Matrix Triangularization Using Arrays of Integrated Optical Givens Rotation Devices

Solving linear equations is centrally important in many large-scale data processing problems. The describing nonlinear systems of equations can be linearized at each time step to produce a linear system of equations that simplifies the problem-solving process. In general, there are two approaches to solving sets of linear equations-direct methods and iterative methods. Optics-based devices and systems offer one means of solving sets of linear equations using a stable, direct method. These devices can employ Givens rotations to perform matrix triangularization. In this article, the authors describe how to solve linear equations using an electro-optical system that employs arrays of optical Givens rotation devices. They examine how to implement this system using two different configurations, parallel and pipelined, and how to calibrate the system to minimize errors.