Monolithic Phononic Crystals with a Surface Acoustic Band Gap from Surface Phonon-Polariton Coupling

We theoretically and experimentally demonstrate the existence of complete surface acoustic wave band gaps in surface phonon-polariton phononic crystals, in a completely monolithic structure formed from a two-dimensional honeycomb array of hexagonal shape domain-inverted inclusions in single crystal piezoelectric $Z$-cut lithium niobate. The band gaps appear at a frequency of about twice the Bragg band gap at the center of the Brillouin zone, formed through phonon-polariton coupling. The structure is mechanically, electromagnetically, and topographically homogeneous, without any physical alteration of the surface, offering an ideal platform for many acoustic wave applications for photonics, phononics, and microfluidics.

Figure 1

Schematic of the proposed surface phonon-polariton PC formed from domain-inverted hexagonal inclusions arranged in a honeycomb lattice. (a) The top view illustrates ${\mathit{\alpha }}_1=(a,0)$ and ${\mathit{\alpha }}_2=(a/2,\sqrt{3}a/2)$ as the principal lattice vectors, with lattice constant $a=|{\alpha }_1|=|{\alpha }_2|$ and $d$ as the side length of the hexagon. The 2D reciprocal space is presented for (b) the honeycomb lattice and (c) the overall PC structure.

Figure 2

(a) Slowness curves of $Z$-cut lithium niobate and (b) the corresponding first irreducible Brillouin zone of the honeycomb lattice, with the triangle $J\mathrm{\Gamma }X$ defined by the symmetry of the slowness curve. (c) The SAW band structure calculation of a PC with lattice $d/a=0.2$; the shaded region indicates the SAW band gaps where the SAW propagation parallel to the $x\text{−}y$ plane is prohibited. The inset shows the SAW band structure calculated near the $\mathrm{\Gamma }$ point at around $fa=4000\mathrm{m}/\mathrm{s}$. (d)–(g) The displacement profiles of the SAW modes calculated at $A$, $B$, $C$, and $D$ in Fig. 2.

Figure 3

(a) SAW delay line structure used to experimentally investigate the SAW band structure of the surface phonon-polariton PC. (b) The honeycomb lattice structure is apparent from an optical micrograph of the back side of the substrate after HF etching, with a scanning electron microscope image inset showing the hexagonal domain-inverted inclusion. (c),(d) The measured and (e),(f) theoretical transmission for surface phonons and (g),(h) for electromagnetic waves for the $\mathrm{\Gamma }J$ and $\mathrm{\Gamma }X$ orientations, respectively. The shaded region in (e),(f) denotes the expected band gap according to the band structure in Fig. 2. The insets in (c),(d) show the top view of the calculated magnitude of the surface phonon displacement and the electric field at frequencies below, within, and above the band gap.

Figure 4

Normalized calculated SAW displacement amplitude passing through the PC along the $\mathrm{\Gamma }J$ direction at 125 MHz in (a) the $x\text{−}y$ plane on the top surface and (b) the $x\text{−}z$ plane, with (c) reference to the full 3D structure. (d) The calculated reflection and the transmission on and 8 wavelengths below the surface, all normalized to the input power.