Generalized optical theorem for scattering in inhomogeneous media.

Area of Science:

• Wave physics
• Acoustics
• Electromagnetism

Background:

• Scattering of waves in complex media is a fundamental problem in physics.
• Previous methods often struggle with inhomogeneous and bounded environments.

Purpose of the Study:

• To develop a flexible method for analyzing wave scattering in bounded, inhomogeneous media.
• To define and analyze an effective scattering amplitude within such environments.

Main Methods:

• Utilizing the method of pseudopotentials.
• Employing spherical harmonic expansion of scattering amplitudes.
• Developing multipole decomposition of Green functions for bounded media.

Main Results:

• An effective scattering amplitude for the bounded medium is defined.
• A generalized optical theorem for the effective scattering amplitude is derived and analyzed.
• The scattering problem is formulated explicitly in terms of the bounded medium's Green functions.

Conclusions:

• The pseudopotential method offers a flexible approach to wave scattering in bounded, inhomogeneous media.
• This method allows for independent computation of propagation and scattering phenomena.
• The approach leverages known scattering amplitudes in uniform media as input.