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These properties together make Bessel beams extremely useful to research in [[Optical Tweezers|optical tweezing]], as a narrow Bessel beam will maintain its required property of tight focus over a relatively long section of beam and even when partially [[occlusion|occluded]] by the dielectric particles being tweezed. Similarly, particle manipulation with acoustical tweezers may be feasible as it has been found that a [[Bessel beam]] of acoustical waves scatters and produces a [[radiation pressure|radiation force]] resulting from the exchange of momentum between the wave-field and the particle placed along its path <ref> F. G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel
These properties together make Bessel beams extremely useful to research in [[Optical Tweezers|optical tweezing]], as a narrow Bessel beam will maintain its required property of tight focus over a relatively long section of beam and even when partially [[occlusion|occluded]] by the dielectric particles being tweezed. Similarly, particle manipulation with acoustical tweezers may be feasible as it has been found that a [[Bessel beam]] of acoustical waves scatters and produces a [[radiation pressure|radiation force]] resulting from the exchange of momentum between the wave-field and the particle placed along its path <ref> F. G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel
42 beam tweezers, Annals of Physics 323 (2008) 1604-1620 </ref>, <ref> F. G. Mitri, Z. E. A. Fellah, Theory of the acoustic radiation force exerted on a sphere by a standing and quasi-standing zero-order Bessel beam tweezers of variable half-cone angles, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 55 (2008) 2469-2478 </ref>, <ref>
42 beam tweezers, Annals of Physics 323 (2008) 1604-1620 </ref>, <ref> F. G. Mitri, Z. E. A. Fellah, Theory of the acoustic radiation force exerted on a sphere by a standing and quasi-standing zero-order Bessel beam tweezers of variable half-cone angles, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 55 (2008) 2469-2478 </ref>, <ref> F. G. Mitri, Langevin acoustic radiation force of a high-order Bessel beam 1 on a rigid sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1059-1064 </ref>, <ref> F. G. Mitri, Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: Example of a high-order Bessel beam of quasi-standing waves, European Physical Journal E 28 (2009) 469-478 </ref>, <ref> F. G. Mitri, Negative Axial Radiation Force on a Fluid and Elastic Spheres Illuminated by a High-Order Bessel Beam of Progressive Waves, Journal of Physics A - Mathematical and Theoretical 42
8 (2009) 245202 </ref>.


The [[mathematics|mathematical]] function which describes a Bessel beam is a solution of [[Bessel's differential equation]], which itself arises from separable solutions to [[Laplace's equation]] and the [[Helmholtz equation]] in cylindrical coordinates.
The [[mathematics|mathematical]] function which describes a Bessel beam is a solution of [[Bessel's differential equation]], which itself arises from separable solutions to [[Laplace's equation]] and the [[Helmholtz equation]] in cylindrical coordinates.

Revision as of 23:10, 14 December 2009

A Bessel beam is a field of electromagnetic [1], [2], acoustic or even gravitational radiation wave-field whose amplitude is described by a Bessel function of the first kind. It is particularly important to note that the fundamental zero-order Bessel beam has an amplitude maximum at the origin, whereas a high-order Bessel beam (HOBB) possesses an axial phase singularity at the transverse origin where the amplitude vanishes as expected from the mathematical descriptive nature of the high-order Bessel function of the first kind. A true Bessel beam is non-diffractive. This means that as it propagates, it does not diffract and spread out; this is in contrast to the usual behavior of light (or sound), which spreads out after being focussed down to a small spot.

As with a plane wave a true Bessel beam cannot be created, as it is unbounded and therefore requires an infinite amount of energy Reasonably good approximations can be made, however, and these are important in many optical applications because they exhibit little or no diffraction over a limited distance. Bessel beams are also self-healing, meaning that the beam can be partially obstructed at one point, but will re-form at a point further down the beam axis.

These properties together make Bessel beams extremely useful to research in optical tweezing, as a narrow Bessel beam will maintain its required property of tight focus over a relatively long section of beam and even when partially occluded by the dielectric particles being tweezed. Similarly, particle manipulation with acoustical tweezers may be feasible as it has been found that a Bessel beam of acoustical waves scatters and produces a radiation force resulting from the exchange of momentum between the wave-field and the particle placed along its path [3], [4], [5], [6], [7].

The mathematical function which describes a Bessel beam is a solution of Bessel's differential equation, which itself arises from separable solutions to Laplace's equation and the Helmholtz equation in cylindrical coordinates.

Approximations to Bessel beams are made in practice by focusing a Gaussian beam with an axicon lens to generate a Bessel-Gauss beam.

References

  1. ^ Kishan Dholakia (2002). "Optical micromanipulating using a self-reconstructing light beam". Retrieved 2007-02-06. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
    See also V. Garcés-Chávez (2002). "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam" (PDF). Nature. 419: 145. doi:10.1038/nature01007. Retrieved 2007-02-06. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  2. ^ D. McGloin, K. Dholakia, Bessel beams: diffraction in a new light, Contemporary Physics 46 (2005) 15-28
  3. ^ F. G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel 42 beam tweezers, Annals of Physics 323 (2008) 1604-1620
  4. ^ F. G. Mitri, Z. E. A. Fellah, Theory of the acoustic radiation force exerted on a sphere by a standing and quasi-standing zero-order Bessel beam tweezers of variable half-cone angles, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 55 (2008) 2469-2478
  5. ^ F. G. Mitri, Langevin acoustic radiation force of a high-order Bessel beam 1 on a rigid sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1059-1064
  6. ^ F. G. Mitri, Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: Example of a high-order Bessel beam of quasi-standing waves, European Physical Journal E 28 (2009) 469-478
  7. ^ F. G. Mitri, Negative Axial Radiation Force on a Fluid and Elastic Spheres Illuminated by a High-Order Bessel Beam of Progressive Waves, Journal of Physics A - Mathematical and Theoretical 42 8 (2009) 245202
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