2021/05/15 by José de Jesús Salazar-Arrieta, Salazar-Arrieta, José de Jesús, P. Halevi +1
Physics and Astronomy · #Applied Physics (physics.app-ph) #FOS: Physical sciences #Photorefractive and Nonlinear Optics #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2105.07105
openalex publication_date 2021/05/15 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
We studied electromagnetic wave propagation in a system that is periodic in both space and time, namely a discrete 2D transmission line (TL) with capacitors modulated in tandem externally. Kirchhoff's laws lead to an eigenvalue equation whose solutions yield a band structure (BS) for the circular frequency ω as function of the phase advances kxa and kya in the plane of the TL. The surfaces ω(kxa, kya) display exotic behavior like forbidden ω bands, forbidden k bands, both, or neither. Certain critical combinations of the modulation strength mc and the modulation frequency Ω mark transitions from ω stop bands to forbidden k bands, corresponding to phase transitions from no propagation to propagation of waves. Such behavior is found invariably at the high symmetry X and M points of the spatial Brillouin zone (BZ) and at the boundary ω=(1/2)Ω of the temporal BZ. At such boundaries the ω(kxa, kya) surfaces in neighboring BZs assume conical forms that just touch, resembling a South American toy "diábolo"; the point of contact is thus called a "diabolic point". Our investigation reveals interesting interplay between geometry, critical points, and phase transitions.