The waveguide modes guided by a smooth concave tropospheric layer are considered. The model is chosen so that the effective dielectric susceptibility is a linear segmented function of height. The calculations are made explicitly for a model that is linear with height except for a single inversion layer. It is shown that such a layer will support whispering-gallery or earth-detached modes with exceedingly small attenuation even when the refractive index contrast is four or five N units.
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