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(Left) A thin cylindrical magnonic waveguide with a curved section is shown together with the curvilinear coordinate system used in the calculations. (Right) A helical waveguide connected to two straight waveguides is shown. (Center) The coordinate dependence of the “geometrical” field term is schematically shown for the waveguides shown on the left and on the right. l is the length-coordinate along the waveguide.
The grayscale of the map shows the transmission coefficient of spinwaves through a barrier formed due to the curvature of the nanowire magnonic waveguide, as defined by Eq. (6). The lines of spectra are plotted using Eqs. (9)–(11) for the waveguide structures shown in the top part of the figure, i.e., for barriers formed by a U-turn, by a helix, and by a straight section connecting two helices, respectively. The calculations using Eq. (9) are performed assuming of 2π. The inset magnifies the region of the main map marked by the arrow.
The gray and white colors on the map correspond to the band gaps and allowed magnonic bands in the spectrum of spin waves (Eq. (7)) propagating in a periodically curved nanowire magnonic waveguide, e.g., such as those shown in the insets. The lines of spectra are plotted using Eqs. (9)–(11) for the different ratios between the radius of curvature and the exchange length and for the different values of a. The calculations using Eq. (9) are performed assuming of 2π.
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