Optical Forces Arising from Phase Gradients

We demonstrate both theoretically and experimentally that phase gradients in a light field can be used to create a new category of optical traps complementary to the more familiar intensity-gradient traps known as optical tweezers. We further show that the work done by phase-gradient forces is path dependent and briefly discuss some ramifications of this nonconservativity.

Figure 1

(a) Schematic representation of the optimized holographic optical trapping system using shape-phase holography to project extended optical traps. (b) Experimental realization of a holographic line trap carrying a phase gradient in the $\widehat{\mathit{x}}$ direction, imaged in the plane of best focus. (c) Focal pattern of a holographic ring trap with $\ell =30$.

Figure 2

Dependence of mean velocity $v$ on phase-gradient $q$. Insets: Axial slices in the $xz$ plane through the line trap’s three-dimensional intensity distribution at two values of $q$.

Figure 3

(a) Phase-gradient barrier and (b) phase-gradient well in a uniformly bright line trap. (1) Two $1.5\mu \mathrm{m}$ diameter silica spheres trapped on the line. (2) The uniform in-plane intensity of the focused line. (3) Axial section through the measured intensity, showing the divergence (a3) and convergence (b3) due to the phase profile. Scale bar indicates $5\mu \mathrm{m}$.

Figure 4

Colloidal transport driven by azimuthal phase gradients in holographic ring traps. (a) Computed axial section through a holographic ring trap of radius $R=20\mu \mathrm{m}$ and helicity $\ell =30$. (b) Volumetric representation of the measured three-dimensional intensity field in a holographic ring trap of radius $R=20\mu \mathrm{m}$ and $\ell =10$. Data points show the peak speed $v$ of a single colloidal silica sphere circulating around the ring in (b) as a function of topological charge $\ell$.