Scattering and Gradient Forces from the Electromagnetic Stress Tensor Acting on a Dielectric Sphere

Area of Science:

• Classical electromagnetism
• Dielectric particle dynamics
• Optical forces

Background:

• The Clausius-Mossotti factor is often used in optical force calculations.
• Previous derivations relied on ad hoc physical models.
• A rigorous derivation from fundamental principles is lacking.

Purpose of the Study:

• To derive scattering and gradient forces on spherical particles.
• To rigorously incorporate the Clausius-Mossotti factor.
• To validate the derivation against established literature.

Main Methods:

• Utilizing the Maxwell stress tensor for force calculation.
• Applying the Mie solution for dielectric particle response.
• Deriving optical forces from first principles of electromagnetism.

Main Results:

• The Clausius-Mossotti factor arises naturally from the rigorous derivation.
• Expressions for scattering and gradient forces are derived.
• The derived limits match existing literature.

Conclusions:

• The Clausius-Mossotti factor can be rigorously derived from classical electromagnetism.
• This approach avoids reliance on ad hoc physical models.
• The findings provide a fundamental basis for optical force calculations.