Algebraic topology and applications to photonic integrated circuits

Photonic integrated circuits (PICs) offer unique opportunities to advance technology in areas such as computing, sensing and health care diagnostics but are still fully based on application specific chip design concepts. Application-specific photonic integrated circuits (ASPICs) are currently dominant PICs, in which particular circuits/chips are designed to optimally perform particular functionalities. They require a considerable number of design and fabrication iterations leading to long development times. A different approach inspired by electronic Field Programmable Gate Arrays (FPGAs) is the programmable photonic processor, where a common hardware implemented by a two-dimensional photonic waveguide mesh realizes different functionalities through programming. Realisation of such circuits is a crucial step in the wide deployment of PICs. In this project a mathematical model based on homotopy theory of hypergraphs and their persistent homology will be first developed and then implemented for the design of silicon photonics programmable circuits. The mathematical model will address optimisation of programmable PICs to perform many functionalities with minimum electrical and optical power consumptions and loss, and to address isolation of areas on the chip that are not operating correctly (e.g. due to fabrication errors or damages occurred during the operation) such that the PIC still can be performed all/majority of the functions it has been designed for.