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

Abstract

We present an optimization framework based on Lagrange duality and the scattering 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.

Physical limits on electromagnetic response

“…The large scale of most practical photonics problems also poses a challenge: current demonstrations of the framework are restricted to 2D [42][43][44]198] or highly symmetric domains in 3D, exploiting efficient spectral basis representations [38,39,68] to limit the size of the associated system matrices. Beyond these early proofof-concept explorations, there is much room for development of standardized packages for evaluating limits (possibly in conjunction with inverse methods) on 3D photonic devices by exploiting general-purpose techniquesnumerical Maxwell solvers employing localized basesand open-source optimization methods [203].…”

“…In particular, information encoded in waves transferred between a source S and receiver region R, in free space, can be quantified via a Frobenius norm, V S V R G 0 (x, x ) 2 , of the vacuum Green's function connecting the two enclosing volumes, V S and V R . Adaptations to describe communication mediated by devices (e.g., lenses and multiplexers), which can strongly modify electromagnetic fields and thus "channel capacity", remain an active area of investigation [43,93].…”

“…(3), any vector field that respects Eq. ( 8) for all possible choices of P (x, ω) actually defines an effective medium scattering structure [43] (a mix between the material properties asserted by V (x, ω) and the background).…”

“…We then focus our discussion on an emerging general methodology for evaluating photonic design bounds based on optimization theory and conservation principles that follow either directly from Maxwell's equations or the identities of scattering theory. Originally developed as an instrument for investigating maximal scattering cross section limits [38][39][40], the framework is applicable to a broad range of design problems where the objective can be expressed as a quadratic function of the fields [41][42][43]. The constraints have clear physical meaning, limiting both the amplitude of the polarization response, important to power transfer, and the extent that the phase of the polarization response can be modified, with consequences on the engineering of resonances.…”

Fundamental limits to multi-functional and tunable nanophotonic response

“…A unique instance of multiple functionalities, that of multiple incident fields (or initial wavefunctions in the quantum case) was proposed in Refs. [58,59], while an alternative formulation of multi-scenario design was proposed in Ref. [60].…”