The scattering of scalar waves by objects embedded in an inhomogeneous medium contained by a bounded volume is discussed using the method of pseudopotentials. The scattering amplitude for the object in an extended uniform medium is assumed known and used as input. The scattering process is described by using an expansion of the scattering amplitude in terms of spherical harmonics. An appropriate multipole decomposition of the Green function in the bounded medium is developed and the effective scattering amplitude in this environment is defined. The generalized optical theorem obeyed by this effective scattering amplitude is obtained and analyzed. The scattering problem is formulated entirely and explicitly in terms of the bounded medium's Green functions. This approach is thus very flexible in regards to the choice of incident field. In the case of waveguides the connection between propagation and scattering is explicit. At the same time it still allows for independent computation of the propagation and scattering aspects of the problem. This is the main advantage of using as input the scattering amplitude in an extended uniform medium.
Articles you may be interested inTerahertz transmission lines based on surface waves in plasmonic waveguides J. Appl. Phys. 104, 083108 (2008); 10.1063/1.3000444Growing evanescent waves in a cutoff rectangular waveguide loaded with an inductive iris and a capacitive postThe scattering of scalar waves by objects located inside a waveguide or a cavity is discussed using the method of pseudopotentials. Pseudopotentials were introduced to simulate short-range potentials in quantum mechanics and proved useful in many-body problems and in problems involving multicentered potentials. In this work it is shown that this approach can also be used to describe the scattering of classical scalar waves by objects confined to the interior of a waveguide or a cavity in terms of the scattering amplitudes of those objects in an extended medium.
The scattering of acoustic waves by objects located inside a waveguide is discussed, assuming that the scattering amplitude for the object in an extended uniform medium is known. The scattering process is described by using an expansion of the scattering amplitude in terms of spherical harmonics. An appropriate multipole decomposition of the waveguide Green's function is developed and the effective scattering amplitude in the waveguide is obtained. An important property of the effective scattering amplitude, the generalized optical theorem, is obtained and its implications for scattering in a waveguide are discussed. The scattering problem is formulated entirely and explicitly in terms of the waveguide Green's functions, which makes this approach very flexible in regard to the choice of the incident field. It also establishes the connection between propagation and scattering and allows for the independent computation of the propagation and scattering aspects of the problem. This is the main advantage of using the scattering amplitude in an extended uniform medium as an input. The connection of this work with previous work in scattering in waveguides is discussed.
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