Abstract
The aim of the paper is to reduce one spectral optimization problem, which involves the minimization of the decay rate |Imκ| of a resonance κ, to a collection of optimal control problems on the Riemann sphere Cˆ. This reduction allows us to apply methods of extremal synthesis to the structural optimization of layered optical cavities. We start from a dual problem of minimization of the resonator length and give several reformulations of this problem that involve Pareto optimization of the modulus |κ| of a resonance, minimum-time control problems on Cˆ, and associated Hamilton-Jacobi-Bellman equations. Various types of controllability properties are studied in connection with the existence of optimizers and with the relationship between the Pareto optimal frontiers of minimal decay and minimal modulus. We give explicit examples of optimal resonances and describe qualitatively properties of the Pareto frontiers near them. A special representation of bang-bang controlled trajectories is combined with the analysis of extremals to obtain various bounds on optimal widths of layers. We propose a new method of computation of optimal symmetric resonators based on minimum-time control and compute with high accuracy several Pareto optimal frontiers and high-Q resonators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
