volume | PIER Journals

Abstract

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 k_xa and k_ya in the plane of the TL. The surfaces ω(k_xa, k_ya) display exotic behavior like forbidden ω bands, forbidden k bands, both, or neither. Certain critical combinations of the modulation strength m_c and the modulation frequency Ω mark transitions from ω stopbands 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(k_xa, k_ya) 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 among geometry, critical points, and phase transitions.

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Dr. Jose Salazar-Arrieta

Dr. Peter Halevi