Abstract

We show that a photon detector, sensitive to the magnetic field or to the gradient of electric field, can help to characterize the quantum properties of spatially-dependent optical fields. We discuss the excitation of an atom through magnetic dipole or electric quadrupole transitions with the photons of a Bessel beam or a Laguerre-Gauss (LG) beams. These spiral beams are shown to be not true hollow beams, due to the presence of magnetic fields and gradients of electric fields on beam axis. This approach paves the way to an analysis at the quantum level of the propagating light beams having a complicated spatial structure.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
    [CrossRef]
  2. S. M. Barnett,"On the quantum core of an optical vortex," J. Mod. Opt. 55, 2279-2292 (2008).
    [CrossRef]
  3. S. M. Barnett and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670-678 (1994).
    [CrossRef]
  4. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
    [CrossRef] [PubMed]
  5. See e.g. : L. Allen, S. M. Barnett, and M. J. Padgett, "Optical Angular Momentum "(IOP, Bristol, 2003).
  6. E. Santamato, "Photon orbital angular momentum: problems and perspectives," Fortschr. Phys. 52, 1141-1153 (2004).
    [CrossRef]
  7. S. J. van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum. Opt. 6, 445-457 (1994).
    [CrossRef]
  8. F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
    [CrossRef]
  9. S. Tojo, M. Hasuo, and T. Fujimoto, "Absorption Enhancement of an Electric Quadrupole Transition of Cesium Atoms in an Evanescent Field," Phys. Rev. Lett. 92, 053001 (2004).
    [CrossRef] [PubMed]
  10. K. G. Lee and H. W. Kihm, "Vector field microscopic imaging of light," Nat. Photonics 1, 53 (2006).
    [CrossRef]
  11. R. H. Dicke, "Angular Momentum of a Real Field," Phys.Rev. 97, 536-539 (1955).
    [CrossRef]
  12. A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
    [CrossRef] [PubMed]
  13. Notice that in nonlinear optics experiments, like in Ref. [11] or S. Barreiro, J. W. R. Tabosa, "Generation of Light Carrying Orbital Angular Momentum via Induced Coherence Grating in Cold Atoms." Phys. Rev. Lett. 90, 133001 (2003), the phase-matched emission implies an averaging over several wavelengths
    [CrossRef] [PubMed]
  14. M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
    [CrossRef] [PubMed]
  15. N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, "Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead," Opt. Express. 13, 10440-10447 ‖2005|.
    [CrossRef] [PubMed]
  16. Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, "Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization," Opt. Lett. 32, 2357-2359 (2007).
  17. V. V. Klimov and M. Ducloy, "Quadrupole transitions near interface: general theory and application to atom inside a planar cavity," Phys. Rev. A 72, 043809 (2005).
    [CrossRef]
  18. V. V. Klimov and D. V. Guzatov, "Plasmonic atoms and Plasmonic molecules," Appl. Phys. A 89, 305-314 (2007).
    [CrossRef]

2008 (1)

S. M. Barnett,"On the quantum core of an optical vortex," J. Mod. Opt. 55, 2279-2292 (2008).
[CrossRef]

2007 (2)

2006 (2)

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

K. G. Lee and H. W. Kihm, "Vector field microscopic imaging of light," Nat. Photonics 1, 53 (2006).
[CrossRef]

2005 (2)

F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
[CrossRef]

V. V. Klimov and M. Ducloy, "Quadrupole transitions near interface: general theory and application to atom inside a planar cavity," Phys. Rev. A 72, 043809 (2005).
[CrossRef]

2004 (2)

S. Tojo, M. Hasuo, and T. Fujimoto, "Absorption Enhancement of an Electric Quadrupole Transition of Cesium Atoms in an Evanescent Field," Phys. Rev. Lett. 92, 053001 (2004).
[CrossRef] [PubMed]

E. Santamato, "Photon orbital angular momentum: problems and perspectives," Fortschr. Phys. 52, 1141-1153 (2004).
[CrossRef]

2003 (1)

Notice that in nonlinear optics experiments, like in Ref. [11] or S. Barreiro, J. W. R. Tabosa, "Generation of Light Carrying Orbital Angular Momentum via Induced Coherence Grating in Cold Atoms." Phys. Rev. Lett. 90, 133001 (2003), the phase-matched emission implies an averaging over several wavelengths
[CrossRef] [PubMed]

2001 (1)

A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

1994 (2)

S. J. van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum. Opt. 6, 445-457 (1994).
[CrossRef]

S. M. Barnett and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670-678 (1994).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

1963 (1)

R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

1955 (1)

R. H. Dicke, "Angular Momentum of a Real Field," Phys.Rev. 97, 536-539 (1955).
[CrossRef]

Allen, L.

