We demonstrate both theoretically and experimentally that gradients in the phase of a light field exert forces on illuminated objects, including forces transverse to the direction of propagation. This effect generalizes the notion of the photon orbital angular momentum carried by helical beams of light. We further demonstrate that these forces generally violate conservation of energy, and briefly discuss some ramifications of their non-conservativity.Light's ability to exert forces has been recognized since Kepler's De Cometis of 1619 described the deflection of comet tails by the sun's rays. Maxwell demonstrated that the momentum flux in a beam of light is proportional to the intensity and can be transferred to illuminated objects, resulting in radiation pressure that pushes objects along the direction of propagation. This axial force has been distinguished from the transverse torque exerted by helical beams of light carrying orbital angular momentum (OAM) [1]. We demonstrate theoretically and confirm experimentally that OAM-induced torque is a special case of a general class of forces arising from phase gradients in beams of light. We also demonstrate that phase-gradient forces are generically non-conservative, and combine them with the conservative forces exerted by intensity gradients to create novel optical traps with structured force profiles.Our experimental demonstrations of phase-gradient forces make use of extended optical traps created through shape-phase holography [2,3,4] in an optimized [5] holographic optical trapping [6,7] system. Holographically sculpted intensity gradients enable these generalized optical tweezers [8] to confine micrometer-scale colloidal particles to one-dimensional curves embedded in three dimensions. Independent control over the intensity and phase profiles along the curve then provide an ideal model system for characterizing the forces generated by phase gradients in beams of light. OPTICAL FORCES DUE TO PHASE GRADIENTSThe vector potential describing a beam of light of frequency ω and polarizationε may be written in the form A(r, t) = A(r) exp (i ωt)ε.(1)Assuming uniform polarization (and therefore a form of the paraxial approximation), the spatial dependence,is characterized by a non-negative real-valued amplitude, u(r), and a real-valued phase Φ(r). For a plane wave propagating in theẑ direction, Φ(r) = −kz, where k = n m ω/c is the light's wavenumber, c is the speed of light in vacuum, and n m is the refractive index of the medium. Imposing a transverse phase profile ϕ(r) on the wavefronts of such a beam yields the more general formwhereẑ · ∇ϕ = 0 and where the the direction of the wavevector,now varies with position. The associated electric and magnetic fields are given in the Lorenz gauge by E(r, t) = − ∂A(r, t) ∂t and (5)where µ is the magnetic permeability of the medium, which we assume to be linear and isotropic. Following the commonly accepted Abraham formulation [9], the momentum flux carried by the beam iswhere I(r) = u 2 (r) is the light's intensity, and where w...

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The video stream captured by an in-line holographic microscope can be analyzed on a frame-by-frame basis to track individual colloidal particles' three-dimensional motions with nanometer resolution, and simultaneously to measure their sizes and refractive indexes. Through a combination of hardware acceleration and software optimization, this analysis can be carried out in near real time with off-the-shelf instrumentation. An efficient particle identification algorithm automates initial position estimation with sufficient accuracy to enable unattended holographic tracking and characterization. This technique's resolution for particle size is fine enough to detect molecular-scale coatings on the surfaces of colloidal spheres, without requiring staining or fluorescent labeling. We demonstrate this approach to label-free holographic flow cytometry by detecting the binding of avidin to biotinylated polystyrene spheres.

The video stream captured by an in-line holographic microscope can be analyzed on a frame-by-frame basis to track individual colloidal particles' three-dimensional motions with nanometer resolution, and simultaneously to measure their sizes and refractive indexes. An efficient particle-tracking algorithm automates initial position estimation with sufficient accuracy to enable unattended holographic particle tracking and characterization. In this work, we demonstrated this approach to flow visualization in a microfluidic channel and also to flow cytometry of micrometer-scale colloidal spheres.