Trapping by an optical tweezer

Following Ref. (32), we begin by computing the optical force experienced by a colloidal sphere in a conventional point-like optical tweezer as a function of the sphere's radius, $a$ , and its refractive index $n_p$ . The incident light field is obtained by setting $\varphi_j = 0$ for all of the pixels in the DOE. We focus our attention on the axial force profile, which tends to be weaker than the longitudinal force profile. Failure to achieve axial trapping is the principal failure mode of conventional optical tweezers.

The results, summarized in Fig. 2, are similar in many respects to those reported in Ref. (32). Most tellingly, Fig. 2(a) and Fig. 3 of (32) both demonstrate that particles with diameters larger than $\lambda/2$ can be trapped only if their relative refractive index is below roughly 1.4. The large domains of high-index trapping in (32) are reduced to discrete islands of stability in Fig. 2 due in part to the influence of the relay optics on the light's polarization, which was not considered in (32).

Both sets of results predict that high-index spheres can be trapped in a single-beam optical tweezer provided they are sufficiently small. This is an important observation for holographic assembly of photonic structures (33), many of which rely on high-index materials for their interesting and useful optical properties.

Figure 3 of (32) suggests that spheres smaller than roughly $\lambda/4$ cannot be trapped at all, and that the condition for marginal trapping depends strongly on refractive index for small index mismatches. This differs qualitatively from Fig. 2, which shows stable trapping for very small spheres, even with modest relative refractive indexes. The difference in this case can be ascribed to the earlier study's use of Matlab's spherical Hankel functions, which are inaccurate for large indexes and small arguments. Consequently, Fig. 2 should be considered a more faithful guide for designing optical trapping experiments.