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Electromagnetic wave propagation in optical fiber amplifiers obeys Maxwell equations. Using coupled mode theory, the full Maxwell system within an optical fiber amplifier is reduced to a simpler model. The simpler model is made more efficient through a new scale model, referred to as an equivalent short fiber, which captures some of the essential characteristics of a longer fiber. The equivalent short fiber can be viewed as a fiber made using artificial (unphysical) material properties that in some sense compensates for its reduced length. The computations can be accelerated by a factor approximately equal to the ratio of the original length to the reduced length of the equivalent fiber. Computations using models of two commercially available fibers -one doped with ytterbium, and the other with thulium -show the practical utility of the concept. Extensive numerical studies are conducted to assess when the equivalent short fiber model is useful and when it is not.

Raman fiber lasers have been proposed as potential candidates for scaling beyond the power limitations imposed on near diffraction-limited rare-earth doped fiber lasers. One limitation is the modal instability (MI) and we explore the physics of this phenomenon in Raman fiber amplifiers (RFAs). By utilizing the conservation of number of photons and conservation of energy in the absence of loss, the 3 × 3 governing system of nonlinear equations describing the pump and the signal modal content are decoupled and solved analytically for cladding-pumped RFAs. By comparing the extracted signal at MI threshold for the same step index-fiber, it is found that the MI threshold is independent of the length of the amplifier or whether the amplifier is co-pumped or counter-pumped; dictated by the integrated heat load along the length of fiber. We extend our treatment to gain-tailored RFAs and show that this approach is of limited utility in suppressing MI. Finally, we formulate the physics of MI in core-pumped RFAs where both pump and signal interferences participate in writing the time-dependent index of refraction grating.

We propose a three dimensional Discontinuous Petrov-Galerkin Maxwell approach for modeling Raman gain in fiber laser amplifiers. In contrast with popular beam propagation models, we are interested in a truly full vectorial approach. We apply the ultraweak DPG formulation, which is known to carry desirable properties for high-frequency wave propagation problems, to the coupled Maxwell signal/pump system and use a nonlinear iterative scheme to account for the Raman gain. This paper also introduces a novel and practical full-vectorial formulation of the electric polarization term for Raman gain that emphasizes the fact that the computer modeler is only given a measured bulk Raman gain coefficient. Our results provide promising qualitative corroboration of the model and methodology used.

Cladding-pumped Raman fiber amplifiers (RFA) have been proposed as gain media to achieve power scaling. It is wellknown that the onset of the modal instability (MI) phenomenon is a limiting factor for achieving higher output powers in Yb-doped fiber amplifiers with good beam quality. In this paper, we present an analytical approach to the investigation of the MI phenomenon in high-power, cladding-pumped RFAs. By utilizing the conservation of the number of photons and the conservation of energy in the absence of loss, the nonlinear equations for the propagation of the pump power and the total signal power can be decoupled from one another. Decoupling lead to exact solutions for the pump power and transverse modes signal powers. Further we investigate various MI suppression techniques including increasing the seed power and gain-tailored design.