  The existence of an infinite number of perfect nonradiating modes in
elliptical nanofibers is demonstrated. Dispersion laws are found for TM and TE
perfect modes in circular and elliptical waveguides with an arbitrary
eccentricity. Numerical simulations in Comsol Multiphysics have shown that
these modes can be excited by plane waves of a certain parity and have
extremely low radiative losses and extremely high quality factors. The found
modes can be used to create highly sensitive nanosensors and other optical
nanodevices where radiation losses should be minimal.
