Isospectral open cavities and gratings
arXiv:2401.06136 · doi:10.1098/rspa.2023.0853
Abstract
Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances whilst simultaneously being physically compact. To aid this design challenge we develop a methodology to allow isospectral twinning of reference cavities with either smaller or larger ones, enforcing their spectra to coincide so that open resonators are identical in terms of their complex eigenfrequencies. For open systems the spectrum is not purely discrete and real, and we pay special attention to the accurate twinning of leaky modes associated with complex valued eigenfrequencies with an imaginary part orders of magnitude lower than the real part. We further consider twinning of 2D gratings, and model these with Floquet-Bloch conditions along one direction and perfectly matched layers in the other one; complex eigenfrequencies of special interest are located in the vicinity of the positive real line and further depend upon the Bloch wavenumber. The isospectral behaviour is illustrated, and quantified, throughout by numerical simulation using finite element analysis.
References in corpus (11)
- Hiding Under the Carpet: a New Strategy for Cloaking
- General Relativity in Electrical Engineering
- A complementary media invisibility cloak that can cloak objects at a distance outside the cloaking shell
- Acoustic cloaking theory
- Achieving control of in-plane elastic waves
- Focussing Light Using Negative Refraction
- Quasimodal expansion of electromagnetic fields in open two-dimensionnal structures
- A spherical perfect lens
- Leaky wave characterisation using spectral methods
- Cloaking strategy for Love waves
- Isospectral open cavities and gratings