Bounds on Wave Scattering

Resonance phenomena enable many of the strongest wave–matter interactions in physics. We recently developed an analytical technique, based only on power-flow and energy-conservation considerations, that yields a new class of single-frequency and broad-bandwidth limits to resonant enhancement of the scattering properties of any structure. The method was originally motivated by plasmonic design—at optical frequencies, metals enable exciting plasmonic and metamaterial behavior, but also introduce dissipative losses—where they resolved a fundamental question about the extent to which losses can be suppressed while achieving strong, subwavelength resonances. 

This work opens new questions in photonics. For some applications and frequencies we have found known structures that approach the limits, but for others, current designs fall far short. One important application is to molecular imaging, where achieving the bounds on spontaneous-emission rates would enable transformative improvements in imaging capabilities. Another important avenue is to design structured media that mimic plasmonic resonances away from their natural frequencies. Counter-intuitively, using a metal at frequencies 3-5x smaller than its plasma frequencies can exhibit improvements on the order of 100-1000x, with the proper geometrical design. We have designed tailored distributions of nanodisks to approach these limits, as recently demonstrated experimentally by a collaborator.
 
Going forward, developing fundamental limits to exotic phenomena in wave physics will be an important facet to convert new physical principles into real technological advances.
 
Select publications:
  • Fundamental limits to optical response in absorptive systems, O. D. Miller, A. G. Polimeridis, M. T. Homer Reid, C. W. Hsu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, Opt. Express 24, 3329 (2016)
  • Shape-independent limits to near-field radiative heat transfer, O. D. Miller, S. G. Johnson, and A. W. Rodriguez, Phys. Rev. Lett. 115, 204302 (2015) 
  • Fundamental limits to extinction by metallic nanoparticles, O. D. Miller, C. W. Hsu, M. T. H. Reid, W. Qiu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, Phys. Rev. Lett. 112, 123903 (2014)