Momentum conservation in partially coherent wave fields

S. M. Kim and Greg Gbur
Momentum flow in electromagnetic wave systems has become a topic of considerable importance in recent years with the development of optical tweezers and spanners. Although momentum conservation has been explored for deterministic wave fields, the corresponding laws for partially coherent wave fields have yet to be completely determined. In this paper we derive the frequency-domain representation for the Maxwell stress tensor for partially coherent fields and sources.

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Angular momentum of focused beams: Beyond the paraxial approximation

Paula B. Monteiro, Paulo A. Maia Neto, and H. Moysés Nussenzveig

We investigate in detail the focusing of a circularly polarized Laguerre-Gaussian laser beam [ orbital angular momentum per photon; =1(−1) for left- (right-) handed polarization] by a high-numerical-aperture objective. The diffraction-limited focused beam has unexpected properties resulting from a strong interplaybetween the angular spatial structure and the local polarization in the nonparaxial regime. In the region near the beam axis, and provided that ||=" align="bottom" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; font-size: 100%; ">2 and  and have opposite signs, the energy locally counterpropagates and the projection of the electric field onto the focal plane counter-rotates with respect to the circular polarization of the incident beam. We explicitly show that the total angular momentum flux per unit power is conserved after focusing, as expected by rotational symmetry, but the spin and orbital separate contributions change.

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Bacterial translocation motors investigated by single molecule techniques

Jean-Francois Allemand  & Berenike Maier

Translocation of DNA and protein fibers through narrow constrictions is a ubiquitous and crucial activity of bacterial cells. Bacteria use specialized machines to support macromolecular movement. A very important step toward a mechanistic understanding of these translocation machines is the characterization of their physical properties at the single molecule level. Recently, four bacterial transport processes have been characterized by nanomanipulation at the single molecule level, DNA translocation by FtsK and SpoIIIE, DNA import during transformation, and the related process of a type IV pilus retraction. With all four processes, the translocation rates, processivity, and stalling forces were remarkably high as compared with single molecule experiments with other molecular motors. Although substrates of all four processes proceed along a preferential direction of translocation, directionality has been shown to be controlled by distinct mechanisms.

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Optical tweezers with tips grown at the end of fibers by photopolymerization

Sándor Valkai, László Oroszi, and Pál Ormos

We present a method to build an optical tip at the end of a single-mode optical fiber. The tip is grown by a self-writing process: photopolymerization by the light coming from the optical fiber. We developed a technique to produce a flat end surface on the tip. The good optical quality of the tip and the output laser beam was demonstrated by the fact that a counterpropagating optical trap could be constructed by using the tips with parameters comparable to regular fiber traps. Because of the small size of the tips, the tweezers require a much smaller space than regular fiber traps.

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Optomechanics

Florian Marquardt and Steven M. Girvin

Coherent optical systems combined with micromechanical devices may enable development of ultrasensitive force sensors and quantum information processing technology, as well as permit observation of quantum behavior in large-scale structures.

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Trapping of a microsphere pendulum resonator in an optical potential

J. M. Ward, Y. Wu, V. G. Minogin, and S. Nic Chormaic

We propose a method to spatially confine or corral the movements of a micropendulum via the optical forces produced by two simultaneously excited optical modes of a photonic molecule comprising two microspherical cavities. We discuss how the cavity-enhanced optical force generated in the photonic molecule can create an optomechanical potential of about 10 eV deep and 30 pm wide, which can be used to trap the pendulum at any given equilibrium position by a simple choice of laser frequencies. This result presents opportunities for very precise all-optical self-alignment of microsystems.

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Moving live dissociated neurons with an optical tweezer

Pine J, Chow G.

The use of an optical tweezer for moving dissociated neurons was studied. The main features of the tweezers are outlined as well as the general principles of its operation. Infrared beams at 980 and 1064 nm were used, focused so as to make a trap for holding neurons and moving them. Absorption by cells at those wavelengths is very small. Experiments were done to evaluate nonsticky substrate coatings, from which neurons could be easily lifted with the tweezers. The maximum speed of cell movement as a function of laser power was determined. Detailed studies of the damage to cells as a function of beam intensity and time of exposure were made. The 980 nm beam was much less destructive, for reasons that are not understood, and could be used to safely move cells through distances of millimeters in times of seconds. An illustrative application of the use of the tweezers to load neurons without damage into plastic cages on a glass substrate was presented. The conclusion is that optical tweezers are an accessible and practical tool for helping to establish neuron cultures of cells placed in specific locations.