S. M. Barnett and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670-678 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Araoka, F.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Barnett, S. M.

S. M. Barnett,"On the quantum core of an optical vortex," J. Mod. Opt. 55, 2279-2292 (2008).
[CrossRef]

S. M. Barnett and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670-678 (1994).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Bokor, N.

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, "Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization," Opt. Lett. 32, 2357-2359 (2007).

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, "Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead," Opt. Express. 13, 10440-10447 ‖2005|.
[CrossRef] [PubMed]

Clade, P.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Clays, K.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Dicke, R. H.

R. H. Dicke, "Angular Momentum of a Real Field," Phys.Rev. 97, 536-539 (1955).
[CrossRef]

Ducloy, M.

V. V. Klimov and M. Ducloy, "Quadrupole transitions near interface: general theory and application to atom inside a planar cavity," Phys. Rev. A 72, 043809 (2005).
[CrossRef]

Fujii, M.

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, "Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization," Opt. Lett. 32, 2357-2359 (2007).

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, "Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead," Opt. Express. 13, 10440-10447 ‖2005|.
[CrossRef] [PubMed]

Fujimoto, T.

S. Tojo, M. Hasuo, and T. Fujimoto, "Absorption Enhancement of an Electric Quadrupole Transition of Cesium Atoms in an Evanescent Field," Phys. Rev. Lett. 92, 053001 (2004).
[CrossRef] [PubMed]

Glauber, R. J.

R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

Guzatov, D. V.

V. V. Klimov and D. V. Guzatov, "Plasmonic atoms and Plasmonic molecules," Appl. Phys. A 89, 305-314 (2007).
[CrossRef]

Hasuo, M.

S. Tojo, M. Hasuo, and T. Fujimoto, "Absorption Enhancement of an Electric Quadrupole Transition of Cesium Atoms in an Evanescent Field," Phys. Rev. Lett. 92, 053001 (2004).
[CrossRef] [PubMed]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Iketaki, Y.

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, "Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization," Opt. Lett. 32, 2357-2359 (2007).

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, "Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead," Opt. Express. 13, 10440-10447 ‖2005|.
[CrossRef] [PubMed]

Kihm, H. W.

K. G. Lee and H. W. Kihm, "Vector field microscopic imaging of light," Nat. Photonics 1, 53 (2006).
[CrossRef]

Klimov, V. V.

V. V. Klimov and D. V. Guzatov, "Plasmonic atoms and Plasmonic molecules," Appl. Phys. A 89, 305-314 (2007).
[CrossRef]

V. V. Klimov and M. Ducloy, "Quadrupole transitions near interface: general theory and application to atom inside a planar cavity," Phys. Rev. A 72, 043809 (2005).
[CrossRef]

Lee, K. G.

K. G. Lee and H. W. Kihm, "Vector field microscopic imaging of light," Nat. Photonics 1, 53 (2006).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Natarajan, V.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Persoons, A.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Santamato, E.

E. Santamato, "Photon orbital angular momentum: problems and perspectives," Fortschr. Phys. 52, 1141-1153 (2004).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Tojo, S.

S. Tojo, M. Hasuo, and T. Fujimoto, "Absorption Enhancement of an Electric Quadrupole Transition of Cesium Atoms in an Evanescent Field," Phys. Rev. Lett. 92, 053001 (2004).
[CrossRef] [PubMed]

van Enk, S. J.

S. J. van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum. Opt. 6, 445-457 (1994).
[CrossRef]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Verbiest, T.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Watanabe, T.

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, "Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization," Opt. Lett. 32, 2357-2359 (2007).

