Noncommuting limits and effective properties for oblique propagation of electromagnetic waves through an array of aligned fibres

We consider formulations for the Helmholtz operator for conically propagating modes on an array of high contrast ferromagnetic cylindrical inclusions in the limit when their wavelength outside the inclusions tends to infinity. If one considers a trajectory in the coordinates (frequency, conical parameter), then the effective phase refractive index will depend on this trajectory in the vicinity of the origin.