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A '''Bessel beam''' is a field of electromagnetic, acoustic or even gravitational radiation whose amplitude is described by a [[Bessel function of the first kind]].<ref>{{cite web|url=http://www.st-andrews.ac.uk/~atomtrap/Research/reconstruct.htm| author=Kishan Dholakia|author2=David McGloin|author3=Vene Garcés-Chávez| title=Optical micromanipulating using a self-reconstructing light beam| year=2002| accessdate=2007-02-06}}<br>See also {{cite journal|author=V. Garcés-Chávez| coauthors= D. McGloin, H. Melville, W. Sibbett and K. Dholakia| title=Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam| journal=Nature| volume= 419| year=2002| url=https://wcm.dundee.ac.uk/media/dundeewebsite/eep/documents/aomg/Nature.pdf| accessdate=2012-12-30| doi=10.1038/nature01007| pages=145–7|pmid=12226659|issue=6903| bibcode=2002Natur.419..145G}}</ref><ref>D. McGloin, K. Dholakia, Bessel beams: diffraction in a new light, Contemporary Physics 46 (2005) 15-28</ref> A true Bessel beam is non-diffractive. This means that as it propagates, it does not [[diffraction|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. 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]].
A '''Bessel beam''' is a field of electromagnetic, acoustic or even gravitational radiation whose amplitude is described by a [[Bessel function of the first kind]].<ref>{{cite web|url=http://www.st-andrews.ac.uk/~atomtrap/Research/reconstruct.htm| author=Kishan Dholakia|author2=David McGloin|author3=Vene Garcés-Chávez| title=Optical micromanipulating using a self-reconstructing light beam| year=2002| accessdate=2007-02-06}}<br>See also {{cite journal|author=V. Garcés-Chávez| coauthors= D. McGloin, H. Melville, W. Sibbett and K. Dholakia| title=Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam| journal=Nature| volume= 419| year=2002| url=https://wcm.dundee.ac.uk/media/dundeewebsite/eep/documents/aomg/Nature.pdf| accessdate=2012-12-30| doi=10.1038/nature01007| pages=145–7|pmid=12226659|issue=6903| bibcode=2002Natur.419..145G}}</ref><ref>D. McGloin, K. Dholakia, Bessel beams: diffraction in a new light, Contemporary Physics 46 (2005) 15-28</ref> A true Bessel beam is non-diffractive. This means that as it propagates, it does not [[diffraction|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. 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]].


As with a [[plane wave]] a true Bessel beam cannot be created, as it is unbounded and would require an infinite amount of [[energy]]. Reasonably good approximations can be made, however, and these are important in many [[optics|optical]] applications because they exhibit little or no diffraction over a limited distance. Approximations to Bessel beams are made in practice by focusing a [[Gaussian beam]] with an [[axicon]] lens to generate a Bessel-Gauss beam, by axisymmetric diffraction gratings <ref>{{cite journal|last=Jiménez|first=N.|coauthors=V. Romero-García, R. Picó, A. Cebrecos, V. J. Sánchez-Morcillo, L. M. Garcia-Raffi, J. V. Sánchez-Pérez and K. Staliunas. |title=Acoustic Bessel-like beam formation by an axisymmetric grating|journal=European Physics Letters|date= 2 April 2014|volume=106|issue=2|pages=24005|doi=10.1209/0295-5075/106/24005|url=http://epljournal.edpsciences.org/articles/epl/abs/2014/08/epl16221/epl16221.html|accessdate=14 July 2014|bibcode = JimenezBessels}}</ref>, or by placing a narrow annular aperture in the [[far field]].<ref>{{cite journal|last=Durnin|first=J.|coauthors=J. J. Miceli, Jr. and J. H. Eberly|title=Diffraction-free beams|journal=Physical Review Letters|date=13 April 1987|volume=58|issue=15|pages=1499–1501|doi=10.1103/PhysRevLett.58.1499|url=http://prl.aps.org/abstract/PRL/v58/i15/p1499_1|accessdate=13 October 2012|bibcode = 1987PhRvL..58.1499D }}</ref>
As with a [[plane wave]] a true Bessel beam cannot be created, as it is unbounded and would require an infinite amount of [[energy]]. Reasonably good approximations can be made, however, and these are important in many [[optics|optical]] applications because they exhibit little or no diffraction over a limited distance. Approximations to Bessel beams are made in practice by focusing a [[Gaussian beam]] with an [[axicon]] lens to generate a Bessel-Gauss beam, by axisymmetric diffraction gratings <ref>{{cite journal|last=Jiménez|first=N.|coauthors=V. Romero-García, R. Picó, A. Cebrecos, V. J. Sánchez-Morcillo, L. M. Garcia-Raffi, J. V. Sánchez-Pérez and K. Staliunas. |title=Acoustic Bessel-like beam formation by an axisymmetric grating|journal=Europhysics Letters|date= 2 April 2014|volume=106|issue=2|pages=24005|doi=10.1209/0295-5075/106/24005|url=http://epljournal.edpsciences.org/articles/epl/abs/2014/08/epl16221/epl16221.html|accessdate=14 July 2014}}</ref>, or by placing a narrow annular aperture in the [[far field]].<ref>{{cite journal|last=Durnin|first=J.|coauthors=J. J. Miceli, Jr. and J. H. Eberly|title=Diffraction-free beams|journal=Physical Review Letters|date=13 April 1987|volume=58|issue=15|pages=1499–1501|doi=10.1103/PhysRevLett.58.1499|url=http://prl.aps.org/abstract/PRL/v58/i15/p1499_1|accessdate=13 October 2012|bibcode = 1987PhRvL..58.1499D }}</ref>


