About the Heisenberg's uncertainty principle and the determination of effective optical indices in integrated photonics at high sub-wavelength regime

TL;DR

This paper explores how Heisenberg's uncertainty principle influences the determination of effective optical indices in nanophotonics, highlighting the fundamental limits of precision at sub-wavelength scales.

Contribution

It introduces a formula linking the uncertainty of effective indices to the spatial dimensions of nanostructures, connecting quantum principles with integrated photonics.

Findings

Uncertainty of effective index inversely proportional to nanostructure size

Heisenberg's principle impacts eigenvalue precision in photonics

Fuzziness of eigenvalues below certain volume limits

Abstract

Within the Heisenberg's uncertainty principle it is explicitly discussed the impact of these inequalities on the theory of integrated photonics at sub-wavelength regime. More especially, the uncertainty of the effective index values in nanophotonics at sub-wavelength regime, which is defined as the eigenvalue of the overall opto-geometric problems in integrated photonics, appears directly stemming from Heisenberg's uncertainty. An apt formula is obtained allowing us to assume that the incertitude and the notion of eigenvalue called effective optical index or propagation constant is inversely proportional to the spatial dimensions of a given nanostructure yielding a transfer of the fuzziness on relevant senses of eigenvalues below a specific limit's volume.