Efficient operator method for modelling mode mixing in misaligned optical cavities

TL;DR

This paper introduces an efficient operator method to model mode mixing in misaligned optical cavities, enabling fast calculations and analysis of complex mode structures caused by mirror misalignments.

Contribution

The authors extend the mode mixing method to handle arbitrary mirror shapes and transverse misalignments, improving computational speed and analytical capabilities.

Findings

Fast calculation of cavity modes with misaligned mirrors

Unveiling complex mode structures due to transverse misalignment

Extension of existing methods to arbitrary mirror geometries

Abstract

The transverse field structure and diffraction loss of the resonant modes of Fabry-P\'erot optical cavities are acutely sensitive to the alignment and shape of the mirror substrates. We develop extensions to the `mode mixing' method applicable to arbitrary mirror shapes, which both facilitate fast calculation of the modes of cavities with transversely misaligned mirrors and enable the determination and transformation of the geometric properties of these modes. We show how these methods extend previous capabilities by including the practically-motivated case of transverse mirror misalignment, unveiling rich and complex structure of the resonant modes.