Calculation of the scattering amplitude from discrete eigenvalues.

Area of Science:

• Physics
• Wave phenomena
• Electromagnetism

Background:

• Calculating scattering amplitude is crucial for understanding wave interactions.
• Traditional methods often involve complex numerical simulations.
• A direct link to wave number spectrum has been sought.

Purpose of the Study:

• To establish a direct method for calculating scattering amplitude from wave equation eigenvalues.
• To connect scattering amplitude with the wave number spectrum.
• To demonstrate this connection using electromagnetic wave scattering by dielectric slabs.

Main Methods:

• Solving the stationary wave equation with an absorbing boundary condition.
• Calculating discrete eigenvalues from the solved wave equation.
• Analyzing the relationship between eigenvalues and scattering amplitude.
• Applying the method to electromagnetic wave scattering by dielectric slabs.

Main Results:

• The scattering amplitude for a spherically symmetric target can be directly computed from discrete eigenvalues.
• A direct connection between scattering amplitude and the wave number spectrum is established.
• The transmission coefficient for dielectric slab arrays is fully determined by eigenvalue spacing.

Conclusions:

• The eigenvalue spectrum provides a direct route to calculating scattering amplitudes.
• This approach simplifies the analysis of wave scattering phenomena.
• The findings have implications for designing optical and electromagnetic devices.