Boundary Integral Method and Applications for Chaotic Optical Microcavities
Datum
2020-09-24
Autor:innen
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University of Oregon
Zusammenfassung
Optical microcavities offer many application possibilities in addition to being model systems for studying chaotic dynamics in the wave regime. However these systems are only analytically solvable for the simplest geometries. In order to study strongly deformed geometries, numerical methods must be used. The open nature of cavities results in complex wavenumbers for their quasi-bound modes which makes finding resonances more difficult. We discuss the main methods available for understanding these resonances.
We implement a numerical package for finding resonances, computing their spatial field patterns and projecting onto surface of section plots via Husimi distributions. This software has been implemented in Julia, a modern programming language with performance and ease of use in mind. This software is available as open source, and is designed to be reusable for arbitrary two dimensional geometries.
Using this package we describe a novel phenomenon that can occur in strongly deformed geometries with concavities, which we name folded chaotic whispering-gallery modes. In these cavities, folded chaotic WGMs allow for high-Q modes suitable for spectroscopy or laser applications with an important innovation, the ability to attach waveguides to the cavity. The similarities to WGMs are surprising given a theorem by Mather which rules out their existence in the ray picture. High-Q resonances occur within certain wavelength windows and we investigate the peak structure in the spectrum. The periodic orbits in the corresponding billiard system are unstable and exist within the chaotic region of phase space. The fact that such high-Q modes exist based around these orbits implies a form of wave localization.
Another geometry is investigated, deformed boundaries of constant width. These are smooth curves similar to Reuleaux polygons. They have no symmetry axis, and in the ray picture have a unidirectional nature. We investigate these in open optical cavities. We find that nearly degenerate modes of opposite rotational direction can be simultaneously present, but have emission at different boundary locations. This suggests a non-reciprocal process achieved through purely geometric means which may allow for the separation of chiral components of light and applications such as optical microdiodes.
Beschreibung
Schlagwörter
boundary integral method, chaos, folded whispering gallery, microcavities, optics