Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates

Area of Science:

• Wave scattering theory
• Acoustics
• Optics
• Quantum mechanics

Background:

• The optical theorem is fundamental for plane wave scattering, relating extinction cross-section to forward scattering amplitude.
• Existing theories primarily focus on infinite plane waves, limiting applicability to complex beam geometries.

Purpose of the Study:

• To extend and generalize the optical theorem for two-dimensional (2D) beams of arbitrary character in a cylindrical coordinate system.
• To derive generalized analytical expressions for extinction, absorption, and scattering cross-sections for scalar monochromatic acoustical wavefronts.

Main Methods:

• Application of scalar resonance scattering theory.
• Development of generalized analytical expressions in a cylindrical coordinate system.
• Analysis of scalar monochromatic acoustical wavefronts.

Main Results:

• The optical theorem is successfully generalized for 2D beams in cylindrical coordinates, accommodating arbitrary beam shapes and object geometries.
• New analytical expressions for extinction, absorption, and scattering cross-sections were derived.
• An interference scattering cross-section term was identified, detailing interactions between diffracted Franz waves and resonance elastic waves.

Conclusions:

• The generalized optical theorem provides a more versatile framework for wave scattering analysis beyond plane waves.
• This extended theory is applicable to diverse 2D objects in arbitrary positions within a beam.
• Findings are relevant for multiple scattering phenomena, radiation force, and torque calculations in various scientific fields.