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Current-induced terahertz oscillations in plasmonic crystal
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25.Equation (9) becomes invalid in vicinity of points πN/Tb where γ is small and the conditions are not fulfilled. One can show that near these points γ is proportional to |w – πN/Tb| while Eq. (9) predicts γ ∝ (w – πN/Tb)2.
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27.At the first glance, a more simple realization of the device is possible. One can deplete the channel in regions a in such a way that u = Va = sa. In this case, the drift velocities in the sections b will be different and correspond to Va < sa in the sections with odd numbers (counted from the source) and Va > sa in the even sections. One can show, however, that the condition u < u* needed for instability is not satisfied for such a device.
28.Strictly speaking, the wave vector of a plasma wave (proportional to Ω/(sc – Vc)) diverges at the points, corresponding to Vc = sc = u. However, this singularity is cured by accounting for diffusion or finite viscosity, neglected in our theory. Here, for simplicity, we assume that the diffusion length (or analogous length related to finite viscosity) is larger than Lc. This assumption (together with assumption ) guarantees that regions c do not affect the BC between a and b.
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