Twinning cavities - Making a garage sound identical to a cathedral

Abstract

Bounded domains have discrete eigenfrequencies/spectra, and cavities with different boundaries and areas have different spectra. A general methodology for isospectral twinning, whereby the spectra of different cavities are made to coincide, is created by combining ideas from across physics including transformation optics, inverse problems and metamaterial cloaking. We extend this to open cavities where the spectrum is no longer purely discrete and real, and we pay special attention to twinning of leaky modes in 2D open cavities associated with complex valued eigenfrequencies with an imaginary part orders of magnitude lower than the real part. 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.