Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves

Area of Science:

• Computational Electromagnetics
• Mathematical Physics

Background:

• Solving Maxwell's equations is crucial for understanding electromagnetic phenomena.
• Traditional methods can be computationally intensive for complex dielectric structures.

Purpose of the Study:

• To develop a compact and accurate numerical method for solving Maxwell's vector wave equations.
• To enable efficient computation of electromagnetic modes in spherical dielectric configurations.

Main Methods:

• Series expansion of field components and dielectric profiles using spherical Bessel functions, Legendre polynomials, and complex exponentials (BLF).
• Formulation of a compact eigenvalue matrix for Maxwell's equations.
• Solving the matrix to obtain frequencies and field profiles.

Main Results:

• The BLF basis functions lead to a compact eigenvalue matrix formulation.
• The method accurately solves for steady-state electromagnetic modes.
• Numerical results are validated against complementary techniques.

Conclusions:

• The developed BLF matrix method offers an accurate and efficient approach for analyzing electromagnetic modes in spherical dielectric systems.
• This technique is suitable for desktop PC computations, enhancing accessibility.