The time-domain Cartesian multipole expansion of electromagnetic fields

Area of Science:

• Electromagnetism and Computational Physics

Background:

• Analytical solutions for Maxwell's equations are limited for practical transient phenomena.
• Numerical methods are computationally expensive and memory-intensive.
• Existing semi-analytical methods like multipole expansion can be complex for real-world applications.

Purpose of the Study:

• To develop a novel semi-analytical method for time-domain solutions of Maxwell's equations.
• To address the limitations of analytical and numerical approaches for complex current distributions.
• To enable efficient analysis of transient electromagnetic phenomena.

Main Methods:

• Development of the time-domain Cartesian multipole expansion.
• Introduction of the concept of current "pixels" for arbitrary planar geometries.
• Application to imaging intricate current distributions.

Main Results:

• Derivation of semi-analytical solutions for arbitrary localized time-varying current distributions.
• Successful application in imaging complex current distributions.
• Validation against analytical and finite-difference time-domain (FDTD) methods.

Conclusions:

• The time-domain Cartesian multipole expansion offers an efficient semi-analytical alternative to numerical simulations.
• The method simplifies the study of transient electromagnetic fields for complex geometries.
• This approach enhances the feasibility of analyzing broadband electromagnetic phenomena.