Algebraic topology and applications to photonic integrated circuits

光子集成电路（PIC）为计算、传感和医疗诊断等领域的技术进步提供了独特的机会，但仍然完全基于特定应用的芯片设计概念。专用光子集成电路（ASPIC）是目前占主导地位的PIC，其中特定的电路/芯片被设计为最佳地执行特定的功能。它们需要大量的设计和制造迭代，导致长的开发时间。受电子现场可编程门阵列（FPGA）启发的不同方法是可编程光子处理器，其中由二维光子波导网格实现的公共硬件通过编程实现不同的功能。实现这种电路是广泛部署PIC的关键一步。在这个项目中，一个数学模型的基础上同伦理论超图和他们的持续同源性将首先开发，然后实现硅光子可编程电路的设计。数学模型将解决可编程PIC的优化，以执行具有最小电和光功耗和损耗的许多功能，并解决芯片上未正确操作的区域的隔离（例如，由于操作期间发生的制造错误或损坏），使得PIC仍然可以执行其设计的所有/大部分功能。

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.