[(a)–(c)] Vortex configurations in a hexagonal Josephson junction with each side equal to 20 Josephson penetration lengths . The color scale denotes the magnetic field density given by the gradient of the superconducting phase difference . [(d)–(f)] Propagation of the Josephson plasma waves with frequency . The plasma frequency of the Josephson transmission lines is , where is that of the hexagonal junction. The width of the attached Josephson transmission lines is in normalized units. The damping is absent. [(d)–(f)] correspond to the vortex configurations (a)–(c). The color scale depicts the relative amplitude of the plasma waves as a ratio of the transverse electric field to its maximal value for each simulation. (d) and (e) show mode transfers from planelike waves to alternating wave mode in the upper branches. Numerical solutions showing the spatiotemporal evolution of the waves are available online (Ref. 17).
Dependence of the transmission coefficient on the plasma wave frequency . The peaks and dips are related to the matching of the plasma wavelength to the length of the vortex lines. The plasma frequency of the Josephson transmission lines is , where is that of the hexagonal junction.
Dependence of the transmission coefficient on the applied magnetic field for two fixed frequencies, and . The abrupt steps are associated with the penetration of a new vortex when a magnetic field is increased. The associated change in energy of the arrangement of vortices in the hexagonal Josephson contact is shown in the inset.
Schematic of a three-terminal electromagnetic wave controller based on a hexagonal-shaped Josephson junction. The three terminals or ports, , , and , are used to input/output electromagnetic waves by means of the attached transmission lines , , and (shown in gray). The currents , , and flowing along the top and bottom parallel electrodes (shown in blue), connected to the edges of the hexagonal junction, control the value of the magnetic field.
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