Piezoelectric Transduction of a Wavelength-Scale Mechanical Waveguide

We present a piezoelectric transducer in thin-film lithium niobate that converts a 1.7-GHz microwave signal to a mechanical wave in a single mode of a 1-$\mu \mathrm{m}$-wide waveguide. We measure a $-12$-dB conversion efficiency that is limited by material loss. The design method we employ is widely applicable to transduction in wavelength-scale structures in emerging phononic circuits such as those needed for efficient piezo-optomechanical converters and spin-phonon transducers.

Figure 1

Suspended transducers patterned in $300$-nm-thick X-cut LN on silicon, designed to excite the SH0 mode of a 1-$\mu \mathrm{m}$-wide waveguide at $1.7\mathrm{GHz}$. They comprise an aluminum IDT 3.4 $\mu \mathrm{m}$ wide and $100\mathrm{nm}$ thick, and a 10-$\mu \mathrm{m}$-long linear horn. In the false-color SEM image (c), LN is blue, aluminum is yellow, and the ${\mathrm{Xe}\mathrm{F}}_2$ release etch front is burgundy. FEM analysis (b) shows that the horn scatters the SH0 mode of the IDT efficiently into the SH0 mode of the 1-$\mu \mathrm{m}$-wide waveguide. The bands and Bloch functions of the IDT and waveguide which constitute the asymptotic state of the horn are plotted on the left (a) and right (d), respectively. Waves propagate along $y$, and the colors indicate the displacement along $z$.

Figure 2

(a) Adiabatic elastic horns do not generate wide mechanical beams. The SH0 and SH1 modes ($u_z$ plotted at left) transition to degenerate antisymmetric and symmetric edge supermodes, respectively (right). Below $5\mu \mathrm{m}$, the SH waves (red) are well resolved. The Lamb waves are plotted in light blue. (b) A linear horn scatters the SH0 mode of the 3.4-$\mu \mathrm{m}$-wide IDT efficiently into SH0 of the 1-$\mu \mathrm{m}$-wide output waveguide. (c) By decomposing the power in the waveguide, we find that transduction of spurious modes, i.e., the isolation, is better than $-10\mathrm{dB}$ away from the nodes in the conductance over a $200$-MHz bandwidth. The largest spurious component is the SH1 mode, plotted in red.

Figure 3

By computing the linear response $Y\left(\omega \right)$ and decomposition $\{a_m\}$, we study the $N$-dependence of the transmission $t_{b\mu }$ from a $50\mathrm{\Omega }$ transmission line to the SH0 mode. (a) Microwave reflections $S_{11}$ decrease with $N$. Lower-loss devices are matched with smaller $N$. (b) As the reflections drop, the fraction of the total power lost increases, diminishing transmission into the SH0 mode. (c) These competing effects lead to an optimal $N$ for maximizing ${\left|t_{b\mu }\right|}^2$, which increases with $Q_i$. Numerical results (points) are smoothed with a moving-window average (curve) for clarity.

Figure 4

(a) $\left|S_{11}\right|$ of an $N=40$ transducer; (b) $\left|S_{11}\right|$ restricted to the SH0 and SH2 responses. (c) Conductance $G$ and susceptance $\chi$ of the SH0 mode, overlaid on FEM results [labeled N$.G(\omega )$ and N$.\chi (\omega )$]. (d) $\left|S_{21}\right|$: for an ideal delay line with no insertion loss, this would equal the two-port mismatch $1-|S_{11}{|}^2/2-|S_{22}{|}^2/2$, shown in red (see Appendix pp7). (e) For $L=800\mu \mathrm{m}$, the heights of the echoes in the impulse response are fitted (inset) to extract the round-trip loss. We filter the echoes (intervals shaded blue, red, and green) to compute the single-, triple-, and quintuple-transit $S_{21}$, plotted in corresponding colors (inset), used to extract $|t_{b\mu }|$ as described in Sec. 5.

Figure 5

Butterworth–Van Dyke circuit modified to include mechanical loss.

Figure 6

(a) SH mode of a unit cell of the transducer. (b) Response near dc fitted for the static capacitance $C_0$. (c) The pole in the susceptance centered at the series resonance frequency $f_s$ is fitted for the net conductance and used with $C_0$ to compute $k_{\mathrm{eff}}^2$. (d) In addition to the pole in the admittance, there is a pole in the reactance centered at the parallel resonance frequency $f_p$.

Figure 7

Modes of a LN waveguide at $1.7\mathrm{GHz}$. The colors in these plots visualize the dominant displacement field. Light blue arrows show the direction of displacement.

Figure 8

(a) Signal-flow graph for a two-port device. (b) Paths for the single-, triple-, and quintuple-transit values (colored blue, red, and green, respectively) corresponding to the $S_{21}$ curves of matching color in (c). (c) $S_{21}$ filtered by path.