# Optical Trapping, Sizing, and Probing Acoustic Modes of a Small Virus
## 1 Introduction  
Optical tweezers are under development since [PERSON]'s seminal work, first reported in 1970 [1]. Optical trapping since burgeoned into a wide field ranging from studies on micron- and nanometer-scale biological systems, to fundamental physics of ultra-cold ions and atoms [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27], as well as advanced methods to manipulate nanometer-scale materials such as via holographic optical tweezers [28; 29; 30; 31]. While viruses were trapped before by optical tweezers, this was only for the largest viruses that are extremely elongated and, thus, easier to trap (e.g., Tobacco Mosaic Virus) [2], or just large (HIV) [3]. To stably trap smaller viruses with reasonable power, it is necessary to make use of field enhancement via plasmonic effects from nanostructures [4]. This is because simple optical tweezers take advantage of an intrinsic gradient force within the focus of a laser beam, due to the variation in intensity from beam waist to center. This is limited to a size scale on the order of hundreds of nanometers, due to the diffraction limit. In contrast, plasmonic trapping takes advantage of local field enhancement in the vicinity of nanometer structured metals [3; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20] and, thus, can overcome the diffraction limit. One such scheme is to create nanometer-scale apertures in metals, and to focus the trapping laser onto these apertures [3; 5; 6; 7; 8; 9; 10; 11; 17; 18; 19; 20; 21; 22; 27]. In particular, double nanohole (DNH) apertures were developed which create extremely high local field strengths in the area in between opposing sharp edges where the two holes meet. In this work, such DNH apertures are found to enable the trapping of one of the smallest virus particles reported, at powers low enough to leave the virus particles intact for several hours of experiment time. As a demonstration of possibilities to characterize individually trapped virus particles, two techniques were performed in this work. The particles were sized via an established autocorrelation analysis technique [5; 6; 7; 8], and the acoustic modes were probed using an extraordinary acoustic Raman (EAR) method [9; 10; 22]. When a particle is trapped, it is subject to a gradient force field which tends to move it toward the position of a potential minimum. Due to Brownian motion, the particle will undergo random displacements. The restoring force from the optical trap is akin to that of a spring, proportional to the displacement to a first-order approximation. There is also drag due to the surrounding media, which is proportional to the radius of a spherical particle, to first order. If the restoring force of the optical trap is sufficient to overcome these thermally driven movements, the particle will remain within the trap and the displacements of the position will manifest as variations in the transmission signal. Analysis on these variations can be used to characterize both the trap stiffness and the particle diameter [5; 6; 7; 8]. Details of this analysis are covered in Section 2. Determination of elastic properties and, in particular, vibrational frequencies of viral structures is much sought after [32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48]. Characteristic frequencies can be used as a \"fingerprint\" to identify viruses. It was also proposed to resonantly excite viruses to selectively destroy them, while leaving the surrounding material undisturbed as a potential method of treatment of disease [49; 50; 51; 52]. This study demonstrates an easily implemented technique to directly measure the frequencies of acoustic modes of very small individual virus particles for the purpose of a fundamental understanding of their biophysics, diagnostics, or targeted destruction of the contagion. The advantage of the technique used here to determine the vibrational frequencies is that individual, optically trapped particles can be probed, and the frequency regime in the GHz is accessible.