Maximal single-frequency electromagnetic response

$\mathbb{T}$-Operator Limits on Optical Communication: Metaoptics, Computation, and Input-Output Transformations

“…Archi-tectures possessing impressive field-transformation capabilities have already been demonstrated, from free-space (grating) couplers [33,34] to beam steering [35,36] and polarization control [37,38], suggesting that large-scale optimization methods may allow scattering attributes to be tailored to a far greater degree than what has been seen in past intuition-based designs. Simultaneously, ramifying from the core ideas of Lagrange duality and interpreting physical relations as optimization constraints expounded below [39][40][41][42], a string of recent articles on improved bounds for scattering phenomena (including radiative heat transfer [32], absorbed power [43], scattered power [44], and Purcell enhancement [45]) have shown that, in some cases, only modest improvements over standard designs are even hypothetically attainable [44][45][46][47][48][49][50][51][52][53].…”

Global $\mathbb{T}$ operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections

“…The scheme, capturing all structuring possibilities as well as fundamental wave limitations contained in Maxwell's equations, can be applied provided only three specified attributes: the material the device will be made of, the volume it may occupy, and the source that it will interact with. In addition to conservation of real power, which sets an upper bound on the magnitude of a system's polarization response, consideration of an analogous optical theorem for reactive power, introducing the polarization phase, is shown to severely limit the ability of certain materials to create resonances, leading to significantly tighter limits compared to related works [71,72].…”

Fundamental bounds for scattering from absorptionless electromagnetic structures

“…The T-operator formalism has also been used to provide rigorous bounds on scattering from subwavelength particles [16][17][18][19]. Careful accounting of the cooperative effects of radiation and absorption in electromagnetic scatterers has been used to compute scattering bounds [20]. While the approaches in refs.…”

“…While the approaches in refs. [13][14][15][16][17][18][19][20] have been very successful in providing useful bounds on absorptive electromagnetic structures, they cannot be straightforwardly applied to absorptionless electromagnetic structures. Bounds on frequency-averaged performance of absorptionless electromagnetic structures have also been provided based on analytical continuation of Maxwell's equations [21], but these bounds are very loose if single-frequency performance is of interest.…”

“…Furthermore, while we have focused on the problem of bounding fields from absorption-less electromagnetic devices, the procedure outlined in this paper can be integrated with the approaches outlined in refs. [13][14][15][16][17][18][19][20] to provide tighter bounds for absorptive electromagnetic devices. Finally, we note that the general techniques introduced in this paper are not specialized to bounding electromagnetic scattering, but easily extendible to wave-scattering problems in other fields such as accoustics or quantum physics.…”