Hopf solutions of Maxwell equations: analysis and simulation by FDTD

• Published in: 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA) p. 1001
• Main Authors: Valverde, A. M., Angulo, Luis D., Cabello, Miguel R., Bretones, Amelia R., Gomez Martin, Rafael, Garcia, Salvador G.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-09-2019
• Subjects: Analytical models; Antenna arrays; Electromagnetic fields; Finite difference methods; Mathematical model; Time-domain analysis; Topology
• DOI: 10.1109/ICEAA.2019.8879048

This contribution studies a particular solution of Maxwell wave equations known as Hopfions by making use of the well-known Finite Difference Time Domain (FDTD) method. Hopfions are a family of solutions, in which the field lines are closed, forming different knot topologies that are preserved during its time evolution. These solutions have been studied in different analytical ways (e.g. [1]), but which to the best of our knowledge they have never been simulated before. Their simulation can be of interest because they are demonstrated to exist, not from purely analytical arguments, but from the direct numerical resolutions of the Maxwell's curl equations. This numerical solution would ease the study of how these fields could interact with other structures made of different materials, with other Hopfions, and on how they could be possibly be generated with antenna arrays.