Shape optimization techniques were first developed in the context of mechanical engineering and, more recently, applied to photonic components for data communication. Here, motivated by the growing application potential of mid-infrared photonics driven by chemical sensing and spectroscopy, we present the design by shape optimization of passive components operating in this wavelength range. A focus is placed on the creation of designs that are fabricable and robust to manufacturing uncertainties.Keywords shape optimization · level-set · mid-IR photonics
IntroductionDriven by data communication in the near-IR wavelength range, silicon photonics has experienced tremendous developments in the last few decades. The transposition of this scientific and industrial success to the mid-IR (wavelengths comprised between 3 µm and 12 µm) has been envisioned some time ago [21] and is currently under rapid progress, with noteworthy developments in materials, passive and active components, laser sources, photodetectors and sensors [6]. Due to the strong absorption bands situated in this wavelength range, applications are found, for instance, in trace gas sensing, spectroscopy and imaging of biological tissues [6].In the last decades, shape optimization techniques, boosted by additive manufacturing technologies, have been successfully applied to mechanical engineering [2]. More recently, shape optimization appeared in the domain of silicon photonics, first with simulations and designs of passive devices [8,12] and then with micro-fabrication and experimental demonstrations [15,19,7].In the context of optimal design of photonic components, most contributions rely on density methods [8,12]. This popular paradigm, originally introduced in the context of structural mechanics as a heuristic approximation of mathematical homogenization, and known in this context as the SIMP method [3], amounts to trade the conventional "black-and-white" representation of a design for a "grayscale" density function, with continuous values in the whole interval [0, 1]. This considerably simplifies the optimization process, but raises the need for an approximate modeling of the physical equations, which have to be expressed in terms of the density function, as well as issues about the interpretation of the resulting design, and notably of its "grayscale" regions, where the density function takes intermediate values in (0, 1).On the other hand, more "geometric" methods, featuring a clear representation of the boundary of the optimized shape, have been considered, relying for instance on the concepts of shape and topological N. Lebbe Univ.