Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave

Area of Science:

• Optics and Photonics
• Computational Electromagnetics

Background:

• Electromagnetic plane waves in absorbing media are typically inhomogeneous.
• Existing solutions for scattering by spherical particles lack explicit scattering component expressions and rely on complex hypergeometric functions.

Purpose of the Study:

• To develop a simplified analytical solution for the scattering of inhomogeneous plane waves by spherical particles.
• To derive new explicit expressions for the angular dependency of far-field scattering components (phase function).

Main Methods:

• Developed a new solution utilizing associated Legendre functions with argument zero.
• Derived recurrence formulas for practical evaluation of the scattering components.
• Performed numerical examples to validate the new expressions against existing methods in limiting cases.

Main Results:

• Obtained new explicit expressions for the scattering phase function of inhomogeneous plane waves.
• Demonstrated that the difference in scattering phase function due to inhomogeneity is significant for oblique incidence.
• The new method is computationally simpler than existing approaches.

Conclusions:

• The developed theory offers a more accessible and explicit method for calculating light scattering in absorbing media.
• The findings are relevant for enhancing the performance of dye-based random lasing and solar cells.
• The simplified approach facilitates better prediction of scattering behavior in practical applications.