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This article presents an ultraweak discontinuous Petrov-Galerkin (DPG) formulation of the time-harmonic Maxwell equations for the vectorial envelope of the electromagnetic field in a weakly-guiding multi-mode fiber waveguide. This formulation is derived using an envelope ansatz for the vector-valued electric and magnetic field components, factoring out an oscillatory term of exp(-ikz) with a user-defined wavenumber k, where z is the longitudinal fiber axis and field propagation direction. The resulting formulation is a modified system of the time-harmonic Maxwell equations for the vectorial envelope of the propagating field. This envelope is less oscillatory in the z-direction than the original field, so that it can be more efficiently discretized and computed, enabling solutions to the vectorial DPG Maxwell system in fibers that are 1000x longer than previously possible. Different approaches for incorporating a perfectly matched layer for absorbing the outgoing wave modes at the fiber end are derived and compared numerically. The resulting formulation is used to solve a 3D Maxwell model of an ytterbium-doped active gain fiber amplifier, coupled with the heat equation for including thermal effects. The nonlinear model is then used to simulate thermally-induced transverse mode instability (TMI). The numerical experiments demonstrate that it is computationally feasible to perform simulations and analysis of real-length optical fiber laser amplifiers using discretizations of the full vectorial time-harmonic Maxwell equations. The approach promises a new high-fidelity methodology for analyzing TMI in high-power fiber laser systems and is extendable to including other nonlinearities.
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Accurate and efficient modeling of the transverse mode instability in high energy laser amplifiers
We study the transverse mode instability (TMI) in the limit where a single higher-order mode (HOM) is present. We demonstrate that when the beat length between the fundamental mode and the HOM is small compared to the length scales on which the pump amplitude and the optical mode amplitudes vary, TMI is a three-wave mixing process in which the two optical modes beat with the phase-matched component of the index of refraction that is induced by the thermal grating. This limit is the usual limit in applications, and in this limit TMI is identified as a stimulated thermal Rayleigh scattering (STRS) process. We demonstrate that a phase-matched model that is based on the three-wave mixing equations can have a large computational advantage over current coupled mode methods that must use longitudinal step sizes that are small compared to the beat length.
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- Award ID(s):
- 1809622
- PAR ID:
- 10230537
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Express
- Volume:
- 29
- Issue:
- 12
- ISSN:
- 1094-4087; OPEXFF
- Format(s):
- Medium: X Size: Article No. 17746
- Size(s):
- Article No. 17746
- Sponsoring Org:
- National Science Foundation
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