The properties of Bessel beams<ref>F. O. Fahrbach, P. Simon, A. Rohrbach, Microscopy with self-reconstructing beams, Nature Photonics 4 (2010) 780–785</ref><ref>F. G. Mitri, Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere. Optics Letters 36 (2011) 766-768</ref> make them extremely useful for [[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 [[wikt:occlusion|occluded]] by the dielectric particles being tweezed. Similarly, particle manipulation with acoustical tweezers may be feasible with a Bessel beam that scatters<ref>P. L. Marston, Scattering of a Bessel beam by a sphere, J. Acoust. Soc. Am. 121 (2007) 753-758</ref><ref>G. T. Silva, Off-axis scattering of an ultrasound bessel beam by a sphere. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 58 (2011) 298-304</ref><ref>F. G. Mitri, G. T. Silva, Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere, Wave Motion 48 (2011) 392-400</ref> and produces a [[radiation pressure|radiation force]] resulting from the exchange of acoustic momentum between the wave-field and a particle placed along its path.<ref>F. G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel 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 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 (2009) 245202</ref><ref>F. G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840-2850</ref><ref>F. G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 23 56 (2009) 1100-1103</ref><ref>P. L. Marston, Axial radiation force of a bessel beam on a sphere and direction reversal of the force, J. Acoust. Soc. Am. 120 (2006) 3518-3524</ref><ref>P. L. Marston, Radiation force of a helicoidal Bessel beam on a sphere, J. Acoust. Soc. Am. 125 (2009) 3539-3547</ref>
The properties of Bessel beams<ref>F. O. Fahrbach, P. Simon, A. Rohrbach, Microscopy with self-reconstructing beams, Nature Photonics 4 (2010) 780–785</ref><ref>F. G. Mitri, Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere. Optics Letters 36 (2011) 766-768</ref> make them extremely useful for [[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 [[wikt:occlusion|occluded]] by the dielectric particles being tweezed. Similarly, particle manipulation with acoustical tweezers may be feasible with a Bessel beam that scatters<ref>P. L. Marston, Scattering of a Bessel beam by a sphere, J. Acoust. Soc. Am. 121 (2007) 753-758</ref><ref>G. T. Silva, Off-axis scattering of an ultrasound bessel beam by a sphere. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 58 (2011) 298-304</ref><ref>F. G. Mitri, G. T. Silva, Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere, Wave Motion 48 (2011) 392-400</ref> and produces a [[radiation pressure|radiation force]] resulting from the exchange of acoustic momentum between the wave-field and a particle placed along its path.<ref>F. G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel 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 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 (2009) 245202</ref><ref>F. G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840-2850</ref><ref>F. G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 23 56 (2009) 1100-1103</ref><ref>P. L. Marston, Axial radiation force of a bessel beam on a sphere and direction reversal of the force, J. Acoust. Soc. Am. 120 (2006) 3518-3524</ref><ref>P. L. Marston, Radiation force of a helicoidal Bessel beam on a sphere, J. Acoust. Soc. Am. 125 (2009) 3539-3547</ref>

Revision as of 23:49, 13 July 2014

Diagram of Axicon and resulting Bessel Beam
Cross-section of the Bessel beam and graph of intensity
Bessel beam re-forming central bright area after obstruction

A Bessel beam is a field of electromagnetic, acoustic or even gravitational radiation whose amplitude is described by a Bessel function of the first kind.[1][2] 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. 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.

As with a plane wave a true Bessel beam cannot be created, as it is unbounded and would require 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. Approximations to Bessel beams are made in practice by focusing a Gaussian beam with an axicon lens to generate a Bessel-Gauss beam, by axisymmetric diffraction gratings [3], or by placing a narrow annular aperture in the far field.[4]

The properties of Bessel beams[5][6] make them extremely useful for 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 with a Bessel beam that scatters[7][8][9] and produces a radiation force resulting from the exchange of acoustic momentum between the wave-field and a particle placed along its path.[10][11][12][13][14][15][16][17][18]

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. The fundamental zero-order Bessel beam has an amplitude maximum at the origin, while a high-order Bessel beam (HOBB) has an axial phase singularity along the beam axis; the amplitude is zero there. HOBBs can be of vortex (helicoidal) or non-vortex types.[19]

X-waves are special superpositions of Bessel beams which travel at constant velocity.

