Hyper-spectral photonic integrated circuits based on recursive inverse design

Manipulating optical spectra with complex spectral responses is central to high-performance photonic computing and sensing, but conventional integrated circuits typically increase features by cascading devices, which scales complexity linearly with cascade depth and is difficult to expand. Here, we introduce hyper-spectral photonic integrated circuits comprising a chain of interconnected reflective nodes. The central idea is to introduce partial reflectivity, thereby leveraging both transmissive and reflective interference within each component node. This architecture expands the accessible delay distribution and exhibits a superlinear complexity growth. We implement the circuits through a recursive inverse-design workflow that jointly exploits node geometry and circuit topology to maximize spectral complexity. Experimentally, a single waveguide incorporating 11 reflective nodes achieves a complexity comparable to at least 100 cascaded Mach-Zehnder interferometer stages. An array of these circuits reconstructs spectra with sub-picometer resolution across an 800 nm bandwidth. This performance bridges optical and microwave frequencies by enabling simultaneous monitoring of optical and radio signals within a single device.