Chiral Rayleigh particles discrimination in dynamic dual optical traps
Introduction
Many important molecules are often chiral, i.e. in nature there are two different molecular configurations called enantiomers that are identical in many physical and chemical characteristics. Chirality is very important in many functional properties of such molecules, so in order to obtain optimal behavior from pharmaceutical compounds, insecticides or herbicides, for example, correct chirality selection is critical. Currently, chiral resolution can be obtained by using different techniques such as gas chromatography, high performance liquid chromatography or capillary electrophoresis [1]. Chiral resolution involves the interaction of the enantiomers with a chiral environment, and in this sense, different authors [2], [3], [4] have recently proposed the use of electromagnetic fields to generate chiral separation paying special attention to the effects of different classes of optical forces. For example, lateral optical forces (LOF) have been studied for chirality sorting by using two interfering plane waves [5], and the LOF effect on paired chiral particles has also been discussed in [6]. LOF generated by evanescent waves that transport spin angular moment has also been proposed for chirality-sorting [3], and anomalous LOF has also been induced on chiral gold helical particles [7]. Furthermore, transverse optical and azimuthal forces generated by using Bessel beams on chiral particles has also been studied in [8], and the optical trapping of chiral nanoparticles by using plasmonic tweezers based on coaxial plasmonic apertures has been reported in [9]. Meanwhile, a study of the optical gradient forces on chiral molecules, Cameron et al. have also studied them showing that it is possible to obtain a Stern Gerlach deflector [4]. Finally, large particles (micrometric) have been sorted in a fluidic medium by using the spin dependent optical forces of chiral particles [10].
The use of gradient force for the movement of dielectric nanoparticles has been demonstrated by many authors by using optical conveyor belts [11]. These optical conveyors for dielectric particles are obtained by means of interference of two counter propagating beams with the same polarization state but slightly temporally dephased. However, when the two beams are orthogonally polarized, it is not possible to obtain a dielectric optical conveyor belt, but a very efficient optical trap is generated.
In this paper we are going to demonstrate that it is possible to obtain optical chiral resolution by using an optical conveyor belt for chiral nanoparticles through the superposition of two orthogonal counter propagating Gaussian beams with different beam waist so that one type of the enantiomer will be trapped and the opposite ones will be transported by the conveyor belt.
To do this, we propose an interference scheme similar to the one used one in reference [10], but it is important to indicate that, because our counter propagating beams are elliptically polarized and temporally dephased, it is possible to obtain an optical conveyor that transports one of the enantiomers (while the others remain trapped in a trap). Moreover, the optical conveyor proposed in this paper, based on focalized temporally dephased beams, can be used for separation of Rayleigh enantiomeric particles.
Section snippets
Forces and chiral particle model
In order to solve the particle dynamics, we have solved the overdamped Langevin equation [12]: where is the optical force, is the position vector of the particle (x(t), y(t), z(t)) at time t, is the frictional force of a particle, and is a random function force with time. has a Gaussian probability distribution with correlation function where kB is Boltzmann’s constant and T is the temperature.
Counter-propagating Gaussian beams
In order to clarify the result developed in the previous section, we first consider two counter-propagating Gaussian Beams (). In this case, it is well known that the generated radial trap is located at so particles will be located at the axial positions, in which case, we are going to analyze only axial potential. For this particular case, taking into account that we obtain that Eqs. (25)–(29) can be rewritten as:
Conclusion
Chiral separation by using chiral optical conveyor has been numerically demonstrated by using two counter propagating LGB. To do this, a configuration based on two counter propagating elliptically polarized and temporally dephased beams has been proposed, resulting in an optical conveyor that transports one enantiomer and an optical trap that catches the other one. Different configurations have been analyzed by using beams with and without topological charges, demonstrating in all cases the
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