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Numerical model for calculations of spatio-temporal variations of amplitudes of counter-propagating pulses in a standing-wave laser cavity is proposed. Proposed model is based on the transport-type equations for the envelopes of oppositely running pulses, spatial discretization along the cavity axis, and calculation of temporal variations both electric field amplitude and active media polarization/inversion at these points.
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L. A. Kochkurov, L. A. Melnikov, S. S. Volchkov, E. V. Ushakova, "Numerical investigation of all-fiber erbium-doped bidirectional ring laser for high-precision sensing," Proc. SPIE 11846, Saratov Fall Meeting 2020: Laser Physics, Photonic Technologies, and Molecular Modeling, 1184603 (4 May 2021); https://doi.org/10.1117/12.2588400