| dc.description.abstract | Resonances are everywhere. They have different manifestations and are used in many applications. In this work, we study multiple systems making use of resonances, with numbers ranging “from one to infinity.”
First, we derive single-frequency bounds for the surface-enhanced Raman scattering (SERS) where resonant nanostructures are used to enhance the Raman signal. These bounds are shape independent and only function of the material constants and the separation distance from the Raman molecule. They can be evaluated analytically or by simple numerical integration.
We then present analytical design criteria for multi-resonant filters in strongly coupled systems where standard approaches (such as coupled mode theory or network synthesis) are not adequate. For this, we develop a quasi-normal mode theory (QNMT) of the scattering matrix that enforces the fundamental constraints of energy conservation and reciprocity even for truncated sums. As an example of application, we design microwave metasurface filters with various orders, bandwidths and types (such elliptic or Chebyshev).
For systems making use of a large number of resonances over a large bandwidth (such as light trapping in solar cells), and in particular for metaparticle arrays, we present approximate frequency/angle-averaged absorption enhancement bounds in the radiative transfer regime and apply the results to ocean buoy energy extraction. Our results, which match full-wave simulations, enable us to propose and quantify approaches to increase performance through careful particle design and/or using external reflectors.
Finally, we study single-mode lasing stability in periodic systems where a full continuum of modes should be taken into account in the nonlinear regime above threshold. In particular, we show that, under the right conditions, single-mode lasing is still possible in an infinite periodic structure, with practical limitations arising from boundary effects and manufacturing inaccuracies. Examples of band-edge (1d) and bound-in-continuum (2d) mode lasing are presented. | |
