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Optics Letters

Stability of radiation-pressure particle traps: an optical Earnshaw theorem

Arthur Ashkin, J. P. Gordon

Published Oct 1, 1983• 180 citations
Publisher

Abstract

We prove an optical radiation Earnshaw theorem: A small dielectric particle cannot be trapped by using only the scattering force of optical radiation pressure. A corollary is that the gradient or dipole force is necessary to any successful optical trap. We discuss the implications of the theorem for recent proposals for the optical trapping of neutral atoms.

DOI
10.1364/ol.8.000511

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Optical forces, or light pressure, was derived by Maxwell, and was demonstrated at the start of the 20th century by Lebedev and by Nichols and Hull. It was studied in the 1908 Ph.D. thesis of Peter Debye on comet tails. A good review is found in Ref. [1] and in the Nobel Lecture of Bill Phillips [2]. The possibility of using such optical forces for controlling the motion and position of matter was discussed in considerable detail in very many of the early papers of Art Ashkin [3, 4], the person we honor at this symposium. In Ref. [3] he described the observation of trapped microspheres in laser light, and suggested that closely related methods could be used for confining atoms to a small region of space in a vacuum chamber. In Ref. [4] he and Jim Gordon warned that you have to think carefully about it. They proved that trapping with forces proportional to the Poynting vector couldn’t work, in analogy to the Earnshaw theorem of electrostatics, but that the trapping in [3] depended on the gradient of intensity. In many other papers he advanced the field, and is widely credited as the inventor of optical tweezers, a topic discussed by other speakers at this symposium.

Frontiers in Optics•Jan 1, 2010•0 citations
We prove an optical radiation Earnshaw theorem: A small dielectric particle cannot be trapped by using only the scattering force of optical radiation pressure. A corollary is that the gradient or dipole force is necessary to any successful optical trap. We discuss the implications of the theorem for recent proposals for the optical trapping of neutral atoms.
Radiation pressure forces have been proposed for making stable optical traps for neutral atoms and other dielectric particles. Recently introduced optodynamic or alternating beam traps based on the scattering force are compared with cw traps based on the gradient force. Trapping experiments on micron-sized dielectric particles are described which demonstrate the basic principles of alternating beam light trapping. The relationship of these traps to the optical Earnshaw theorem is considered. The implications for trapping of recently demonstrated sources of slow atoms are also discussed.
The new principle of radiation-pressure trapping of neutral dielectric particles by means of alternating light beams was demonstrated in an optical levitation experiment. Stable trapping of micron-sized spheres was observed due to alternating scattering-force fields under conditions where stable cw trapping was not possible. Application of this principle to neutral-atom trapping as a means of circumvention of the optical Earnshaw theorem is suggested. A new stable cw optical trap for spheres was also discovered.
Optical forces, or light pressure, was derived by Maxwell, and was demonstrated at the start of the 20th century by Lebedev and by Nichols and Hull. It was studied in the 1908 Ph.D. thesis of Peter Debye on comet tails. A good review is found in Ref. [1] and in the Nobel Lecture of Bill Phillips [2]. The possibility of using such optical forces for controlling the motion and position of matter was discussed in considerable detail in very many of the early papers of Art Ashkin [3, 4], the person we honor at this symposium. In Ref. [3] he described the observation of trapped microspheres in laser light, and suggested that closely related methods could be used for confining atoms to a small region of space in a vacuum chamber. In Ref. [4] he and Jim Gordon warned that you have to think carefully about it. They proved that trapping with forces proportional to the Poynting vector couldn’t work, in analogy to the Earnshaw theorem of electrostatics, but that the trapping in [3] depended on the gradient of intensity. In many other papers he advanced the field, and is widely credited as the inventor of optical tweezers, a topic discussed by other speakers at this symposium.