Robust location of optical fiber modes via the argument principle method

Additional comments including Restrictions and Unusual features: The specified search domain must be meromorphic, in other words be complex analytic containing at most isolated singularities. The locations and orders of these singularities must be known analytically, so we describe how they are determined for our fiber dispersion relation. Branch points and branch cuts must be avoided, though the search domain may be arbitrarily close. We exploit knowledge of our dispersion relation, specifically that roots are located close to singularities, to simplify the method.