We report direct visualization of gigahertz-frequency Lamb waves propagation in aluminum
nitride phononic circuits by transmission-mode microwave impedance microscopy (TMIM).
Consistent with the finite-element modeling, the acoustic eigenmodes in both a horn-shaped
coupler and a sub-wavelength waveguide are revealed in the TMIM images. Using fast Fourier
transform filtering, we quantitatively analyze the acoustic loss of individual Lamb modes along
the waveguide and the power coupling coefficient between the waveguide and the parabolic
couplers. Our work provides insightful information on the propagation, mode conversion, and
attenuation of acoustic waves in piezoelectric nanostructures, which is highly desirable for
designing and optimizing phononic devices for microwave signal processing and quantum
information transduction.The TMIM work was supported by NSF Division of Materials Research Award DMR-2004536
and Welch Foundation Grant F-1814. The data analysis was partially supported by the NSF
through the Center for Dynamics and Control of Materials, an NSF Materials Research Science
and Engineering Center (MRSEC) under Cooperative Agreement DMR-1720595. The phononic
waveguide work was supported by NSF Award EFMA-1741656 and EFMA-1641109. Part of
this work was conducted at the Washington Nanofabrication Facility / Molecular Analysis
Facility, a National Nanotechnology Coordinated Infrastructure (NNCI) site at the University of
Washington with partial support from the National Science Foundation via awards NNCI-
1542101 and NNCI-2025489.Center for Dynamics and Control of Material
