Optimum and standard beam widths for numerical modeling of interface scattering problems

Area of Science:

• Physics
• Wave Phenomena
• Applied Mathematics

Background:

• Gaussian beams are utilized for surface and interface scattering problems in fields like electromagnetics, acoustics, and seismology.
• Key advantages include finite scattering regions, restricted grazing angles, absence of side lobes, and convenient mathematical forms.
• Disadvantages involve non-uniform insonification and beam spreading, complicating analysis.

Purpose of the Study:

• To propose a standard beam parameterization for Gaussian beams.
• To enable uniform comparison of scattering effects across different models by standardizing propagation effects.
• To determine optimal Gaussian beam parameters for minimizing insonified areas in continuous wave and pulse beam problems.

Main Methods:

• Development of a standard beam parameterization for Gaussian beams.
• Analysis of continuous wave (CW) problems to find optimal beams for minimal insonified area at a given incidence angle and amplitude threshold.
• Application of standard parameters to estimate domain size for numerical solutions of pulse beam scattering.

Main Results:

• A standard parameterization is proposed to make propagation effects uniform across models.
• For CW problems, an optimal Gaussian beam minimizes the insonified area for specific incidence conditions.
• Standard parameters aid in estimating the minimum truncated domain for accurate numerical pulse beam solutions.

Conclusions:

• The proposed standard parameterization facilitates direct comparison of scattering phenomena by normalizing propagation effects.
• Optimal Gaussian beam selection is crucial for efficient and accurate scattering analysis, particularly in minimizing the insonified region.
• These parameters are valuable for both theoretical analysis and numerical simulations in wave scattering problems.