Maximum Shannon Capacity of Photonic Structures
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 phot...
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Main Authors | , , , , , , |
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Format | Journal Article |
Language | English |
Published |
03.09.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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, maximum 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. |
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DOI: | 10.48550/arxiv.2409.02089 |