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Nonlinear Guided Waves and Their Applications

Relation between a fiber's effective area and the capture fraction of spontaneous Raman scattering

Rogers H. Stolen

Published Jan 1, 2001• 0 citations
Publisher

Abstract

The spontaneous Raman capture fraction in a single-mode fiber is inversely related to effective area. This relation ties together classical and quantum approaches to stimulated Raman scattering in fibers and has implications for gain and noise in fiber Raman amplifiers.
DOI
10.1364/nlgw.2001.tua2

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The spontaneous Raman capture fraction in a single-mode fiber is inversely related to the effective area of the fiber. This relation ties together classical and quantum approaches to stimulated Raman scattering in fibers and has implications for calculations of gain and noise in fiber Raman amplifiers. The relation between capture fraction and effective area is derived, first, by comparison of the classical and quantum treatments of spontaneous Raman scattering in a fiber and, second, by treatment of the source of the Raman scattered light as oscillating dipoles and calculation of the capture fraction of the dipole radiated power.
Four-wave mixing in the form of Bragg scattering (BS) has been predicted to enable quantum noise-less frequency conversion by analytic quantum approaches. Using a semi-classical description of quantum noise that accounts for loss and stimulated and spontaneous Raman scattering, which are not currently described in existing quantum approaches, we quantify the impacts of these effects on the conversion efficiency and on the quantum noise properties of BS in terms of an induced noise figure (NF). We give an approximate closed-form expression for the BS conversion efficiency that includes loss and stimulated Raman scattering, and we derive explicit expressions for the Raman-induced NF from the semi-classical approach used here. We find that Raman scattering induces a NF in the BS process that is comparable to the 3-dB NF associated with linear amplifiers
We present a theoretical framework for spontaneous Raman scattering that fundamentally bridges quantum-mechanical and nonlinear-optical approaches. By conceptualizing spontaneous Raman scattering as a stimulated Raman gain or loss event seeded by the quantum vacuum field, we rigorously derive the spontaneous Raman cross-section directly from the third-order nonlinear susceptibility. Crucially, this framework predicts the existence of a hitherto unrecognized phenomenon: "spontaneous Raman loss" (sRL), which acts as the vacuum-seeded counterpart to stimulated Raman loss, complementing traditional spontaneous Raman scattering (spontaneous Raman gain, sRG). Furthermore, we establish a rigorous connection to the traditional Kramers-Heisenberg-Dirac (KHD) theory, revealing that the spontaneous process is governed by interference before a detector between the signal field emitted from molecules and the vacuum field itself that stimulates the molecules. This insight uncovers a direct correspondence between the sRG susceptibility and the rotating/counter-rotating interference terms in the KHD formula. Ultimately, we extend the foundational KHD theory by incorporating previously unrecognized essential terms, achieving perfect analytical agreement between the quantum mechanical and nonlinear optical descriptions of Raman scattering.