Generalization of the optical theorem for light scattering from a particle at a planar interface

Area of Science:

• Physics
• Optics
• Electromagnetism

Background:

• The optical theorem relates extinction cross section to forward scattering amplitude.
• Existing generalizations consider particles near interfaces.
• Total internal reflection at interfaces presents unique scattering challenges.

Purpose of the Study:

• To derive a generalized optical theorem for particles embedded within an interface.
• To analyze scattering under total internal reflection conditions.
• To investigate the behavior of far-field scattered light.

Main Methods:

• Derivation of the generalized optical theorem using Maxwell's equations.
• Analysis of scattering amplitudes for particles at interfaces.
• Mathematical formulation for total internal reflection scenarios.

Main Results:

• A novel derivation of the generalized optical theorem for particles embedded in an interface.
• Demonstration that the far-field scattered field is zero parallel to the interface.
• Validation of scattering computations for interface-embedded particles.

Conclusions:

• The derived theorem extends optical theorem applications to interface-embedded particles.
• The zero-field result provides a new physical insight and verification tool.
• Findings are relevant for experiments involving colloidal particles at fluid interfaces.