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, "Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead," Opt. Express. 13, 10440-10447 ‖2005|.
[CrossRef] [PubMed]

Welhs, G.

A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Appl. Phys. A (1)

V. V. Klimov and D. V. Guzatov, "Plasmonic atoms and Plasmonic molecules," Appl. Phys. A 89, 305-314 (2007).
[CrossRef]

Fortschr. Phys. (1)

E. Santamato, "Photon orbital angular momentum: problems and perspectives," Fortschr. Phys. 52, 1141-1153 (2004).
[CrossRef]

J. Mod. Opt. (1)

S. M. Barnett,"On the quantum core of an optical vortex," J. Mod. Opt. 55, 2279-2292 (2008).
[CrossRef]

Nat. Photonics (1)

K. G. Lee and H. W. Kihm, "Vector field microscopic imaging of light," Nat. Photonics 1, 53 (2006).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Welhs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. M. Barnett and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670-678 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

R. J. Glauber, "The Quantum Theory of Optical Coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

Phys. Rev. A (3)

V. V. Klimov and M. Ducloy, "Quadrupole transitions near interface: general theory and application to atom inside a planar cavity," Phys. Rev. A 72, 043809 (2005).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

F. Araoka, T. Verbiest, K. Clays, and A. Persoons," Interactions of twisted light with chiral molecules: An experimental investigation," Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

S. Tojo, M. Hasuo, and T. Fujimoto, "Absorption Enhancement of an Electric Quadrupole Transition of Cesium Atoms in an Evanescent Field," Phys. Rev. Lett. 92, 053001 (2004).
[CrossRef] [PubMed]

Notice that in nonlinear optics experiments, like in Ref. [11] or S. Barreiro, J. W. R. Tabosa, "Generation of Light Carrying Orbital Angular Momentum via Induced Coherence Grating in Cold Atoms." Phys. Rev. Lett. 90, 133001 (2003), the phase-matched emission implies an averaging over several wavelengths
[CrossRef] [PubMed]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Phys.Rev. (1)

R. H. Dicke, "Angular Momentum of a Real Field," Phys.Rev. 97, 536-539 (1955).
[CrossRef]

Quantum. Opt. (1)

S. J. van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum. Opt. 6, 445-457 (1994).
[CrossRef]

Other (2)

See e.g. : L. Allen, S. M. Barnett, and M. J. Padgett, "Optical Angular Momentum "(IOP, Bristol, 2003).

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, "Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead," Opt. Express. 13, 10440-10447 ‖2005|.
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Radial dependence of the electric and magnetic fields of LG beam in the waist plane (kw0 =10, p=6, m=2)

Fig. 2.
Fig. 2.

Space distribution in the waist plane of the real part of the electric field (left) and of the magnetic field (right) in a Laguerre-Gauss beam (kw0 =6,p=6,m=2). Each distribution rotates counterclockwise at the optical frequency.

Fig. 3.
Fig. 3.

Normalized radial distribution of excitation rates of an E2 (M=±1) transitions of an atom placed in the waist plane of LG beams with (p=2, m=2,kw0=6).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Rif=T22δω2+Γ24;T=diEi(r,ω0)+miBi(r,ω0)+QijiEj(r,ω0)
{Ex,Ey}={α,β}eimφ0kdκg(κ)eihzJm(κr);
Ez=0kdκg(κ)κ2heihz[(iαβ)ei(m1)φJm1(κr)(iα+β)ei(m+1)φJm+1(κr)]
Bx=±120kdκg(κ)iκ22hk[(α±iβ)]eihz0;By=± i Bx
E(m) (r,ω)=Eowok{kU(m),kβU(m),i(αU(m)x+βU(m)y)}eikz
U(m)=Cpmw(z)[2rw(z)]mLpm(2r2w2(z))exp(r2zRw02(zR+iz)imφi(2p+m+1)arctan(zzR))
IM=116πB2=E0216π32(p+1)(p+2)π(kw0)4
jz=(m+σ),σ=i(αβ*βα*)
TQ2,1=Qij1iEj(2)(r=0)=(p+1)(p+2)8w02k2πE0QR
TQ0,1=Qij1iEj(0)(r=0)=2(8p+4(kw0)2)kw02πE0QR

Metrics