Optical Tuning of Coupled Nanomechanical Resonators


Hajime Okamoto, Koji Onomitsu, and Hiroshi Yamaguchi
Physical Science Laboratory

 Coupled nanomechanical resonators have recently become the focus of research because they allow the study of interesting physical phenomena, such as synchronization and mode localization[1,2]. They also enable new applications in sensors using the dynamics of the coupled system[3]. The coupling efficiency is determined by the eigenfrequency difference in the resonators. Therefore, frequency tuning is important and desired to control the vibrational coupling. Here, we demonstrate the controlled coupling in nanomechanical resonators by using photothermal stress. By this method, perfect vibrational coupling was realized[4].
 The nanomechanical system has two doubly-clamped beams of 40-µm length, 10-µm width, and 0.8-µm thickness (Fig. 1). The beams consist of top Au gates, AlGaAs/GaAs superlattice, n-GaAs, and i-GaAs layers. The two beams are mechanically coupled through an etching overhang. Each beam can be actuated separately by the piezoelectric effect by applying an a.c. voltage between the gate and the n-GaAs layer. The frequency response of the mechanical vibration was detected using a He:Ne laser via optical interferometry (Fig. 1). The eigenfrequency of the beams was tuned by adjusting the laser power. These measurements were performed in a vacuum at room temperature.
 Figure 2 shows the laser power dependence of the resonance spectra of Beam 2 measured whilst actuating Beam 1. Two coupled vibrational modes are found around the natural frequency: the nearly symmetric and anti-symmetric vibration for the lower- and higher-frequency, respectively. The coupling efficiency between the beams can be controlled by adjusting the laser power (P). Photo-induced thermal stress modifies the eigenfrequency of the beam with changing its spring constant. Increasing P reduces the eigenfrequency difference between the two beams, therefore enhancing the coupling efficiency. The frequency difference between the two coupled modes decreases with increasing P and is minimized at P = 64 µW (Fig. 2). At this laser power, the coupling is maximized and purely symmetric and anti-symmetric vibration is realized. For P > 64 µW, the frequency difference again increases with P increases, i.e., the coupled beams are optically detuned. The realization of the perfectly tunable coupled nanomechanical resonators will offer the opportunity for their high-sensitive sensing applications and for the study of the dynamics of coupled systems.

[1] S. Shim et al., Science 316 (2007) 95.
[2] C. Pierre, J. Sound Vib. 139 (1990) 111.
[3] M. Spletzer et al., Appl. Phys. Lett. 88 (2006) 254102.
[4] H. Okamoto et al., Appl. Phys.Express 2 (2009) 062202.

Fig. 1. Microscope image of the coupled resonators
and an illustration of the measurement setup.
Fig. 2. Laser power dependence of the resonance
spectra of the coupled modes.

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