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Band structure of PC consisting of steel cylinders in water, arranged by a square lattice. The inset represents relevant first Brillouin zone, with the high symmetric directions being marked. The frequency is normalized by , with being the lattice constant and being the sound velocity in water.
(a) Schematic representation of 16-layer PC structure, with the crystal length along the direction being . (b) Unit cell of square lattice, with the positions of high symmetry being marked.
(a) Far-field normalized energy-flux density vs angle, with the line acoustic source embedded in the center [at the position of point in the unit cell, see Fig. 2(b) ] of 2D PC consisting of cylinders. (b) The same as (a), but the source is moved downwards by [at the position of point in the unit cell, see Fig. 2(b) ]. (c) The same as (b), but with a four-layer substrate added. The optimal operating frequencies for the three designs are 0.6152, 0.6158, and 0.6155, respectively.
Near-field amplitude distributions correspond to Figs. 3(a)–3(c) , with darkness and lightness representing strong and weak amplitudes of the displacement fields, respectively.
Radiation character parameters of DAS, including the number of radiation branches , optimal operating frequencies , total radiation enhancement factors , half-power angular widths around the direction, and relevant radiation efficiencies for those cases in Figs. 3(a)–3(c) , respectively.
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