Analysis of microwave ducting in an inhomogeneous troposphere

258

176

A theoretical foundation for the use of the parabolic wave equation/Fourier split‐step method for modeling electromagnetic tropospheric propagation is presented. New procedures are used to derive a scalar Helmholtz equation and to subsequently transform to a rectangular coordinate system without requiring approximations. The assumptions associated with reducing the resulting exact Helmholtz equation to the parabolic wave equation that is used for computations are then described. A similar discussion of the error sources associated with the Fourier split‐step solution technique is provided as well. These discussions provide an important indication of the applicability of the parabolic equation/split‐step method to electromagnetic tropospheric propagation problems. A rigorous method of incorporating an impedance boundary at the Earth's surface in the split‐step algorithm is also presented for the first time. Finally, a few example calculations which demonstrate agreement with other propagation models are provided.

Section: The Impedance Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theoretical description of the parabolic approximation/Fourier split‐step method of representing electromagnetic propagation in the troposphere

Kuttler¹,

Dockery²

1991

258

176

“…This so-called adiabatic approximation has been used extensively in underwater sound [Deavenport, 1966;Nagl et al, 1978] and atmospheric acoustic waves [Pierce, 1965]. Only quite recently has the importance of mode conversion been appreciated when dealing with nonuniform natural wave guides [Bahar and Wait, 1963;Wait, 1968Wait, , 1974Bahar, 1971;McDaniel, 1977;Cho and Wait, 1978;Rutherford and Hawker, 1979; E. Ledinegg et al, private communication, 1975]. In this paper we present a self-contained analysis for propagation in a two-dimensional curved model of the earth, where the refractive index is a function of both height and range.…”

Section: Introductionmentioning

confidence: 99%

Coupled mode analysis for a nonuniform tropospheric wave guide

Wait¹

1980

Self Cite

We employ a two‐dimensional cylindrical model to analyze the normal modes in a laterally nonuniform tropospheric duct. The utilization of the impedance boundary condition at the earth's surface permits us to use a complete field representation in terms of discrete modes only. These modes are chosen to be locally orthogonal so that a tapered‐type nonuniformity can be handled with a systematic accounting of the mode conversion. Explicit formulas are given for the coupling coefficients. It is shown that the general coupled mode analysis reduces to the appropriate form when dealing with an abrupt but small lateral change of the refractive index structure. This step model had been treated previously using a nonrigorous mode matching procedure that neglected reflected waves at the outset.

“…That is to say, if a trapped mode p has been excited by virtue of the primary field being partly converted to p due to lateral inhomogeneity within the line of sight region, the reconversion of p to other trapped modes or back to radiation modes has been ignored. In this respect the theory developed here to estimate conversion from a densely moded region (the line of sight region) to the many weakly attenuated modes is less refined than theory developed for treating mode conversion between discrete guided and leaky modes of a tropospheric system [Cho and Wait, 1978;Wait, 1980]. The latter theory is particularly useful in the VHF band but much more difficult to implement in the microwave range.…”

mentioning

confidence: 97%

Conversion of radiation modes to trapped modes due to lateral inhomogeneity of a simple elevated layer

Pappert¹

1982

It often happens that tropospheric ducts produced by elevated layers have a modal system in the microwave range consisting of many virtually lossless modes. These weakly attenuated modes have their energy localized about the layer and are insignificantly excited by sources far removed from the layer where the modal height gains are characteristically evanescent. Despite such an unfavorable geometry for direct excitation of these essentially loss‐free modes, they may be indirectly excited within the line of sight region by mode conversion processes associated with lateral inhomogeneity of the layer. In this paper an approximate theory is developed for the mode conversion produced within the line of sight region by large‐scale lateral inhomogeneity of an idealized, vertically homogeneous layer. The theory is applied to a 3‐GHz case study with the following results: (1) lateral inhomogeneity associated with layers of low elevation is more effective for converting to lossless modes than is lateral inhomogeneity associated with layers of high elevation; and (2) lateral inhomogeneity near the horizon is more effective than lateral inhomogeneity near the transmitter for converting to lossless modes.