Loxodromes in Open Multi-Section Lasers
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 -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 -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 -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.
Keywords
Cite
@article{arxiv.2305.03115,
title = {Loxodromes in Open Multi-Section Lasers},
author = {Christopher P. J. O'Connor and Sebastian Wieczorek and Andreas Amann},
journal= {arXiv preprint arXiv:2305.03115},
year = {2023}
}