving a reduction of the simulation time by a factor of 3-6 with a significant potential for further improvement. We also fabricate and experimentally test the simulated waveguides by 3D-printing on a silicon photonic chip, and we find good agreement between the simulated and the measured transmission at $\lambda = 1550 \textrm{ nm}$.