Fig. 1: Samples and dispersion relations for the valley phononic plates.
From: Far-field phonon coupling in valley metamaterial circuits
a Experimental samples for the (1) FFC-waveguide, (2) NFC-waveguide, and (3) dual-cavity waveguide circuits. The crystallographic directions [100] and [001] of silicon are aligned with the x- and z-axes, respectively. b (top) PnC plate, (middle) unit cell, and (bottom) Brillouin Zone taken from Sample 1. Geometrical parameters include lattice constant a, pillar side length sl, pillar height hp, silicon wafer thickness et, and substrate thickness es = et - hp. Topological phases are controlled by tuning the rotation angles θ of the triangular pillars. c, d Band structures of the unit cell for θ = 0° (top panels) and θ = ±20° (bottom panels) are shown for Sample 1 in (c) and Samples 2 and 3 in (d). The color scale indicates the ratio of |uz| to the total displacement |ut| in the unit cell, defined by \({\eta }_{z}=\int |{u}_{z}|dV/\int |{u}_{t}|dV\). Insets show unit cell schemes and a zoom-in of the dispersion for θ = 0°.
