# Optical Trapping, Sizing, and Probing Acoustic Modes of a Small Virus
## 1 Introduction
Prior to the development of the EAR technique [9; 10; 22], opto-mechanical methods for measuring mechanical vibrations were limited to a range of frequencies above 100 GHz for the case of traditional Raman scattering [42; 53], and sub-gigahertz for cavity resonator-based approaches [54]. This left a gap of the important GHz range, where characteristic frequencies of structures of nanometer size scale should be found, according to elastic theory [37; 38; 39; 40; 41; 42; 55; 56; 57; 58]. Viruses are of nanometer size scale and, thus, predicted to have vibrational modes in the GHz frequency range. Brillouin scattering can probe the GHz frequency range and, indeed, some Brillouin studies were done on viruses [43; 46; 48; 59; 60]; however, the peaks were difficult to observe possibly due to damping by water or core-shell interactions, as discussed in those works. Moreover, unlike these other opto-mechanical measurement methods, the EAR technique provides a high resolution of vibrational frequencies of individual nanometer-scale particles which are confined by optical trapping, as opposed to measuring ensembles of particles in the case of Raman and Brillouin scattering studies. This technique also has the advantage of directly measuring low-wavenumber Raman active modes of single trapped particles, while avoiding the issue of Rayleigh scatter overwhelming the signal near the zero-loss line, as is the case for traditional elastic light scattering spectroscopy. Previous work using the extraordinary acoustic Raman (EAR) technique investigated small proteins including DNA and polystyrene nanospheres [9; 10; 11; 22], whereas here we report of the study of a virus using the technique, since the vibrational frequencies of viruses were of interest to researchers for some time [35; 37; 38; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57]. The EAR technique involves the application of two lasers. Both lasers are focused on an aperture, forming an aperture-assisted laser tweezer, in which a small particle is trapped. The interference of the two lasers at slightly different wavelengths creates a \"beating\" oscillation in the electric field which then causes a stretching force on the trapped particle through electrostriction. The frequency of this oscillation is controlled by the difference in wavelength of the two lasers. The wavelength of one laser is held fixed, while the other is swept through a wavelength range differing from the fixed-wavelength laser by sub-Angstrom to nanometer values, corresponding to beat frequencies in the GHz range. When the frequency of the beating oscillation produced by the interfering lasers matches the frequency of an acoustic mode of a trapped particle, there is stronger interaction of the electric field with the structure, leading to an increase in the movement of the particle within the trap. The laser transmission through the aperture depends on the position and conformation of the particle within the aperture and, thus, an increase in movement of the particle is observable as an increase in the fluctuations of the transmission signal. It is this variation of fluctuations of laser transmission signal that is detected for the EAR measurement. The previous EAR studies of nanometer-scale particles found peak frequencies which matched well with predicted values from elastic theory. In this work, the bacteriophage PhiX174 was studied--chosen for its small size, low biological safety rating, and history of being extensively studied. It makes a good model system for icosahedral viruses, of which there are many [68; 69; 70], although the techniques used here could be extended to the study of viruses of other size and shape. The size and morphology of PhiX174 is well established from SEM studies and crystallography [71; 72; 73; 74]. PhiX174 is a coliphage which infects _Escherichia coli_ bacteria [75]. Detection of such viruses can indicate the presence of fecal matter in aquatic environments [76].