Quantitative optical imaging method for surface acoustic waves using optical path modulation

A Rayleigh-type surface acoustic wave (SAW) is used in various fields as classical and quantum information carriers because of its surface localization, high electrical controllability, and low propagation loss. Coupling and hybridization between the SAW and other physical systems such as magnetization, electron charge, and electron spin are the recent focuses in phononics and spintronics. A precise measurement of the surface wave amplitude is often necessary to discuss the coupling strengths. However, there are only a few such measurement techniques and they generally require a rather complex analysis. Here we develop and demonstrate a straightforward measurement technique that can quantitatively characterize the SAW. The technique optically detects the surface waving due to the coherently driven SAW by the optical path modulation. Furthermore, when the measurement system operates in the shot-noise-limited regime, the surface slope and displacement at the optical spot can be deduced from the optical path modulation signal. Our demonstrated technique will be an important tool for SAW-related research.

Figure 1

Experimental setup and device for observing optical path modulation and optical polarization modulation induced by SAW. (a) With polarization beam splitter (PBS) and half-wave plate (HWP), the incident light is made linearly polarized with the polarization plane aligned parallel to the direction of SAW propagation ($z$-direction). The light is focused with an objective lens into a diameter of around $3\mu \mathrm{m}$ on the device surface. The angle of incidence is set to ${45}^{\circ }$. The reflected light is then collimated by another objective lens and analyzed in the two balanced detectors indicated as (i) and (ii) with HWP, PBS, beam splitter (BS), periscope-type mirror pair, and prism mirror. (b) Microscope image of a Fabry-Perot type SAW resonator with a coordinate system. The SAW resonator consists of a 0.5-mm-thick YZ-cut ${\mathrm{LiNbO}}_3$ substrate, Bragg mirrors, and interdigitated transducers (IDTs). Bragg mirrors and IDTs are made by depositing $5\mathrm{nm}$ of Ti and $80\mathrm{nm}$ of Au. Two Bragg mirrors composed of 100 fingers of $400\text{−}\mu \mathrm{m}$-long with a $10\text{−}\mu \mathrm{m}$ line and space are placed at a distance of $360\mu \mathrm{m}$. Two IDTs composed of three fingers of $400\text{−}\mu \mathrm{m}$-long with a $10\text{−}\mu \mathrm{m}$ line and space are placed $105\mu \mathrm{m}$ apart from the center between Bragg mirrors, respectively. A $\mathrm{Ti}(5\mathrm{nm}$)/$\mathrm{Au}(80\mathrm{nm}$) film with a length of $520\mu \mathrm{m}$ and a width of $80\mu \mathrm{m}$ is deposited at the center between Bragg mirrors. The SAW resonator is electrically characterized by rf transmission measurement from Port 1 to Port 2 of a vector network analyzer through two IDTs. (c,d) Schematics of light reflection on the surface of the SAW device when the SAW drive is (c) OFF and (d) ON. (e) Setup for measuring beam displacement in the $X$-direction induced by optical path modulation by the SAW. (f) Relationship between slight beam displacement $L$ and output voltage $V$ from the balanced detector.

Figure 2

Spectra of the fundamental SAW resonator mode acquired by (a) electrical transmission measurement, (b) optical path modulation measurement, and (c) optical polarization modulation measurement. (a) Rf transmission spectra (blue dots) from Port 1 to Port 2 with fitting curves (red line). The peak around $85.63\mathrm{MHz}$ corresponds to the fundamental SAW resonator mode. The resonance frequency is almost the same as that in the following optical modulation spectroscopy. (b) Spectra of the optical path modulation signal (blue dots) and the background signal (green dots) with fitting curves (red line). (c) Spectra of the optical polarization modulation signal (blue dots) and the background signal (yellow dots) with fitting curves (red line). (d) Relative amplitudes for the optical path modulation (blue dots) as a function of the rf power that is used for driving the SAW with fitting curves (red line). (e) Relative amplitudes for the the optical path modulation (blue dots) as a function of the optical power $P_i$ into the balanced detector with fitting curves (red line). (f) Total noise power spectral density (blue triangles) and shot-noise power spectral density (green squares) at the measurement frequency $\omega /2\pi =85.625\mathrm{MHz}$ within the bandwidth $\mathrm{\Delta }f=1\mathrm{kHz}$ as a function of the optical power $P_i$ into the balanced detector with fitting curves (red line). The shot-noise power is obtained by subtracting the separately measured electronic noise (black line) from the total noise. Note that we refer to the noise power as the square of the voltage measured by the lock-in amplifier, which is a quantity proportional to the actual noise power.

Figure 3

Imaging results of the SAW resonator by optical path modulation measurement. Color maps of (a) detected optical power into the balanced detector, (b) amplitude, and (c) phase acquired by the lock-in amplifier at a frequency $\omega /2\pi =85.625\mathrm{MHz}$, and (d) evaluated slope amplitude as a function of the position of optical spot. Together with the color maps, cross-sections of (e) the phase and (f) the slope amplitude at the position $x=250\mu \mathrm{m}$ (indicated by white dash lines in the color maps) are shown. The color of dots in (e) and (f) is consistent with the color in (c) and (d), respectively. (g) The $y$-component of the displacement at maximum displacement estimated using the fitting result (red line) in (f).

Figure 4

Schematic illustration of spatial modes of light split by the prism mirror.

Figure 5

(a) Three-dimensional and cross-sectional optical power profiles. (b) Profile in the $X$-direction [same as lower panel in (a)] and the profile transformed into a rectangle, with the area and top height constant.

Figure 6

Physical model of the system in which signals are transformed via SAW resonator mode.

Figure 7

Total noise power density (blue triangles) and shot-noise power density (green squares) as a function of the optical power $P_i^{\mathrm{pol}}$ at a measurement frequency $\omega /2\pi =85.625\mathrm{MHz}$. The shot-noise power density is obtained by subtracting separately measured electronic noise power density (black line) from the total noise power density. Note that we refer to the noise power as the square of the voltage measured by the lock-in amplifier, which is a quantity proportional to the actual noise power.

Figure 8

Position dependence of the optical path modulation signal induced by the SAW. The blue line represents the signal amplitude measured at a measurement frequency of $85.625\mathrm{MHz}$ and normalized by the reflectance at each optical position. The red line represents the results of exponential fittings of its envelope in the Bragg mirror regions (enclosed by the gray rectangle). The penetration lengths defined by the length at which the signal decreases by $1/e$ are about $1.4\mathrm{mm}$ for each, where $e$ is Euler's number. Note that here the SAW is excited through the IDT of Port 1.