Bounds for Scattering from Absorptionless Electromagnetic Structures

Phys. Rev. Applied 14, 014025.

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The design of the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success in applying local optimization methods to electromagnetic device design, it is unclear whether the performance of the resulting designs is close to that of the best possible design. This question remains open for absorptionless electromagnetic devices, since the absence of material loss makes it difficult to provide provable bounds on their scattering properties. We resolve this problem by providing nontrivial lower bounds on performance metrics that are convex functions of the scattered fields. Our bounding procedure relies on accounting for a constraint on the electric fields inside the device, which can be provably constructed for devices with small footprints or low dielectric contrast. We illustrate our bounding procedure by upper bounding the scattering cross sections of lossless dielectric and metallic particles.