FF2C.6.pdf
CLEO:2015 © OSA 2015
Nonreciprocal Optical Interaction of Dissimilar Particles Sergey Sukhov1, Alexander Shalin2, David Haefner1, and Aristide Dogariu1 1
CREOL, The College of Optics and Photonics, University of Central Florida, 4000 Central Florida Blvd., Orlando, Florida 32816-2700, USA 2 National Research University of Information Technologies, Mechanics and Optics, 49 Kronverksky Ave., St. Petersburg 197101, Russia Author e-mail address:
[email protected]
Abstract: We show that optical interaction of dissimilar particles results in apparent violation of actio et reactio principle. Interaction asymmetry in an optically-bound dimer can lead to unexpected movement transversal to the direction of light propagation. OCIS codes: (290.5850) Scattering, particles; (350.4855) Optical tweezers or optical manipulation.
When illuminated by external field, microscopic particles can form stable structures due to their mutual interaction and the corresponding optical forces [1]. This effect, known as optical binding, ceases when the external field is shut down. Optical binding is usually described in terms of a potential landscape with periodic minima and maxima [2]. Particles in this landscape reside in energy minima and tend to maintain certain particle-particle distance. Following this description, the potential forces acting on two bound particles are equal and oppositely directed. However, the forces in the system of optically interacting dissimilar particles are not necessarily reciprocal, which, at first glance appears to violate the actio et reactio principle.
Fig. 1. Geometry of the optically bound system. Two dissimilar particles experience different forces F1 ≠ F2 when illuminated by an external field E0I. As a result, a transversal optical force F⊥ acts on the whole system (represented by semitransparent sphere).
We consider a situation when two dissimilar closely placed spherical particles are illuminated by external optical wave perpendicular to the axis connecting those particles (Figure 1). In the case of a single particle, because of spherical symmetry, there are no forces acting in xy plane. Interaction of particles breaks this spherical symmetry and forces acting along axis connecting particles appear. In the case of particles with dimensions much smaller than a wavelength this transversal optical force can be found with a simple formula [3,4]: Fj =
∂E*j 1 , Re α j E j 2 ∂r
(1)
where α j are polarizabilities of particles and E j are the electric fields at the locations of dipoles. The forces acting on larger particles can be evaluated by integrating the Maxwell stress tensor over surrounding surfaces [5]. Direct calculation of optical forces with Eq.(1) demonstrates their nonreciprocal nature (Figure 2a). This apparent violation of “action and reaction” principle is due to the presence of non-conservative optical forces which appear during particles interaction with the external field. One of the consequences of the asymmetric interaction with the optical field is the occurrence of nonzero force acting on the center of mass in a direction transversal to the illuminating wave propagation. That leads to the transversal motion of the whole optically bound system. The reason for existence of the transversal force can be easily understood when realizing that particles interacting with the external field constitute an open system and momentum balance for the whole system “particles plus field” should be considered. Figure 2b shows the scattering pattern of optically bound system consisting of gold and silver nanoparticles. One can see that this pattern is noticeably asymmetric with respect to 0° and 180° directions. It is this asymmetry that creates recoil force acting in transversal direction. The transversal force acting on particles is directly related to the shape of the scattering function [6]:
FF2C.6.pdf
CLEO:2015 © OSA 2015
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Transversal force [fN]
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silver gold
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0.010 0.005
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0.000 -0.005 210
-0.010 -0.015
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Particle separation [nm]
300 270
Fig. 2. (a) Transverse component of optical forces acting on each of interacting particles. The green and red dots indicate the particle-particle separations of stable and unstable equilibriums, respectively. (b) Scattering diagram for optically bound dissimilar particles. The scattering angle is measured with respect to the dimer’s axis (x-axis in Figure 1).
F⊥ = −
ε 2k 2
∫Ω | f (kˆs = rˆ, k I ) |
2
rˆ⊥ dΩ
(2)
where k is the wavenumber, ε is the dielectric permittivity of surrounding medium, f (kˆs , k I ) denotes field in the far zone the scattered along kˆ s direction. The integration in Eq. (2) is performed over a solid angle of 4π steradians; rˆ is a unit vector corresponding to angle of integration and rˆ⊥ is its projection onto the dimer’s axis. We will discuss different aspects of optical interaction of dissimilar particles such as structural phase transitions, control of directionality of transversal forces etc. This unusual consequence that occurs when the optical symmetry of interaction is broken is a rather general and robust phenomenon. In particular, the appearance of asymmetric forces in a system of otherwise symmetric particles may be of interest for applications of micro-manipulation. In addition, the canonical example of two dissimilar particles discussed here can constitute the elementary unit of artificial “optical matter” that can be created in an “out-of-equilibrium” environment. The optical system of bound particles is a convenient model for studying the statistical mechanics of more complicated many-body systems with non-reciprocal pair interactions. In such non-Hamiltonian systems, the standard Boltzmann description of classical equilibrium breaks down and their statistical mechanics properties have not, so far, been elucidated. [1] [2] [3] [4] [5] [6]
M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233-1236 (1989). L. C. Dávila Romero, J. Rodríguez, D. L. Andrews, “Electrodynamic mechanism and array stability in optical binding,” Opt. Commun. 281, 865–870 (2008). A. Ashkin and J. P. Gordon, “Stability of radiation-pressure particle traps: an optical Earnshaw theorem,” Opt. Lett. 8, 511-513 (1983). P. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065-1067 (2000). J. D. Jackson, Classical Electrodynamics, 2nd ed., (Wiley, 1975). F. Borghese, P. Denti, and R. Saija, Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics (Springer, 2007) Chap.3.
