First Advisor
Jay Gopalakrishnan
Term of Graduation
January 2026
Date of Publication
6-1-2026
Document Type
Dissertation
Language
English
Subjects
Coupled mode theory, Fiber laser amplifiers, Model comparison, Nonlinear ordinary differential equations, Periodic averaging theory, Reduced-order modeling
Physical Description
1 online resource ( pages)
Abstract
Fiber laser amplifier (FLA) models are often implemented without rigorous mathematical justification or thorough numerical validation. Without a proper theoretical basis for assumptions and approximations, or a technical analysis of model performance, there is significant uncertainty about the limitations of any given reduced model and its suitability for an application. This research aims to address the lack of comprehensive assessment of FLA models by directly comparing distinct models and recommending a mathematical alternative to replace heuristic model-reduction techniques. The work in this dissertation is divided into two projects: a comparative study that uses existing FLA models to assess the validity of model approximations for predicting transverse mode instability (TMI) and relative changes in TMI thresholds, and the derivation of an innovative reduced-order FLA model based on mathematically sound approximations.
The TMI comparison project studies the performance of three unique FLA models that can be characterized as high-, mid-, and low-fidelity, respectively, in both the stable regime (below the TMI threshold) and the chaotic regime (above the TMI threshold); any tuning to other models is omitted for the fairest comparison. The high- and mid-fidelity models exhibit exceptional similarity in the stable regime before the onset of TMI; this close agreement is remarkable given that, even in the stable regime, the problem is nonlinear and the mid-fidelity model relies on substantial approximations. As the amplifier transitions from the stable regime to the TMI regime, all three models produce power spectral densities (PSDs) with offset frequencies within the same bandwidth at which TMI is observed. The frequency-space PSD results support the conclusion that all three models accurately capture at least some aspects of the TMI phenomenon. Additionally, this alignment informs a novel interpretation of the TMI nonlinearity as a phase modulation effect. Ultimately, the agreement between the models ends at the stable regime and offset PSD frequencies; TMI regime results indicate that all three models report vastly different TMI thresholds, with no alignment in the relative change in TMI thresholds between fiber configurations beyond the sign of the change in the positive or negative direction. Potential reasons for this discrepancy are presented.
The reduced model development project derives an efficient FLA model based on the mid-fidelity model using the periodic averaging method from dynamical systems. A complete proof of the generalized averaging theorem for a complex vector-valued ODE system of periodic functions is provided. Then, an approximate, nondimensionalized model obtained via Taylor expansions is presented to identify all primary periodicities within the model. Once the requirements of the generalized averaging theorem are satisfied, it is applied to the approximate ODE system, removing all higher frequencies and yielding the reduced model. The new reduced model's increase in computational efficiency is evaluated by determining the coarsest possible longitudinal discretization before significant accumulation of error. Studies on the limitations of averaging with respect to various FLA model parameters are conducted to establish the averaging method as a robust reduction technique. Finally, the mid-fidelity and reduced model results for coupled gain and heat simulations are compared, yielding highly accurate results across three dopant concentrations and further justifying the reduced model as an efficient yet physically consistent replacement for the more costly mid-fidelity model.
Rights
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Recommended Citation
Bryant, Rebecca Nicole, "The Method of Periodic Averaging Applied to Reduced Coupled Mode Theory Models for Fiber Laser Amplifiers" (2026). Dissertations and Theses. Paper 7112.