Controlling photothermal forces and backaction in nano-optomechanical resonators through strain engineering

TL;DR

The paper shows that photothermal forces in nano-optomechanical resonators can be deterministically controlled by engineering the spatial overlap between thermal fluctuations and mechanical strain. Through a theoretical framework and experiments on a nanobeam zipper cavity, the authors demonstrate that tether asymmetry breaks strain symmetry, dramatically altering the thermoelastic overlap and flipping the sign of photothermal backaction without materially affecting optical or mechanical performance. In the unresolved sideband regime, the photothermal contribution can dominate the dynamic linewidth, providing a route to suppress or enhance backaction for cooling or amplification. These findings offer a practical design principle for tuning backaction in nano-optomechanics and open avenues for studying nonlinear and quantum dynamics in strongly photothermally coupled systems.

Abstract

In micro- and nanoscale optomechanical systems, radiation pressure interactions are often complemented or impeded by photothermal forces arising from thermal strain induced by optical heating. We show that the sign and magnitude of the photothermal force can be engineered through deterministic nanoscale structural design, by considering the overlap of temperature and modal strain profiles. We demonstrate this capability experimentally in a specific system: a nanobeam zipper cavity by changing the geometry of its supporting tethers. A single design parameter, corresponding to a nanoscale geometry change, controls the magnitude of the photothermal backaction and even its sign. These insights will allow engineering the combined photothermal and radiation pressure forces in nano-optomechanical systems, such that backaction-induced linewidth variations are deterministically minimized if needed, or maximized for applications that require cooling or amplification at specific laser detuning.

Figures (7)

• Figure 1: a Schematic of the optomechanical (dark blue) and photothermal (red) backaction cycles. b, c, and d Schematic examples of a temperature profile $\tilde{T}_k(\vec{r})$, strain profile ${\mathbf{S}}^x(\vec{r})$, and the integrand of \ref{['eq:Lambdak']} resulting from their multiplication.
• Figure 2: a Definition of the tether asymmetry, $A$, in terms of other tether parameters. b Electric field in the $y$ direction for the even optical mode with frequency 196THz with a 2 scale indicated by the black line. c Imaginary part of the thermal fluctuations at the mechanical frequency. d$S_{xx}$ stress component for the odd mechanical mode with frequency 5.6 MHz. e Component $S_{xx}$ of the normalized strain profile for different values of $A$ evaluated at the cut-line shown by the dashed line in d. f In red and blue we have, respectively, the expected maximal linewidth variation at the blue side of the resonance due to photothermal and optomechanical effect, assuming typical experimental parameters for our devices and considering a temperature of 30K, where the silicon expansion coefficient is negative. As the the optomechanical contributions are small we scaled it by 3 to improve the graph readability.
• Figure 3: a-c SEM micrographs of the tethers of three fabricated devices, with 1 µm scale bar. d, k Simulated $E_y$ mode profile of respectively the symmetric and anti-symmetric optical modes in the device. e-g (h-j) Measured frequency (linewidth) of the mechanical resonator as a function of optical detuning relative to the symmetric optical mode. Measured data is indicated by the blue (orange) dots with error bars. The black line is the complete fit to \ref{['eq:fitfunc']}, with the red (green) line indicating the static (dynamic) contribution. l-n (o-q) Similar to e-j, but for the anti-symmetric optical mode.
• Figure 4: a The slope of the dynamic linewidth variation, $\beta_{\Gamma,\mathrm{dyn}} = \partial \delta \Gamma_\mathrm{dyn} / \partial n_\mathrm{ph}$, normalized by $|g_0|$ and $\beta_{\Omega,\mathrm{stat}}$, with a linear fit to the data for the symmetric (blue) and anti-symmetric (orange) optical modes. b (c) Measured dynamic linewidth variation for devices with various $A$ for the symmetric (anti-symmetric) optical mode. Lines are linear fits to the data using ODR.
• Figure Supplementary Figure 1: Overview of used devices. The asymmetry parameter $A$ varies from -1 to +1 from left to right in steps of 0.5.