Abstract
Visualizing eigenmodes is crucial in understanding the behavior of state-of-the-art micromechanical devices. We demonstrate a method to optically map multiple modes of mechanical structures simultaneously. The fast and robust method, based on a modified phase-lock loop, is demonstrated on a silicon nitride membrane and shown to outperform three alternative approaches. Line traces and two-dimensional maps of different modes are acquired. The high quality data enables us to determine the weights of individual contributions in superpositions of degenerate modes.
Highlights
In recent years, there have been many applications for integrated opto- and electromechanics extending from, e.g., mobile communication [1] and highly sensitive sensors [2,3,4,5,6,7,8]to position detection close to the quantum limit [9,10,11]
The silicon nitride (SiN) membranes are made on chips with 330 nm highstress Si3N4 [19,20,21]
The out-of-plane modes of a square membrane with side lengths a under uniform tension can be calculated analytically [23]
Summary
There have been many applications for integrated opto- and electromechanics extending from, e.g., mobile communication [1] and highly sensitive sensors [2,3,4,5,6,7,8]to position detection close to the quantum limit [9,10,11]. In the development of such devices, an efficient method for mode characterization is instrumental and, a number of techniques including optical interferometry [12,13,14], heterodyne detection [15,16], dark field imaging [8,12], and force microscopy [1,10,17,18] have been developed to visualize mechanical modes Most of these have one or more drawbacks, such as poor sensitivity, lacking phase information, low spatial resolution, or long measurement times. The eigenmodes of the membrane can be unambiguously identified and their mode composition can be determined quantitatively and insights in clamping losses are provided
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