Phononic integrated circuitry and spin-orbit interaction of phonons

Abstract

High-index-contrast optical waveguides are crucial for the development of photonic integrated circuits with complex functionalities. Despite many similarities between optical and acoustic waves, high-acoustic-index-contrast phononic waveguides remain elusive, preventing intricate manipulation of phonons on par with its photonic counterpart. Here, we present the realization of such phononic waveguides and the formation of phononic integrated circuits through exploiting a gallium-nitride-on-sapphire platform, which provides strong confinement and control of phonons. By demonstrating key building blocks analogous to photonic circuit components, we establish the functionality and scalability of the phononic circuits. Moreover, the unidirectional excitation of propagating phononic modes allows the exploration of unconventional spin-orbit interaction of phonons in this circuit platform, which opens up the possibility of novel applications such as acoustic gyroscopic and non-reciprocal devices. Such phononic integrated circuits could provide an invaluable resource for both classical and quantum information processing.

Fig. 1

Phononic integrated circuit. a A notional schematic of a phononic circuit. Input radio-frequency (RF) photons are first converted into phonons by an interdigital transducer (IDT) through the piezoelectric effect of the top gallium nitride (GaN) epi-layer. The phonons are confined, routed through phononic circuit and received by output IDTs. b A schematic cross-section of GaN-on-sapphire strip waveguide with thickness h and width w. c Simulated cross-sectional acoustic energy distribution of a Rayleigh-like mode shown in logarithmic scale, indicating confinement of acoustic wave in the waveguide. The white dashed line marks where the energy density drops to 10⁻³, compared with the highest energy density

Fig. 2

Characterization of phononic waveguide and identification of a traveling Rayleigh-like mode. a The measurement scheme. c An scanning electron microscope (SEM) image of a phononic waveguide. b, d–f, The out-of-plane (z-direction) displacement of a traveling Rayleigh-like mode. The data are measured by sending RF signal at 102 MHz into the IDT and scanning the vibrometer focal point in an area of 400 μm × 400 μm as illustrated in a. The reconstructed image of instant displacement is shown in d. The amplitude or phase at cross-sections of the two-dimensional scan are plotted in b, e, and f and taken at correspondingly colored lines in d. The magenta line in b represents the simulated displacement amplitude cross the waveguide, and the magenta lines in e and f are fitted to traveling acoustic wave with weak reflection (10% reflection)

Fig. 3

Phononic ring resonator and mode identification. a An SEM image of arrays of phononic ring resonators. b A typical spectrum of the phononic ring resonator measured by the vibrometer with the focal point adjusted to the ring. Two sets of modes are observed, corresponding to Rayleigh-like and Love-like mode, marked with magenta and blue arrows, respectively. c The vibrometer image of a Rayleigh-like mode in a waveguide coupled ring resonator (only the displacement on the ring is presented). d, e The vibrometer images of the Rayleigh-like and Love-like modes. f, g Simulated z-direction displacement profile of Rayleigh-like and Love-like modes, in excellent agreement with the experimental results. h, i Simulated 3-d mode profiles of Rayleigh-like and Love-like mode, respectively

Fig. 4

Phononic spin–orbit interaction in a ring resonator. a Device under test. The pair of IDTs function as the input and output of the circuit and address the clockwise (CW) and counter-clockwise (CCW) love-like mode simultaneously. Focused IDTs and shield structure are used to improve signal to noise ratio. b Orbital angular momentum (OAM) carried by Love-like mode. c Left: Zoomed in mode profile of Love-like mode, with displacements indicated by the black arrows. We observe circular trajectory of displacement. Right: Spin-momentum locking—CW and CCW propagating phonons possess spins of opposite direction. The direction of spin of point A (the purple dot in the left panel) is indicated by either cross (right-hand) or dot (left-hand). Dash line indicates the trajectory of displacement (solid dot). d Phase response difference between CW and CCW modes, when the device is subject to in-plane and out-of-plane rotation. The comparison between Δϕ measured with rotation of different direction is a clear signature of SOI. e Applying an out-of-plane CCW rotation to the system, CW and CCW Modes have resonant frequency shift towards the opposite direction, due to the opposite chiralities that they possess. f Phase response measured at various peak rotation rate