The transition from locked to leaky modes in tropospheric radio propagation

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Abstract
The propagation characteristics of a waveguide mode in the troposphere near the ground are studied by the simple phase integral method over a range of frequencies in which the mode changes from locked to leaky. The method is applied to a troposphere with a parabolic distribution for the square of the modified refractive index, and the results are compared with those from an exact analytic method. Particular attention is given to the contour of the phase integral in the complex height plane. This contour changes discontinuously at the transition from a locked to a leaky mode. An alternative phase integral formula is described in which there is no abrupt change at the transition. Some results from this formula are presented, and a derivation of it for locked modes is given.

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