Maximum Shannon Capacity of Photonic Structures

Abstract

Information transfer through electromagnetic waves is an important problem that touches a variety of technologically relevant applications, including computing and telecommunications. Prior attempts to establish limits on optical information transfer have treated waves propagating through known photonic structures (including vacuum). In this article, we address fundamental questions concerning optimal information transfer in photonic devices. Combining information theory, wave scattering, and optimization theory, we formulate bounds on the maximum Shannon capacity that may be achieved by structuring senders, receivers, and their environment. Allowing for arbitrary structuring leads to a non-convex problem that is significantly more difficult than its fixed structure counterpart, which is convex and satisfies a known "water-filling" solution. We derive a geometry-agnostic convex relaxation of the problem that elucidates fundamental physics and scaling behavior of Shannon capacity with respect to device parameters and the importance of structuring for enhancing capacity. We also show that in regimes where communication is dominated by power insertion requirements, bounding Shannon capacity maps to a biconvex optimization problem in the basis of singular vectors of the Green's function. This problem admits analytical solutions that give physically intuitive interpretations of channel and power allocation and reveals how Shannon capacity varies with signal-to-noise ratio. Proof of concept numerical examples show that bounds are within an order of magnitude of achievable device performance and successfully predict the scaling of performance with channel noise. The presented methodologies have implications for the optimization of antennas, integrated photonic devices, metasurface kernels, MIMO space-division multiplexers, and waveguides to maximize communication efficiency and bit-rates.