Abstract
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 given 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 multiwavelength or multiport functionalities are examined in the context of electromagnetic shielding, focusing, near-field resolution, and linear math kernels.
Highlights
As undoubtedly surmised since long before Shannon’s pioneering work on communication [1] or Kirchhoff’s investigation of the laws governing thermal radiation [2], physics dictates that there are meaningful limits on how any measurable quantity may be transferred between a sender and receiver that apply largely independent of the precise details by which transmission is realized
Linear operations are to be inferred by juxtaposition, e.g., E|M|E = dydxE∗(y, ω) · M(y, x, ω) · E(x, ω), where “·” is the vector inner product at a spatial point, the ∗ superscript denotes complex conjugation, and M is a “dyadic” function of the spatial coordinates x and y
All stated relations hold in greater generality, for simplicity in analysis and discussion, we will suppose that all scattering potentials under consideration can be described by a linear electric susceptibility that does not mix field components from distinct spatial points
Summary
As undoubtedly surmised since long before Shannon’s pioneering work on communication [1] or Kirchhoff’s investigation of the laws governing thermal radiation [2], physics dictates that there are meaningful limits on how any measurable quantity may be transferred between a sender and receiver (collectively registers) that apply largely independent of the precise details by which transmission is realized. Beyond well-established considerations such as the need to conserve power in passive systems and the classical diffraction limit of vacuum [28], such contextspecific limits are typically unknown [29] It is seldom clear what level of possible performance improvement should be sensibly supposed, even to within multiple orders of magnitude [30,31,32]. During this brief overview, two innovations for handling generic input-output formulations are introduced: a further generalization on the variety of operator constraints that can be imposed based on the definition of the T -operator, beyond the possibility of local clusters examined in Refs. IV, is strongly tied to the ability of the formulation to properly enforce that every transformation is mediated by single (unique) material scattering geometry
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