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Focusing of high order cylindrical vector beams

M Rashid, O M Maragò and P H Jones

We present the results of calculations of focusing high order cylindrical vector beams in the limit of high numerical aperture. We derive a form of the vectorial diffraction integrals for arbitrary radial and azimuthal mode indices and evaluate these numerically for a number of different modes. We identify combinations of mode indices and lens filling factors that produce focal volume shapes that may be of interest for a number of applications such as optical trapping, two-photon lithography or optical super-resolution. Finally we evaluate the effect of spherical aberration on the focusing.

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Optical sorting of dielectric Rayleigh spherical particles with scattering and standing waves

Adrian Neild, Tuck Wah Ng, and Winston Ming Shen Yii

An all optical method for dielectric Rayleigh particle sorting possesses significant advantages. Here, we describe an approach that applies optical scattering forces to translate varied sized particles differentially from a surface followed by the introduction of an optical standing wave to maintain and tighten the positional tolerance of the differentiated particles in the medium. Numerical simulation demonstrates the workability of this scheme; which is highly dependent on Brownian forces typically dominant at this length scale. It also shows the significant impact of temperature and medium viscosity on the operation of this technique.

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In-situ monitoring of optical deposition of carbon nanotubes onto fiber end

Ken Kashiwagi, Shinji Yamashita, and Sze Y. Set

Carbon nanotubes (CNTs) emerged as an attractive material for nonlinear optical devices. Their quasi-one-dimensional structure provided their unique nonlinear characteristics. However, one of their drawbacks is the handling method. We have proposed and demonstrated optical manipulation of CNTs to deposit them onto cores of optical fiber ends with a simple technique. Although the method is very simple, it requires precise control of the optical power. The method does not posses controllability of the CNT-layer properties. In this paper, we employed optical reflectometry to solve these problems. A 15μm diameter circular region was area-selectively coated by CNTs using highly uniform solution. The preferentially-deposited CNTs were directly, for the first time, observed by a field emission scanning electron microscope (FE-SEM).

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Optical force enhanced by plasmon resonance allowing position-sensitive synthesis and immobilization of single Ag nanoparticles on glass surfaces

Tamitake Itoh, Vasudevanpillai Biju, Mitsuru Ishikawa, Syoji Ito, and Hiroshi Miyasaka

Focused laser light in an aqueous solution of silver nitrate and disodium citrate allowed the synthesis and immobilization of single Ag particles on a glass surface. The as-synthesized Ag particles were free from aggregation. Rayleigh scattering spectra of the Ag particlesshowed a plasmon resonance band at ~490  nm. Analysis of the spectra revealed that the Ag particles have oblate-spindle shapes with ~30  nm diameter. The polarizability of the Ag nanoparticles demonstrated that soon after the formation of the particles at the focal point, optical force repels them out of the focal point and immobilizes on the glass surface. 

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Experimental study of out-of-equilibrium fluctuations in a colloidal suspension of Laponite using optical traps

Pierre Jop, Juan Ruben Gomez-Solano, Artyom Petrosyan and Sergio Ciliberto

We address the issue of the validity of the fluctuation dissipation theorem and the time evolution of viscoelastic properties during ageing of aqueous suspensions of a clay (Laponite RD) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using simultaneously passive and active microrheology techniques. For this purpose we measure the thermal fluctuations of microsized Brownian particles immersed in the colloidal glass and trapped by optical tweezers. We find that several methods based on both microrheology techniques lead to consistent and complementary results and no violation of the FDT is convincingly observed either for any frequency as low as 0.25 Hz or as an increase of the effective temperature during the formation of the viscoelastic glass. Our results are supported by the study of the probability density functions of heat fluctuations between the probe particles and the suspension transferred at different timescales. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.

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Statolith Sedimentation Kinetics and Force Transduction to the Cortical Endoplasmic Reticulum in Gravity-Sensing Arabidopsis Columella Cells

