Multimodal visualization of the optomechanical response of silicon cantilevers with ultrafast electron microscopy

The manner in which structure at the mesoscale affects emergent collective dynamics has become the focus of much attention owing, in part, to new insights into how morphology on these spatial scales can be exploited for enhancement and optimization of macroscopic properties. Key to advancements in this area is development of multimodal characterization tools, wherein access to a large parameter space (energy, space, and time) is achieved (ideally) with a single instrument. Here, we describe the study of optomechanical responses of single-crystal Si cantilevers with an ultrafast electron microscope. By conducting structural-dynamics studies in both real and reciprocal space, we are able to visualize MHz vibrational responses from atomic- to micrometer-scale dimensions. With nanosecond selected-area and convergent-beam diffraction, we demonstrate the effects of spatial signal averaging on the isolation and identification of eigenmodes of the cantilever. We find that the reciprocal-space methods reveal eigenmodes mainly below 5 MHz, indicative of the first five vibrational eigenvalues for the cantilever geometry studied here. With nanosecond real-space imaging, however, we are able to visualize local vibrational frequencies exceeding 30 MHz. The heterogeneously-distributed vibrational response is mapped via generation of pixel-by-pixel time-dependent Fourier spectra, which reveal the localized high-frequency modes, whose presence is not detected with parallel-beam diffraction. By correlating the transient response of the three modalities, the oscillation, and dissipation of the optomechanical response can be compared to a linear-elastic model to isolate and identify the spatial three-dimensional dynamics.