Exploiting geometric biases in inverse nano-optical problems using artificial neural networks.

Solving the inverse problem is a major challenge in contemporary nano-optics. However, frequently not just a possible solution needs to be found but rather the solution that accommodates constraints imposed by the problem at hand. To select the most plausible solution for a nano-optical inverse problem additional information can be used in general, but how to specifically formulate it frequently remains unclear. Here, while studying the reconstruction of the shape of an object using the electromagnetic field in its proximity, we show how to take advantage of artificial neural networks (ANNs) to produce solutions consistent with prior assumptions concerning the structures. By preparing suitable datasets where the specific shapes of possible scatterers are defined, the ANNs learn the underlying scatterer present in the datasets. This helps to find a plausible solution to the otherwise non-unique inverse problem. We show that topology optimization, in contrast, can fail to recover the scatterer geometry meaningfully but a hybrid approach that is based on both, ANNs and a topology optimization, eventually leads to the most promising performance. Our work has direct implications in fields such as optical metrology.

Inverse photonic design of functional elements that focus Bloch surface waves.

Bloch surface waves (BSWs) are sustained at the interface of a suitably designed one-dimensional (1D) dielectric photonic crystal and an ambient material. The elements that control the propagation of BSWs are defined by a spatially structured device layer on top of the 1D photonic crystal that locally changes the effective index of the BSW. An example of such an element is a focusing device that squeezes an incident BSW into a tiny space. However, the ability to focus BSWs is limited since the index contrast achievable with the device layer is usually only on the order of Δn≈0.1 for practical reasons. Conventional elements, e.g., discs or triangles, which rely on a photonic nanojet to focus BSWs, operate insufficiently at such a low index contrast. To solve this problem, we utilize an inverse photonic design strategy to attain functional elements that focus BSWs efficiently into spatial domains slightly smaller than half the wavelength. Selected examples of such functional elements are fabricated. Their ability to focus BSWs is experimentally verified by measuring the field distributions with a scanning near-field optical microscope. Our focusing elements are promising ingredients for a future generation of integrated photonic devices that rely on BSWs, e.g., to carry information, or lab-on-chip devices for specific sensing applications.