On the pole expansion of electromagnetic fields

Area of Science:

• Electromagnetism and Optics
• Computational Physics

Background:

• Quasi-normal modes (resonant states) are used to calculate electromagnetic field properties.
• Existing pole expansion formulations for these modes are not unique and can have dispersive coefficients.

Purpose of the Study:

• To explore alternative formulations for pole expansion of electromagnetic fields.
• To introduce a method using the Mittag-Leffler theorem for constant weight factors.
• To compare the performance and applicability of different formulations.

Main Methods:

• Application of the Mittag-Leffler theorem to electromagnetic field pole expansion.
• Development of formulations with constant weight factors.
• Comparison using analytical and numerical examples.

Main Results:

• All tested formulations show comparable accuracy.
• Formulations with dispersive coefficients offer slightly better global convergence.
• Alternative expansions can provide superior local accuracy and faster computation.

Conclusions:

• The choice of formulation impacts the efficiency of describing electromagnetic response.
• This work provides guidance for selecting appropriate resonant state expansions.
• Understanding these formulations is key for efficient electromagnetic simulations.