Overdamped modes and optimization of resonances in layered cavities
We study the problem of optimizing the imaginary parts Im ω of quasi-normal-eigenvalues ω associated with the equation y’’ = -ω^2 B y . It is assumed that the coefficient B(x), which describes the structure of an optical or mechanical resonator, is constrained by the inequalities 0 b_1 B(x) b_2 . Extremal quasi-normal-eigenvalues belonging to the imaginary line i R are studied in detail. As an application, we provide examples of ω with locally minimal |Im ω| (without additional restrictions on Re ω) and show that a structure generating an optimal quasi-normal-eigenvalue on i R is not necessarily unique., number=3, journal=Methods of Functional Analysis and Topology, author=Karabash, I. M. and Logachova, Olga M. and Verbytskyi, Ievgen V., year=2017, month=Sep., pages=252–260