Optimizing optical tweezing with directional scattering in composite microspheres

R. Ali, F. A. Pinheiro, F. S. S. Rosa, R. S. Dutra, and P. A. Maia Neto

Phys. Rev. A 98, 053804 – Published 5 November 2018

Abstract

We demonstrate that achieving zero backward scattering (ZBS), i.e., the first Kerker condition, allows for optical tweezing of high-index microspheres, which cannot be trapped using standard techniques. For this purpose, we propose an alternative material platform based on composite metamaterials. By tuning the volume filling fraction of inclusions and the microsphere radius, stable trapping can be achieved provided that ZBS is combined with the condition for destructive interference between the fields reflected at the external and internal interfaces of the microsphere when located at the focal point. By using the Mie-Debye-spherical aberration theory, we also show that the ZBS condition is even more useful in realistic, standard optical tweezer setups, in which spherical aberration is unavoidable due to refraction at the interface between the glass slide and the water-filled sample. Altogether, our findings not only pave the way for possible new trapping designs and applications but also unveil the role of backscattering in the physics of optical tweezers.

Received 6 June 2018

DOI:https://doi.org/10.1103/PhysRevA.98.053804

Physics Subject Headings (PhySH)

Classical optics Metamaterials

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

R. Ali^1,*, F. A. Pinheiro¹, F. S. S. Rosa¹, R. S. Dutra², and P. A. Maia Neto¹

¹Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil
²LISComp-IFRJ, Instituto Federal de Educação, Ciência e Tecnologia, Rua Sebastião de Lacerda, Paracambi, RJ, 26600-000, Brazil

^*r.ali@if.ufrj.br

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 5 — November 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Real (solid) and imaginary (dash) parts of the composite effective refractive index $n_{emg} = \sqrt{ε_{emg} μ_{emg}}$ , calculated with the extended Maxwell Garnett theory, versus volume filling fraction. The inset illustrates the composite made of ${SiO}_{2}$ spherical inclusions (radius $8 nm$ ) distributed inside a $SiC$ sphere.
Reuse & Permissions
Figure 2
(a) Dimensionless backscattering efficiency $Q_{b}$ versus volume filling fraction $f,$ showing almost zero backscattering efficiency around $f = 0.5$ for a composite microsphere of radius $r = 1825 nm .$ (b) Real and imaginary parts of the dimensionless dipolar Mie coefficients versus filling fraction. The solid red (light gray) and black lines represent $Re (a_{1})$ and $Re (b_{1}),$ respectively. They intersect at $f = 0.5,$ as indicated by a vertical line, which happens to be quite close to the intersection of $Im (a_{1})$ and $Im (b_{1}),$ represented by dashed red (light gray) and black lines.
Reuse & Permissions
Figure 3
Dimensionless axial force efficiency $Q_{z}$ as a function of position (in units of sphere radius) along the laser axis for (a) sphere radius $r = 1825 nm$ with filling fractions $f = 0$ (dotted line), $f = 0.37$ (dashed line), $f = 0.5$ (solid line), and $f = 0.55$ (solid-dotted line) and (b) $r = 1500 nm$ with $f = 0$ (dotted line), $f = 0.43$ (dashed line), $f = 0.5$ (solid-dotted line), and $f = 0.58$ (solid line).
Reuse & Permissions
Figure 4
(a) Scheme representing Mie scattering when the sphere center is located at the focal point of the incident beam. In this case, the resulting dimensionless force efficiency $Q_{z} (z = 0)$ , plotted as a function of the sphere radius $r$ in (b) for $f = 0.5$ and in (c) for $f = 0.58,$ can be interpreted in terms of the interference between the fields reflected at planes $Π_{1}$ and $Π_{2} .$ (d),(e) Dimensionless backscattering efficiency $Q_{b}$ versus $r$ for (d) $f = 0.5$ and (e) $f = 0.58$ . The vertical lines indicate the filling fractions used in Figs. 5 and 6. Optimal trapping is achieved by selecting $r$ to be a simultaneous minimum of both $Q_{z}$ and $Q_{b}$ (solid vertical lines).
Reuse & Permissions
Figure 5
Dimensionless axial force efficiency $Q_{z}$ as a function of position (in units of sphere radius) along the laser axis for (a) $f = 0.5$ with radii $r = 1300 nm$ (dashed line), $1630 nm$ (dotted line), and $1825 nm$ (solid line) and for (b) $f = 0.58$ with radii $r = 1490 nm$ (solid line), $1636 nm$ (dashed line), and $1700 nm$ (dotted line). Such radii correspond to minima of $Q_{z} (z = 0), Q_{b}$ , or both.
Reuse & Permissions
Figure 6
Same conventions as in Fig. 5, with the spherical aberration introduced by the glass-water interface taken into account. Here $z = 0$ represents the paraxial focal point, which is at a distance $L = 7 r$ above the glass slide, as illustrated by the inset (a). The point of maximum energy density (diffraction focus) is located in between the paraxial focus and the glass slide ( $z < 0$ ). In inset (b), the negative values of the axial force efficiency $Q_{z}$ are shown as a density plot in the plane defined by the values of microsphere radius and position (in units of sphere radius).
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information