Physics of optical tweezers.

We outline the basic principles of optical tweezers as well as the fundamental theory underlying optical tweezers. The optical forces responsible for trapping result from the transfer of momentum from the trapping beam to the particle and are explained in terms of the momenta of incoming and reflected or refracted rays. We also consider the angular momentum flux of the beam in order to understand and explain optical torques. In order to provide a qualitative picture of the trapping, we treat the particle as a weak positive lens and the forces on the lens are shown. However, this representation does not provide quantitative results for the force. We, therefore, present results of applying exact electromagnetic theory to optical trapping. First, we consider a tightly focused laser beam. We give results for trapping of spherical particles and examine the limits of trappability in terms of type and size of the particles. We also study the effect of a particle on the beam. This exact solution reproduces the same qualitative effect as when treating the particle as a lens where changes in the convergence or divergence and in the direction of the trapping beam result in restoring forces acting on the particle. Finally, we review the fundamental theory of optical tweezers.

[1]  Stephen M. Barnett,et al.  Optical Angular Momentum , 2003 .

[2]  J. Maxwell.  A Treatise on Electricity and Magnetism , 1873, Nature.

[3]  H. Rubinsztein-Dunlop,et al.  Measurement of the index of refraction of single microparticles. , 2006, Physical review letters.

[4]  J. Lock,et al.  Partial-wave representations of laser beams for use in light-scattering calculations. , 1995, Applied optics.

[5]  G. Mie.  Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen , 1908 .

[6]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[7]  H. Rubinsztein-Dunlop,et al.  Orientation of biological cells using plane-polarized Gaussian beam optical tweezers , 2003, physics/0308105.

[8]  R. Atkinson.  Energy and Angular Momentum in Certain Optical Problems , 1935 .

[9]  Robert C. Gauthier,et al.  Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects , 1997 .

[10]  Norman R. Heckenberg,et al.  Optical Particle Trapping with Higher-order Doughnut Beams Produced Using High Efficiency Computer Generated Holograms , 1995 .

[11]  H. Rubinsztein-Dunlop,et al.  Optical application and measurement of torque on microparticles of isotropic nonabsorbing material , 2003, physics/0309122.

[12]  H. Inaba,et al.  Optical trapping and rotational manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams , 1991 .

[13]  Yael Roichman,et al.  Holographic optical trapping. , 2006, Applied optics.

[14]  D. Grier.  A revolution in optical manipulation , 2003, Nature.

[15]  C. cohen-tannoudji,et al.  Nobel Lecture: Manipulating atoms with photons , 1998 .

[16]  Peter Lebedew.  Experimental Investigation of the Pressure of Light , 1902 .

[17]  M E Friese,et al.  Optical torque controlled by elliptical polarization. , 1998, Optics letters.

[18]  C. cohen-tannoudji.  Manipulating atoms with photons , 1998 .

[19]  Norman R. Heckenberg,et al.  Optical measurement of microscopic torques , 2001 .

[20]  Norman R. Heckenberg,et al.  Angular momentum of a strongly focused Gaussian beam , 2008 .

[21]  E. F. Nichols,et al.  Pressure Due to Light and Heat Radiation , 1902 .

[22]  G Gouesbet,et al.  Prediction of reverse radiation pressure by generalized Lorenz-Mie theory. , 1996, Applied optics.

[23]  H. Rubinsztein-Dunlop,et al.  Optical alignment and spinning of laser-trapped microscopic particles , 1998, Nature.

[24]  Michael W. Berns,et al.  Radiation trapping forces on microspheres with optical tweezers , 1993 .

[25]  M. Nieto-Vesperinas,et al.  Time-averaged total force on a dipolar sphere in an electromagnetic field. , 2000, Optics letters.

[26]  D. Griffiths.  Introduction to Electrodynamics , 2017 .

