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We present an optimization framework based on Lagrange duality and the scattering $mathbb{T}$ operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of input fields, i.e., constraints on achievable optical transformations and the characteristics of structured materials as communication channels. Implications of these bounds on the performance of representative optical devices having multi-wavelength or multiport functionalities are examined in the context of electromagnetic shielding, focusing, near-field resolution, and linear computing.
The inverse problem in optics, which is closely related to the classical question of the resolving power, is reconsidered as a communication channel problem. The main result is the evaluation of the maximum number $M_epsilon$ of $epsilon$-distinguish
We present a method based on the scattering $mathbb{T}$ operator, and conservation of net real and reactive power, to provide physical bounds on any electromagnetic design objective that can be framed as a net radiative emission, scattering or absorp
We show how the central equality of scattering theory, the definition of the $mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem of optimiz
Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, potentially replacing bulky components. A central stepping stone towards realizing this promise is the demonstration of multifunct
The polarization of light is utilized in many technologies throughout science and engineering. The ability to transform one state of polarization to another is a key enabling technology. Common polarization transformers are simple polarizers and pola