Finding resonance poles by means of Cauchy integrals

Guided modes in photonic structures are characterized by a propagation constant that is a root of pole of some operator. It is shown that the operatorial calculus of Dunford and Schwartz, i.e. the extension of Cauchy integrals to operators, provides a mean for the numerical computation of dispersion curves. The theory is developed and then applied in the case of a microstructured fibre.