Extended Self-similarity in Multimode Optical Fiber Speckles

TL;DR

This paper demonstrates that Extended Self-Similarity (ESS), typically used in nonlinear systems, also appears in linear systems like multimode optical fibers, showing broader applicability of ESS in complex physical systems.

Contribution

It reveals that ESS scaling can occur in purely linear optical systems, expanding the understanding of where ESS can be applied beyond nonlinear dynamics.

Findings

ESS scaling observed in linear multimode fiber speckles

Scaling exponents match Kolmogorov's classical exponents

Robust extended scaling range identified in intensity structure functions

Abstract

Extended Self-Similarity (ESS) is a widely used tool for uncovering universal power-law scaling in systems dominated by nonlinear interactions. This work demonstrates that ESS scaling can also emerge in a system governed by purely linear physics: the propagation of coherent light in a multimode fiber. The system produces complex speckle patterns arising solely from deterministic linear mode interference. We analyze the intensity structure functions of these speckles and observe a robust extended scaling range. The measured scaling exponents align with the classical Kolmogorov scaling exponents. This finding establishes that the statistical signatures captured by ESS are not exclusive to nonlinear systems, revealing a broader applicability of this scaling framework to complex linear systems.