Application of supersymmetric quantum mechanics to the problem of micro-bending loss in optical waveguides*

The theoretical framework of supersymmetric quantum mechanics (SUSY-QM) has found many applied physics applications, especially in photonics. We use SUSY-QM to address the micro-bending issue in optical fibers. Micro-bending is caused by undesirable interactions in fiber cables, leading to signal loss in communication networks. Starting with a refractive index profile for a planar optical waveguide, we use the formalism presented in Ref. [1] to model the micro-bending attenuation by a Fokker-Planck equation. The planar waveguide is a preliminary model for future analysis of optical fibers. We then apply the SUSY-QM transformation to the Fokker-Planck equation to find a new refractive index profile with a different micro-bending attenuation profile. We observe that for a broad class of monomial refractive index profiles, including the conventional parabolic profile, it is always possible to obtain an index profile with a larger micro-bending attenuation. However, obtaining a smaller attenuation is not always possible and is restricted to a subset of index profiles. We identify this subset [2].

[1] M. Rousseau, J. Arnaud, Opt. Commun. 25, 333 (1978).
[2] S. Ward, R. Allahverdi, A. Mafi, arXiv:2009.11847.