Considerations on boundary conditions in transformation optics for complete field computation in generic waveguides

Transformation optics is a powerful tool allowing remapping a generic domain into another yet maintaining a correspondence of the solution of Maxwell's equations within the two domains. Transformation optics has been used in the past to conveniently solve for modes in a generic waveguide by transforming its cross-section into a circular one. Such a transformation needs particular care in enforcing boundary conditions in the transformed, circular, domain. In this paper, a theoretical treatment of boundary conditions is presented, allowing for an accurate computation of all field components in a generic waveguide.