Upper bounds on absorption and scattering

Abstract

C Radiation modes 30 D Material models 33Abstract A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell's factor and local field enhancement where a dimer is used as a practical example.

Approaching the upper limits of the local density of states via optimized metallic cavities

“…[13], which are useful for lossless dielectrics (where the single-frequency LDOS bound diverges). Conversely, it is possible that incorporating additional constraints, such as considering a more complete form of the optical theorem, may lower the LDOS bounds [20][21][22][23]. There has also been recent interest in the magnetic LDOS, corresponding to magnetic-dipole radiation [50], and we expect that qualitatively similar results (albeit with different optimal shapes) would be obtained for the magnetic LDOS (or some combination of magnetic and electric, although trying to optimize both simultaneously would likely encounter difficulties similar to those for optimizing multiple polarizations).…”

“…3. Although it is possible that even tighter LDOS bounds could be obtained in future results by incorporating additional physical constraints [20][21][22][23], we believe that our results show that the existing bounds are already closely related to attainable performance and provide useful guidance for optical cavity design. In this work, we optimize the total electric LDOS, which is the sum of the absorbed and radiated powers from electric dipoles (Sec.…”

“…By actually solving Maxwell's equations for various geometries, we can investigate how closely the bound can be approached (how "tight" the bound is). It is possible that incorporating additional constraints may lead to tighter bounds in the future [20][21][22][23], but our results below already show that Eq. 2is achievable within an order of magnitude.…”

Stored Energies and Q-Factor of Two-Dimensionally Periodic Antenna Arrays

“…From the conjugate symmetry of the kernel g it follows that W em,2 is real. Finally, we combine (28), (31), and (38) to write the current representation of the electric stored energy…”

“…An approach to include dielectric substrates has been considered in [16] for a dipole array. Another method to obtain a more general treatment of dielectric inclusions of arbitrary shapes is to extend the work [31] to periodic structures.…”