Computationally fast EM field propagation through axi-symmetric media using cylindrical harmonic decomposition

Area of Science:

• Computational electromagnetics
• Wave propagation theory
• Optics and photonics

Background:

• Efficiently simulating electromagnetic (EM) fields in complex media is crucial for designing advanced optical devices.
• Axially symmetric media present unique challenges for computational modeling due to their rotational symmetry.

Purpose of the Study:

• To develop a computationally fast and systematic procedure for propagating arbitrary vector EM fields through axially symmetric media.
• To introduce a reusable transfer matrix approach for reduced computational load in EM simulations.

Main Methods:

• Cylindrical harmonic decomposition of input excitation fields using a generalized discrete Fourier-Hankel transform.
• Pre-computation of a transfer matrix representing the medium in a discrete, cylindrical-harmonic basis via 2.5D finite element simulations.
• Application of the transfer matrix for efficient field propagation, particularly for transverse sizes exceeding 30 wavelengths.

Main Results:

• The proposed method enables computationally fast propagation of vector EM fields in axially symmetric media.
• The transfer matrix approach significantly reduces computational cost for large transverse dimensions.
• Numerical validation was performed on diverse media, including gradient-index lenses, invisibility cloaks, and perfect lenses.

Conclusions:

• The cylindrical harmonic field propagator offers an efficient and robust solution for EM field propagation in axially symmetric systems.
• The reusable transfer matrix method is a significant advancement for computational electromagnetics, enabling faster simulations of complex optical phenomena.