[27]  H. Ukita,et al.  Theoretical Demonstration of a Newly Designed Micro-Rotator Driven by Optical Pressure on a Light Incident Surface , 1997 .

[28]  H. Rubinsztein-Dunlop,et al.  Calculation of the T-matrix: general considerations and application of the point-matching method , 2003 .

[29]  G. J. Brakenhoff,et al.  Theoretical study of optically induced forces on spherical particles in a single beam trap. I: Rayleight scatterers , 1992 .

[30]  Norman R. Heckenberg,et al.  Computational modeling of optical tweezers , 2004, SPIE Optics + Photonics.

[31]  Otto.  Algebraic structure of embedded Abelian chiral gauge theories. , 1993, Physical review. D, Particles and fields.

[32]  P. A. Maia Neto,et al.  Theory of trapping forces in optical tweezers , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[33]  J. Humblet,et al.  Sur le moment d'impulsion d'une onde électromagnétique , 1943 .

[34]  M J Padgett,et al.  Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. , 2002, Physical review letters.

[35]  A. Ashkin,et al.  History of optical trapping and manipulation of small-neutral particle, atoms, and molecules , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[36]  S. Chu.  Nobel Lecture: The manipulation of neutral particles , 1998 .

[37]  H. M. Nussenzveig,et al.  Theory of optical tweezers , 1999 .

[38]  Steven M Block,et al.  Resource Letter: LBOT-1: Laser-based optical tweezers. , 2003, American journal of physics.

[39]  J. Maxwell.  A Dynamical Theory of the Electromagnetic Field , .

[40]  Gérard Gouesbet,et al.  VALIDITY OF THE LOCALIZED APPROXIMATION FOR ARBITRARY SHAPED BEAMS IN THE GENERALIZED LORENZ-MIE THEORY FOR SPHERES , 1999 .

[41]  Steven M. Block,et al.  Making light work with optical tweezers , 1992, Nature.

[42]  G. Gouesbet.  EXACT DESCRIPTION OF ARBITRARY-SHAPED BEAMS FOR USE IN LIGHT-SCATTERING THEORIES , 1996 .

[43]  J. Lock.  Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force. , 2004, Applied optics.

[44]  A. M. Stewart,et al.  Angular momentum of the electromagnetic field: the plane wave paradox resolved , 2005 .

[45]  L A B A M Clyde Hardin,et al.  The scientific work of the reverend John Michell , 1966 .

[46]  John Henry Poynting,et al.  The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light , 1909 .

[47]  A. Ashkin.  Acceleration and trapping of particles by radiation pressure , 1970 .

[48]  P. Waterman.  Matrix formulation of electromagnetic scattering , 1965 .

[49]  Johannes Courtial,et al.  3D manipulation of particles into crystal structures using holographic optical tweezers. , 2004, Optics express.

[50]  N. A. Logan.  Survey of some early studies of the scattering of plane waves by a sphere , 1965 .

[51]  H. Rubinsztein-Dunlop,et al.  Multipole Expansion of Strongly Focussed Laser Beams , 2003 .

[52]  B. U. Felderhof,et al.  Force, torque, and absorbed energy for a body of arbitrary shape and constitution in an electromagnetic radiation field , 1996 .

[53]  E. F. Nichols,et al.  A Preliminary Communication on the Pressure of Heat and Light Radiation , 1901 .

[54]  James H. Crichton,et al.  THE MEASURABLE DISTINCTION BETWEEN THE SPIN AND ORBITAL ANGULAR MOMENTA OF ELECTROMAGNETIC RADIATION , 2000 .

[55]  S. Chu.  The manipulation of neutral particles , 1998 .

[56]  Miles J. Padgett,et al.  The mechanism for energy transfer in the rotational frequency shift of a light beam , 2004 .

[57]  Kishan Dholakia,et al.  Optical tweezers in a new light , 2003 .

[58]  Michael W. Berns,et al.  Laser trapping in cell biology , 1990 .

