A substantially improved treatment of intrinsic modes in tapered optical waveguides

The intrinsic modes are synthesized by self-consistent multiple reflected plane wave spectra, which furnish a spectral integral that satisfies exactly the wave equation and boundary conditions in the tapered environment away from the apex. For comparison to the local modes, and for numerical implementation so far, the spectral integrand has been approximated in a form suitable for small taper angles. This approximation introduces errors for larger tapers. It is shown that, by an alternative treatment of the plane wave spectra, the exact integrand can be restructured so that the integral is readily computable, with convergence improved for larger tapers. From this new form, it is verified by numerical tests that the previous errors are removed, and that an intrinsic mode is indeed a self-contained field solution which is decoupled from the other intrinsic modes.