Polarization effects in optically bound particle arrays Christopher D. Mellor Physical Biochemistry, National Institute for Medical Research, Mill Hill, London, NW7 1AA, U.K.
Thomas A. Fennerty and Colin D. Bain* Department of Chemistry, Durham University, South Rd., Durham DH1 3LE, U.K.
[email protected]
Sub-micron polystyrene spheres spontaneously assemble into twodimensional arrays in the evanescent field of counterpropagating laser beams at the silica–water interface. The symmetry and dynamics of these arrays depends on the particle size and the polarization of the two laser beams. Here we describe the polarization effects for particles with diameters of 390–520 nm, which are small enough to form regular 2-D arrays yet large enough to be readily observed with an optical microscope. We report the observation of rectangular arrays, three different types of hexagonal arrays and a defective array in which every third row is missing. The structure of the arrays is determined by both optical trapping and optical binding. Optical binding can overwhelm optical trapping and give rise to an array that is incommensurate with the interference fringes formed by two laser beams of the same polarization. © 2006 Optical Society of America OCIS Codes: (170.4520) Optical confinement and manipulation; (160.4670) Optical materials; (240.6700) Surfaces.
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(C) 2006 OSA
Received 29 August 2006; accepted 2 October 2006
16 October 2006 / Vol. 14, No. 21 / OPTICS EXPRESS 10079
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1. Introduction Sub-micron colloidal particles can be trapped at an interface by the evanescent wave of a totally internally reflected laser beam. With a single laser beam [1], there is a tangential component to the radiation pressure that drives the colloidal particles along the surface. If two counter-propagating laser beams are employed, the spatially averaged radiation pressure is zero and stable trapping is observed [2, 3, 4]. For polystyrene spheres (PS) in water trapped at the silica-water interface, these particles assemble into lines parallel to the plane of incidence (for diameters 2a > 700 nm) and into two-dimensional arrays for smaller particles (300 < 2a < 700 nm). In a preliminary communication [3] we reported the formation of either hexagonal or rectangular arrays depending on the particle size and the presence or absence of interference between the two laser beams. In this paper, we explore in greater detail the effect of the polarization of the laser beams on the structure of 2-D arrays. We show the competition between optical trapping and optical binding [5] leads to some new and unexpected structures. 2. Experimental methods A 500-mW, CW, SLM diode-pumped Nd:YVO4 laser (Laser Quantum, Forte-S, λ = 1064 nm) was gently focused into a fused silica prism at an angle just above the critical angle (θc = 67°) for total internal reflection at the silica–water interface (see Figs. 1 and 2). A half-wave plate was used to control the polarization of the incident beam, either s or p. After exiting the back face of the prism, the laser beam was retro-reflected by a spherical gold mirror that refocuses the beam to the same point on the silica surface as the incident beam. The spot size was ca. 15 × 30 μm at the surface where optical trapping occurs. A quarter-wave plate was used to select the polarization of the reflected beam, either parallel or perpendicular to the incident beam. With the quarter-wave plate set to rotate the polarization by 90°, less than 1% of the reflected beam was passed by a polarizer set parallel to the incident beam: the two laser beams are therefore accurately orthogonal. A calculation of the Fresnel coefficients for reflection at the silica-water interface shows that the y-component, Ey, of the electric field (for s-polarized light) and the z-component, Ez, of the electric field (for p-polarized light) were equal in magnitude to within the accuracy to which the angle of incidence was set. At angles close to the critical angle, Ex