[59]  H. Rubinsztein-Dunlop,et al.  Optical trapping of absorbing particles , 2003, physics/0310022.

[60]  He,et al.  Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. , 1995, Physical review letters.

[61]  A. Ashkin,et al.  Optical trapping and manipulation of neutral particles using lasers. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[62]  G. Spalding,et al.  Computer-generated holographic optical tweezer arrays , 2000, cond-mat/0008414.

[63]  S. Barnett,et al.  Local transfer of optical angular momentum to matter , 2005 .

[64]  C. Tropea,et al.  Light Scattering from Small Particles , 2003 .

[65]  Norman R. Heckenberg,et al.  Two controversies in classical electromagnetism , 2006, SPIE Optics + Photonics.

[66]  S. Kuo,et al.  Using Optics to Measure Biological Forces and Mechanics , 2001, Traffic.

[67]  A G Hoekstra,et al.  Radiation forces in the discrete-dipole approximation. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[68]  Tomasz Grzegorczyk,et al.  Ab initio study of the radiation pressure on dielectric and magnetic media. , 2005, Optics express.

[69]  S. Chu,et al.  Observation of a single-beam gradient force optical trap for dielectric particles. , 1986, Optics letters.

[70]  Duncan A. Robertson,et al.  Rotational frequency shift of a light beam , 1998 .

[71]  James Clerk Maxwell,et al.  VIII. A dynamical theory of the electromagnetic field , 1865, Philosophical Transactions of the Royal Society of London.

[72]  H. Rubinsztein-Dunlop,et al.  Numerical modelling of optical trapping , 2001 .

[73]  P. Waterman,et al.  SYMMETRY, UNITARITY, AND GEOMETRY IN ELECTROMAGNETIC SCATTERING. , 1971 .

[74]  Norman R. Heckenberg,et al.  Microrheology using dual-beam optical tweezers and ultrasensitive force measurements , 2005, SPIE OPTO.

[75]  J. Lock.  Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration. , 2004, Applied optics.

[76]  Halina Rubinsztein-Dunlop,et al.  Optical microrheology using rotating laser-trapped particles. , 2004, Physical review letters.

[77]  Bruce T. Draine,et al.  The discrete-dipole approximation and its application to interstellar graphite grains , 1988 .

[78]  W. Phillips.  Nobel Lecture: Laser cooling and trapping of neutral atoms , 1998 .

[79]  Stephen R. Quake,et al.  The dynamics of partially extended single molecules of DNA , 1997, Nature.

[80]  M W Berns,et al.  Parametric study of the forces on microspheres held by optical tweezers. , 1994, Applied optics.

[81]  Norman R. Heckenberg,et al.  Optical torque and symmetry , 2004, SPIE Optics + Photonics.

[82]  David G. Grier,et al.  Optical tweezers in colloid and interface science , 1997 .

[83]  A. Ashkin.  Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. , 1992, Methods in cell biology.

[84]  J. H. Poynting.  XV. On the transfer of energy in the electromagnetic field , 1884, Philosophical Transactions of the Royal Society of London.

[85]  Miles J. Padgett,et al.  IV The Orbital Angular Momentum of Light , 1999 .

[86]  Michael W Berns,et al.  Internet‐based robotic laser scissors and tweezers microscopy , 2005, Microscopy research and technique.

[87]  Samarendra K. Mohanty,et al.  Self-rotation of red blood cells in optical tweezers: prospects for high throughput malaria diagnosis , 2004, Biotechnology Letters.

[88]  Norman R. Heckenberg,et al.  Optically driven micromachines: progress and prospects , 2005, SPIE Micro + Nano Materials, Devices, and Applications.

[89]  Toshimitsu Asakura,et al.  Radiation forces on a dielectric sphere in the Rayleigh scattering regime , 1996 .

[90]  E. Riis,et al.  Laser cooling and trapping of neutral atoms , 1997 .