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arXiv · 2305.03115

Loxodromes in Open Multi-Section Lasers

Christopher P. J. O'Connor·Sebastian Wieczorek·Andreas Amann
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Abstract

We introduce a formalism to efficiently calculate lasing modes and optical power flow in multi-section 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 $\mathcal{Z}$-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 $\mathcal{Z}$-plane. In a multi-section laser, we obtain loxodromes for individual sections of the laser. Then, a multi-section 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 $\mathcal{Z}$-plane onto the Riemann sphere. Our formalism simplifies analysis of lasing modes in open multi-section lasers and provides new insight into the mode geometry and degeneracy.

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Christopher P. J. O'Connor, Sebastian Wieczorek, Andreas Amann. 2023-05-04. Loxodromes in Open Multi-Section Lasers. https://doi.org/10.1103/physreva.107.053520

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