Journal: Microsystems & Nanoengineering
Article Title: Mechano-mechanical parametric coupling in MEMS between GHz and kHz frequency regimes at room temperature
doi: 10.1038/s41378-025-01111-1
Figure Lengend Snippet: a Schematic of a conventional cavity optomechanical system. The system consists of an optical cavity mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document} a ^ and a mechanical oscillator mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{b}$$\end{document} b ^ . b Schematic of the proposed system, where the SAW cavity mode replaces the optical cavity mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document} a ^ , and the silicon micro-cantilever structure is the oscillator mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{b}$$\end{document} b ^ . c Schematic of interaction between the SAW cavity mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document} a ^ , with frequency ω c , and the cantilever mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{b}$$\end{document} b ^ , with frequency Ω m . The interaction is characterized by the coupling strength g 0 , the mechanical damping rate Γ, and the cavity decay rate κ . d Conceptual frequency spectrum illustrating the SAW cavity mode at ω c , externally driven at the pump frequency (black arrow), and the resulting sidebands at ω c ± Ω m (red and blue lines) due to coupling with the mechanical mode Ω m . Red arrows represent energy emitted by the SAW cavity toward the oscillator, and blue arrows represent energy absorbed by the cavity from the oscillator. e Schematic of the experimental setup for measuring mechano-mechanical coupling. The laser Doppler vibrometer (LDV) system, including the MSA 500 and LDV controller, measures the mechanical displacement of the cantilever. A PZT actuator excites the cantilever, controlled through a junction box. The RF signal for exciting the SAW cavity mode is generated by a signal generator and passes through a coupler and tuner for impedance matching. The response of the SAW cavity is monitored using a Vector Network Analyzer (VNA), which can be switched to a Spectrum Analyzer (SA) mode to observe the sidebands in the frequency spectrum. A PC is used for data acquisition and control
Article Snippet: For the characterization of the cantilever’s mechanical modes, we use an LDV system (MSA 500, Polytec) to scan the cantilever surface and measure its displacement across a range of frequencies.
Techniques: Generated, Plasmid Preparation, Control
![a Schematic of a conventional cavity optomechanical system. The system consists of an optical cavity mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document} a ^ and a mechanical oscillator mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{b}$$\end{document} b ^ . b Schematic of the proposed system, where the SAW cavity mode replaces the optical cavity mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document} a ^ , and the silicon micro-cantilever structure is the oscillator mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{b}$$\end{document} b ^ . c Schematic of interaction between the SAW cavity mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{a}$$\end{document} a ^ , with frequency ω c , and the cantilever mode \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{b}$$\end{document} b ^ , with frequency Ω m . The interaction is characterized by the coupling strength g 0 , the mechanical damping rate Γ, and the cavity decay rate κ . d Conceptual frequency spectrum illustrating the SAW cavity mode at ω c , externally driven at the pump frequency (black arrow), and the resulting sidebands at ω c ± Ω m (red and blue lines) due to coupling with the mechanical mode Ω m . Red arrows represent energy emitted by the SAW cavity toward the oscillator, and blue arrows represent energy absorbed by the cavity from the oscillator. e Schematic of the experimental setup for measuring mechano-mechanical coupling. The laser Doppler vibrometer <t>(LDV)</t> system, including <t>the</t> <t>MSA</t> 500 and LDV controller, measures the mechanical displacement of the cantilever. A PZT actuator excites the cantilever, controlled through a junction box. The RF signal for exciting the SAW cavity mode is generated by a signal generator and passes through a coupler and tuner for impedance matching. The response of the SAW cavity is monitored using a Vector Network Analyzer (VNA), which can be switched to a Spectrum Analyzer (SA) mode to observe the sidebands in the frequency spectrum. A PC is used for data acquisition and control](https://pub-med-central-images-cdn.bioz.com/pub_med_central_ids_ending_with_3657/pmc12783657/pmc12783657__41378_2025_1111_Fig1_HTML.jpg)
