Mechanical Mode Dependence of Bolometric Backaction in an Atomic Force Microscopy Microlever

Two backaction (BA) processes generated by an optical cavity-based detection device can deeply transform the dynamical behavior of an atomic force microscopy microlever: the photothermal force or the radiation pressure. Whereas noise damping or amplifying depends on the optical cavity response for radiation pressure BA, we present experimental results carried out under vacuum and at room temperature on the photothermal BA process which appears to be more complex. We show for the first time that it can simultaneously act on two vibration modes in opposite directions: Noise on one mode is amplified, whereas it is damped on another mode. Basic modeling of photothermal BA shows that the dynamical effect on the mechanical mode is laser spot position-dependent with respect to mode shape. This analysis accounts for opposite behaviors of different modes as observed.

Figure 1

The optical fiber-based interferometer is sensitive to oscillator motion. A microsphere is glued on the lever, thus placing a mode 1 node almost at the end of the structure. The back of the lever and the optical fiber end are forming a poor finesse cavity: As indicated in the inset, intracavity intensity is cavity length-dependent with period $\lambda /2$, where ${\lambda }_L=670\mathrm{nm}$ is the laser wavelength. Modulation $\Delta I_0/I_0$ is nevertheless expected to be very weak.

Figure 2

In graphs (a) and (b), dissipation rates for modes 0 and 1 are plotted against laser intensity in arbitrary units, at each cavity detuning $z_{+0}$ and $z_{-0}$. At 2000 a.u., optical power is on the order of $500\mu \mathrm{W}$. Graphs (c) and (d) display the resonance frequency shift generated by thermal force and lever heating: For mode 1, the latest process appears to be the dominant one, since the frequency shift is decreasing in both cases whatever the cavity detuning. Graph (d) reveals the change of resonant frequency produced by heating through the dotted line: As a result, it accounts for the slope difference between the two branches $z_{+0}$ and $z_{-0}$. The hatched area is related to the instability behavior that we observed on mode 0 for $z_{-0}$, when making ${\gamma }_0$ negative. Mechanical parameters for mode 0 and 1 are acquired simultaneously through thermal mechanical noise analysis: Brownian motion peaks are fitted with a Lorentzian shape curve, whose parameters are ${\omega }_i$, ${\gamma }_i$, curve area $⟨z_i^2⟩$, and pedestal $y_i$.

Figure 3

In graphs (a) and (b), the Brownian motion of mode $i$, $i=0,1$, $⟨z_i^2⟩$ is plotted against laser intensity, which is proportional to damping rate ${\gamma }_i$. For each cavity position ($z_{\pm 0}$), mechanical noise suits relation $T_{\mathrm{eff}}=k⟨z_i^2⟩/k_B={\gamma }_i/({\gamma }_i+\Delta {\gamma }_i)$. Graph (c) displays the noise spectrum density around the fundamental resonant frequency, when increasing laser intensity. According to cavity detuning, Brownian motion is damped ($z_{+0}$) or enhanced ($z_{-0}$).