Extended Self-similarity in Multimode Optical Fiber Speckles

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.