Mathieu beams and parabolic (Weber) beams [20] are other types of non-diffractive beams that have the same non-diffractive and self-healing properties of Bessel beams but different transverse structures.

Accelerating Bessel beams

In 2012 it was theoretically proved [21] and experimentally demonstrated [22] that, with a special manipulation of their initial phase, Bessel beams can be made to accelerate along arbitrary trajectories in free space. These beams can be considered as hybrids that combine the symmetric profile of standard Bessel beam with the self-acceleration property of Airy beam and its counterparts. Previous efforts to produce accelerating Bessel beams included beams with helical [23] and sinusoidal [24] trajectories as well as the early effort for beams with piecewise straight trajectories.[25]

See also

References

  1. ^ Kishan Dholakia; David McGloin; Vene Garcés-Chávez (2002). "Optical micromanipulating using a self-reconstructing light beam". Retrieved 2007-02-06.
    See also V. Garcés-Chávez (2002). "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam" (PDF). Nature. 419 (6903): 145–7. Bibcode:2002Natur.419..145G. doi:10.1038/nature01007. PMID 12226659. Retrieved 2012-12-30. {{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. ^ Jiménez, N. (2 April 2014). "Acoustic Bessel-like beam formation by an axisymmetric grating". Europhysics Letters. 106 (2): 24005. doi:10.1209/0295-5075/106/24005. Retrieved 14 July 2014. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  4. ^ Durnin, J. (13 April 1987). "Diffraction-free beams". Physical Review Letters. 58 (15): 1499–1501. Bibcode:1987PhRvL..58.1499D. doi:10.1103/PhysRevLett.58.1499. Retrieved 13 October 2012. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  5. ^ F. O. Fahrbach, P. Simon, A. Rohrbach, Microscopy with self-reconstructing beams, Nature Photonics 4 (2010) 780–785
  6. ^ F. G. Mitri, Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere. Optics Letters 36 (2011) 766-768
  7. ^ P. L. Marston, Scattering of a Bessel beam by a sphere, J. Acoust. Soc. Am. 121 (2007) 753-758
  8. ^ G. T. Silva, Off-axis scattering of an ultrasound bessel beam by a sphere. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 58 (2011) 298-304
  9. ^ F. G. Mitri, G. T. Silva, Off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid sphere, Wave Motion 48 (2011) 392-400
  10. ^ F. G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers, Annals of Physics 323 (2008) 1604-1620
  11. ^ 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
  12. ^ F. G. Mitri, Langevin acoustic radiation force of a high-order Bessel beam on a rigid sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1059-1064
  13. ^ 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
  14. ^ 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 (2009) 245202
  15. ^ F. G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840-2850
  16. ^ F. G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 23 56 (2009) 1100-1103
  17. ^ P. L. Marston, Axial radiation force of a bessel beam on a sphere and direction reversal of the force, J. Acoust. Soc. Am. 120 (2006) 3518-3524
  18. ^ P. L. Marston, Radiation force of a helicoidal Bessel beam on a sphere, J. Acoust. Soc. Am. 125 (2009) 3539-3547
  19. ^ F. G. Mitri, Linear axial scattering of an acoustical high-order Bessel trigonometric beam by compressible soft fluid spheres, J. Appl. Phys. 109 (2011) 014916
  20. ^ M.A. Bandres, J.C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wave fields," Opt. Lett. 29, 44-46 (2004).
  21. ^ Chremmos, Ioannis; Zhigang Chen; Christodoulides; Demetrios, Efremidis, Nikolaos (2012). "Bessel-like optical beams with arbitrary trajectories". Optics Letters. 37 (23): 5003. Bibcode:2012OptL...37.5003C. doi:10.1364/OL.37.005003.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  22. ^ Juanying, Zhao (2013). "Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories". Optics Letters. 38 (4): 498. Bibcode:2013OptL...38..498Z. doi:10.1364/OL.38.000498. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  23. ^ Jarutis, Vygandas; Matijošius, Aidas; DiTrapani, Paolo; Piskarskas, Algis (2009). "Spiraling zero-order Bessel beam". Optics Letters. 34 (14): 2129. Bibcode:2009OptL...34.2129J. doi:10.1364/OL.34.002129.
  24. ^ Morris, JE; Čižmár, T; Dalgarno, HIC; Marchington, RF; Gunn-Moore, FJ; Dholakia, K (2010). "Realization of curved Bessel beams: propagation around obstructions". Journal of Optics. 12 (12): 124002. Bibcode:2010JOpt...12l4002M. doi:10.1088/2040-8978/12/12/124002.
  25. ^ Rosen, Joseph; Yariv, Amnons (1995). "Snake beam: a paraxial arbitrary focal line". Optics Letters. 20 (20): 2042. Bibcode:1995OptL...20.2042R. doi:10.1364/OL.20.002042.
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