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Loxodromes in open multisection lasers

Christopher P. J. O'Connor, Sebastian Wieczorek, and Andreas Amann

School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland

Phys. Rev. A 107, 053520 – Published 26 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.053520

Abstract

We introduce a formalism to efficiently calculate lasing modes and optical power flow in multisection lasers with open boundaries. The formalism is underpinned by a projection of the complex-valued electric field and its spatial derivative onto a suitably extended complex $Z$ plane to reduce the order of the problem and simplify analysis. In a single-section laser, we show that a laser mode is a loxodrome on the extended complex $Z$ plane. In a multisection laser, we obtain loxodromes for individual sections of the laser. Then, a multisection mode is constructed by continuously concatenating individual loxodromes from each section using the open boundary conditions. A natural visualization of this construction is given by stereographic projection of the extended complex $Z$ plane onto the Riemann sphere. Our formalism simplifies the analysis of lasing modes in open multisection lasers and provides insight into the mode geometry and degeneracy.

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Loxodromes in open multisection lasers

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