Nonconservative dynamics of optically trapped high-aspect-ratio nanowires

Wen Jun Toe, Ignacio Ortega-Piwonka, Christopher N. Angstmann, Qiang Gao, Hark Hoe Tan, Chennupati Jagadish, Bruce I. Henry, and Peter J. Reece

Phys. Rev. E 93, 022137 – Published 24 February 2016

Abstract

We investigate the dynamics of high-aspect-ratio nanowires trapped axially in a single gradient force optical tweezers. A power spectrum analysis of the dynamics reveals a broad spectral resonance of the order of kHz with peak properties that are strongly dependent on the input trapping power. A dynamical model incorporating linear restoring optical forces, a nonconservative asymmetric coupling between translational and rotational degrees of freedom, viscous drag, and white noise provides an excellent fit to experimental observations. A persistent low-frequency cyclical motion around the equilibrium trapping position, with a frequency distinct from the spectral resonance, is observed from the time series data.

Received 13 August 2015

DOI:https://doi.org/10.1103/PhysRevE.93.022137

Physics Subject Headings (PhySH)

Nanowires

Optical tweezers Stochastic processes & statistics

Polymers & Soft Matter

Authors & Affiliations

Wen Jun Toe¹, Ignacio Ortega-Piwonka², Christopher N. Angstmann², Qiang Gao³, Hark Hoe Tan³, Chennupati Jagadish³, Bruce I. Henry², and Peter J. Reece^1,*

¹School of Physics, The University of New South Wales, Sydney NSW 2052, Australia
²School of Mathematics and Statistics, The University of New South Wales, Sydney NSW 2052, Australia
³Research School of Physics and Engineering, The Australian National University, Canberra ACT 2601, Australia

^*p.reece@unsw.edu.au

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Issue

Vol. 93, Iss. 2 — February 2016

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Images

Figure 1
Schematic of our experimental setup and geometry within the optical trap with relevant coordinates and angles. In the experimental arrangement a diode pumped solid state laser is used with adaptive optics to create a diffraction limited spot within the focal plane of the objective (OBJ). The nanowires are trapped near the end of the wire and aligned along the laser axis. Light scattering from the nanowire is collected by the condenser (COND) and used to perform back focal plane interferometry with a position sensitive detector (PSD).
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Figure 2
Schematic illustration of the coordinate system used in the model for the dynamics of the nanowire.
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Figure 3
(a) Experimental power spectrum of a nanowire trapped approximately 10 $μ m$ from the cover slip (blue dots). The dashed (red) line is a Lorentzian fit which is characteristic of Brownian dynamics in an optical trap; and the solid (black) is the presented model. (b) Experimental power spectrum of the same nanowire trapped approximately 50 $μ m$ from the cover slip (red dots). The solid (black) line is the fitted spectrum from the presented model. (c) Autocorrelation function of the nanowire motion approximately 10 $μ m$ from the cover slip (dashed) and approximately 50 $μ m$ from the cover slip (solid). The inset is a bright field image of the untrapped nanowire.
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Figure 4
Power spectral density of a single nanowires held at a fixed trapping power measured for different trapping powers. The peak frequency shifts given by the $\sqrt{ε}$ increases linearly with trapping power, while the Brownian fluctuations are strongly suppressed. The solid lines represent the fitted model which includes nonconservative cross-coupling between translation and rotation. The arrow indicates how the power spectral density changes with increasing trapping power.
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Figure 5
Fitting parameters of the power spectral density data presented in Fig 4. (a) $ε$ increase quadratically and $μ$ linearly with trapping power, which corresponds to linear increase in both the peak frequency and width. (b) The noise strength $α$ shows no clear dependence on trapping power indicating a constant temperature, while $β / α$ increases quadratically with trapping power. All dependencies are consistent with a trap stiffness that is linearly proportional to the trapping intensity in the presence of asymmetric coupling.
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Figure 6
(a) A winding number plot of the nanowire motion for different trapping powers. Small time-scale fluctuations in the winding decorate a clear linear increase with time, indicating persistent cycling in one direction. (b) The rate of winding, given by the gradient of the winding plots, is observed to increase approximately trapping power for lower powers and plateau at higher powers.
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