Guenther Leitz, Byung-Ho Kang, Monica E.A. Schoenwaelder and L. Andrew Staehelin

The starch statolith hypothesis of gravity sensing in plants postulates that the sedimentation of statoliths in specialized statocytes (columella cells) provides the means for converting the gravitational potential energy into a biochemical signal. We have analyzed the sedimentation kinetics of statoliths in the central S2 columella cells of Arabidopsis thaliana. The statoliths can form compact aggregates with gap sizes between statoliths approaching <30 nm. Significant intra-aggregate sliding motions of individual statoliths suggest a contribution of hydrodynamic forces to the motion of statoliths. The reorientation of the columella cells accelerates the statoliths toward the central cytoplasm within <1 s of reorientation. During the subsequent sedimentation phase, the statoliths tend to move at a distance to the cortical endoplasmic reticulum (ER) boundary and interact only transiently with the ER. Statoliths moved by laser tweezers against the ER boundary experience an elastic lift force upon release from the optical trap. High-resolution electron tomography analysis of statolith-to-ER contact sites indicate that the weight of statoliths is sufficient to locally deform the ER membranes that can potentially activate mechanosensitive ion channels. We suggest that in root columella cells, the transduction of the kinetic energy of sedimenting statoliths into a biochemical signal involves a combination of statolith-driven motion of the cytosol, statolith-induced deformation of the ER membranes, and a rapid release of kinetic energy from the ER during reorientation to activate mechanosensitive sites within the central columella cells.

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Colloidal Attraction Induced by a Temperature Gradient

R. Di Leonardo, F. Ianni and G. Ruocco

Colloidal crystals are of extreme importance for applied research and for fundamental studies in statistical mechanics. Long-range attractive interactions, such as capillary forces, can drive the spontaneous assembly of such mesoscopic ordered structures. However, long-range attractive forces are very rare in the colloidal realm. Here we report a novel strong, long-ranged attraction induced by a thermal gradient in the presence of a wall. By switching the thermal gradient on and off, we can rapidly and reversibly form stable hexagonal 2D crystals. We show that the observed attraction is hydrodynamic in nature and arises from thermally induced slip flow on particle surfaces. We used optical tweezers to measure the force law directly and compare it to an analytical prediction based on Stokes now driven by Marangoni-like forces.

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Constraining validity of the Minkowski energy-momentum tensor

Robert N. C. Pfeifer, Timo A. Nieminen, Norman R. Heckenberg, and Halina Rubinsztein-Dunlop

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimentalverification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modeling optical tweezers. These simplifications are based on neglecting the Minkowski tensor's material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions that must be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett et al., we find their prediction in agreement with that obtained using the total energy-momentum tensor.

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Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?

E. A. Hinds and Stephen M. Barnett

We consider forces on an atom due to a plane-wave light pulse. The standard view of the optical dipole force indicates that red-detuned light should attract the atom towards high intensity. While the atom is inside the pulse, this would increase the average momentum per photon from p0 to p0n, where n is the average refractive index due to the presence of the atom. We show, however, that this is the wrong conclusion and that the dispersive forces repel the atom from the light in this particular case, giving the photons a momentum p0/n. This leads us to identify Abraham's optical momentum with the kinetic momentum transfer. The form due toMinkowski is similarly associated with the canonical momentum. We consider the possibility of demonstrating this in the laboratory, and we note an unexpected connection with the Aharonov-Casher effect.

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Manipulation of microparticles in colloidal liquids by Z-scan-based optical trapping

Jin Liu, Qiao-Feng Dai, Tian-Hua Feng, Hai-Ying Liu, Li-Jun Wu, Qi Guo, Wei Hu, Song-Hao Liu, Sheng Lan, Achanta Venu Gopal, and Vyacheslav A. Trofimov

Manipulation of microparticles in colloidal liquids by using Z-scan-based optical trapping is systematically investigated. A physical model for the creation and annihilation of ordered structures in Z-scan-based optical trapping is presented theoretically and verified experimentally. Disordered, ordered, and intermediate states appearing in Z-scan trapping experiments are discussed and the conditions for realizing phase transition and observing self-induced transparency are clarified. We experimentally demonstrate the high quality and good stability of the formed structures, the sequential trapping of individual microparticles, and the multiple trapping processes. The dependence of the quality of theformed structures on trapping power, scanning speed, and the size and material of microparticles are identified.

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FDTD approach to optical forces of tightly focused vector beams on metal particles

Jian-Qi Qin, Xi-Lin Wang, Ding Jia, Jing Chen, Ya-Xian Fan, Jianping Ding, and Hui-Tian Wang

We propose an improved FDTD method to calculate the optical forces of tightly focused beams on microscopic metal particles. Comparison study on different kinds of tightly focused beams indicates that trapping efficiency can be altered by adjusting the polarization of the incident field. The results also show the size-dependence of trapping forces exerted on metal particles. Transverse tapping forces produced by different illumination wavelengths are also evaluated. The numeric simulation demonstrates the possibility of trapping moderate-sized metal particles whose radii are comparable to wavelength.

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