Radio Science

Instability of the roots of the modal equation for the tropospheric waveguide


  • Mireille F. Levy


The waveguide modes obtained in the study of electromagnetic wave propagation in the troposphere depend spectacularly on the smoothness of the refractivity profile. The trilinear profile always yields an infinite number of nondiffractive waveguide modes, whereas holomorphic profiles only give a finite number of nondiffractive modes. If the trilinear profile is approximated by a holomorphic profile, which is always possible in the continuous case, then most of the nondiffractive modes disappear. This instability of the modes suggests using holomorphic profiles for field calculations.