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Radiation-pressure-driven micro-mechanical oscillator

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As Q factor is boosted in microscale optical resonant systems there will be a natural tendency for these systems to experience a radiation-pressure induced instability. The instability is manifested as a regenerative oscillation (at radio frequencies) of the mechanical modes of the microcavity. The first observation of this radiation-pressure-induced instability is reported here. Embodied within a microscale, chip-based device reported here this mechanism can benefit both research into macroscale quantum mechanical phenomena [1] and improve the understanding of the mechanism within the context of LIGO [2]. It also suggests that new technologies are possible which will leverage the phenomenon within photonics.

©2005 Optical Society of America

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Figures (5)

Fig. 1.
Fig. 1. Panel A illustrates the “below threshold” behavior where the optical pump wave at frequency ω is not strong enough to induce mechanical oscillations of the micro-toroid. Panel B illustrates the “above threshold” case for the n=3 vibrational mode. Mechanical oscillation at frequency Ω creates optical stokes (ω-Ω) and anti-stoked sidebands (ω+Ω) in the transmitted pump wave. Inset of panel B shows the exaggerated cross-section of the third order mode and variation of the toriod radius as a result of these oscillations.
Fig. 2.
Fig. 2. The measured, spectral content of pump-power (at 1550 nm) transmission as observed on an electrical spectrum analyzer (bandwidth set at 100kHz). Two families of frequencies are observed. Those at lower frequency are driven by oscillation of an n=1 vibrational mode and those at higher frequency by an n=3 mode. Harmonics of the fundamental mechanical frequency are caused by the nonlinear transfer characteristic of the waveguide resonator system (see footnote 8). The inset shows the numerically modelled cross-sectional plot (exaggerated for clarity) of the strain field for the first and third vibrational eigen-modes of a toroidal silica micro-cavity on a silicon post. The stress field is superimposed (color coded). As evident from the modelling, the mechanical oscillations cause a displacement of the toroidal periphery and thereby induce a shift in the whispering gallery mode resonant frequency.
Fig. 3.
Fig. 3. Numerical calculation (solid line) and measured (points) dispersion relation for the fundamental (n=1) and third order (n=3) flexural modes of a micro-toroid as a function of the free hanging length of the disk structure. The inset shows the agreement between the numerical and measured frequencies.
Fig. 4.
Fig. 4. Measured amplitude response (points) of the mechanical vibrations of an n=1 mechanical mode as a function of driving-force frequency (modulation frequency of the pump power). Circles (green), triangles (red), and stars (blue) represent the data for 2µW, 5µW and 9µW of average pump power. The inset shows the effect of the optical power on the linewidth of the mechanical oscillator inferred from the theoretical fits (such as the solid lines in the main Fig.). A linear fit shows a threshold of 11µW for the mechanical oscillations and an intrinsic quality factor of 630 for the measured mechanical mode of the toroidal structure.
Fig. 5.
Fig. 5. Measured mechanical oscillator displacement as a function of the optical pump power showing threshold behaviour. Oscillations initiate at about 20µW of input power and start to saturate for higher values of pump power. This saturation is associated with the lower optical-mechanical coupling at displacements large enough to shift the resonant frequency of the optical mode by greater than its linewidth. Inset shows the dependence of measured threshold power on optical quality factor. Data taken from Ref. [14]. These data were obtained using different optical modes in a single micro-toroid (so that only optical Q would be varied). The slope of the fit in a log-log scale is 3±0.3, which agrees well with inverse cubic behaviour expected for radiation-pressure-induced regenerative oscillations (as opposed to inverse quadratic behaviour for photothermal effects).

Equations (1)

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γ = γ 0 ( 1 P P threshold ) , P threshold = K opt− mesh Q c Q total 4 Q mech f ( d )
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