Photoacoustic model for laser-induced acoustic desorption of nanoparticles

TL;DR

This work establishes a photoacoustic-based theoretical framework to optimize laser-induced acoustic desorption (LIAD) of nanoparticles for vacuum trapping. By formulating the LIAD problem with the scalar wave equation, the authors derive key scaling laws for surface acceleration, identify optimal beam waist sizes set by acoustic diffraction, and introduce a material-dependent figure of merit to guide substrate choice. The model is validated against literature and demonstrates that compact, sub-nanosecond laser systems can rival traditional lab setups with much higher pulse energies, enabling practical, space-ready LIAD implementations. The approach provides a principled path to rational LIAD design and material optimization, with explicit bounds and regimes governed by pulse duration, spot size, and substrate properties.

Abstract

Laser-induced acoustic desorption (LIAD) enables loading nanoparticles into optical traps under vacuum for levitated optomechanics experiments. Current LIAD systems rely on empirical optimization using available laboratory lasers rather than systematic theoretical design, resulting in large systems incompatible with portable or space-based applications. We develop a theoretical framework using the photoacoustic wave equation to model acoustic wave generation and propagation in metal substrates, enabling systematic optimization of laser parameters. The model identifies key scaling relationships: surface acceleration scales as $τ^{-2}$ with pulse duration, while acoustic diffraction sets fundamental limits on optimal spot size $w \gtrsim \sqrt{vτd}$. Material figures of merit combine thermal expansion and optical absorption properties, suggesting alternatives to traditional aluminum substrates. The framework validates well against experimental data and demonstrates that compact laser systems with sub-nanosecond pulse durations can achieve performance competitive with existing laboratory-scale implementations despite orders-of-magnitude lower pulse energies. This enables rational design of minimal LIAD systems for practical applications.

Figures (3)

• Figure 1: Acoustic wave propagation and diffraction through metal substrates. Cross-sectional views show the acoustic velocity $u(r,z,t)$ at time instances (lower rows are earlier times) during propagation from laser-heated front surface ($z=0$) towards the particle-laden surface ($z>0$). The dimensionless focusing parameter $\eta=w/(v\tau)=d_{\mathrm{evo}}/w$ is discussed in the text. Left and right columns correspond to the systems of Nikkhou et al. ($\eta = 0.6$) and Bykov et al. ($\eta = 3.1$) respectively; horizontal dashed lines indicate their substrate thicknesses ($d/d_{\mathrm{evo}} = 1.55$ and $0.30$ respectively), showing that the Nikkhou pulse has largely evolved while the Bykov pulse is still evolving.
• Figure 2: Acoustic pulse evolution in the thin-skin limit for different diffraction regimes. Normalized acceleration $a/a_{\mathrm{nat}}$ (scaled to peak) as a function of dimensionless coordinates $z/d_{\mathrm{evo}}$ and $vt/d_{\mathrm{evo}}$ for (a) $\eta = 0.6$ (Nikkhou et al., $d/d_{\mathrm{evo}} = 1.55$), (b) $\eta = 1.4$ (intermediate), and (c) $\eta = 3.1$ (Bykov et al., $d/d_{\mathrm{evo}} = 0.30$). The dimensionless parameter $\eta = w/(v\tau)$ characterizes the diffraction regime and determines the evolution shape. Vertical dashed lines mark these substrate thicknesses; gray diagonal line shows the characteristic ($vt = z$). Computed from analytical solution Eq. \ref{['eq:analytical_acceleration']}.
• Figure 3: Photoacoustic response comparison for literature (Bykov et al., 2019; Nikkhou et al., 2021) and commercial systems: (a) displacement, (b) velocity, and (c) acceleration. The time axis centers on acoustic transit time (thickness/v) to ease direct comparison. The surface is confirmed to return to zero displacement after the pulse. Passive Q-switched systems perform competitively, insofar as they achieve comparable or larger surface accelerations, despite lower pulse energies. This model predicts that aluminium substrates show lower peak accelerations than optimized materials like stainless steel or titanium.