Abstract

Energy characteristics of the superposition of TE- and TM-polarized electromagnetic Bessel beams are studied. For some phase differences between TE and TM waves the components of the Poynting vector vary in sign. We call this situation “negative propagation,” because locally the beam may behave like a wave propagating in the direction opposite to the conventional one. We predict the following phenomena, which should confirm negative beam propagation: reflection of the beam from a circular aperture and unusual movement of microparticles in the beam.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
    [CrossRef]
  2. Z. Bouchal and M. Olivik, "Nondiffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
    [CrossRef]
  3. Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
    [CrossRef]
  4. J. Arlt and M. J. Padgett, "Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam," Opt. Lett. 25, 191-193 (2000).
    [CrossRef]
  5. M. Padgett, J. Courtial, and L. Allen, "Light's orbital angular momentum," Phys. Today 5, 35-40 (2004).
    [CrossRef]
  6. B. Z. Katsenelenbaum, "What is the direction of the Poynting vector?" J. Commun. Technol. Electron. 42, 119-120 (1997).
  7. J. Bajer and R. Horák, "Nondiffractive fields," Phys. Rev. E 54, 3052-3054 (1996).
    [CrossRef]
  8. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  9. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  10. P. Sprangle and B. Hafizi, "Comment on nondiffracting beams," Phys. Rev. Lett. 66, 837 (1991).
    [CrossRef] [PubMed]
  11. Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
    [CrossRef]

2004

M. Padgett, J. Courtial, and L. Allen, "Light's orbital angular momentum," Phys. Today 5, 35-40 (2004).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

J. Arlt and M. J. Padgett, "Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam," Opt. Lett. 25, 191-193 (2000).
[CrossRef]

1998

Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
[CrossRef]

1997

B. Z. Katsenelenbaum, "What is the direction of the Poynting vector?" J. Commun. Technol. Electron. 42, 119-120 (1997).

1996

J. Bajer and R. Horák, "Nondiffractive fields," Phys. Rev. E 54, 3052-3054 (1996).
[CrossRef]

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

1995

Z. Bouchal and M. Olivik, "Nondiffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

1991

P. Sprangle and B. Hafizi, "Comment on nondiffracting beams," Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

1987

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Allen, L.

M. Padgett, J. Courtial, and L. Allen, "Light's orbital angular momentum," Phys. Today 5, 35-40 (2004).
[CrossRef]

Arlt, J.

Asakura, T.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Bajer, J.

J. Bajer and R. Horák, "Nondiffractive fields," Phys. Rev. E 54, 3052-3054 (1996).
[CrossRef]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
[CrossRef]

Z. Bouchal and M. Olivik, "Nondiffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
[CrossRef]

Courtial, J.

M. Padgett, J. Courtial, and L. Allen, "Light's orbital angular momentum," Phys. Today 5, 35-40 (2004).
[CrossRef]

Durnin, J.

Hafizi, B.

P. Sprangle and B. Hafizi, "Comment on nondiffracting beams," Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

Harada, Y.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Horák, R.

J. Bajer and R. Horák, "Nondiffractive fields," Phys. Rev. E 54, 3052-3054 (1996).
[CrossRef]

Katsenelenbaum, B. Z.

B. Z. Katsenelenbaum, "What is the direction of the Poynting vector?" J. Commun. Technol. Electron. 42, 119-120 (1997).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Olivik, M.

Z. Bouchal and M. Olivik, "Nondiffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

Padgett, M.

M. Padgett, J. Courtial, and L. Allen, "Light's orbital angular momentum," Phys. Today 5, 35-40 (2004).
[CrossRef]

Padgett, M. J.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Sprangle, P.

P. Sprangle and B. Hafizi, "Comment on nondiffracting beams," Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
[CrossRef]

J. Commun. Technol. Electron.

B. Z. Katsenelenbaum, "What is the direction of the Poynting vector?" J. Commun. Technol. Electron. 42, 119-120 (1997).

J. Mod. Opt.

Z. Bouchal and M. Olivik, "Nondiffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
[CrossRef]

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Opt. Lett.

Phys. Rev. E

J. Bajer and R. Horák, "Nondiffractive fields," Phys. Rev. E 54, 3052-3054 (1996).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

P. Sprangle and B. Hafizi, "Comment on nondiffracting beams," Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

Phys. Today

M. Padgett, J. Courtial, and L. Allen, "Light's orbital angular momentum," Phys. Today 5, 35-40 (2004).
[CrossRef]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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 (5)

Fig. 1
Fig. 1

(a) Longitudinal and (b) azimuthal components of the Poynting vector versus the normalized radial coordinate for Bessel beams of the order m = 1 , 2 , 3 , 4 . Parameters: ε = 1.0 , μ = 1.0 , q k = 0.9 , c 1 = 1 , c 2 = i .

Fig. 2
Fig. 2

(a) Longitudinal and (b) azimuthal components of the Poynting vector versus the normalized radial coordinate for the Bessel beam of the order m = 2 and different transverse wavenumbers q. Parameters: ε = 1.0 , μ = 1.0 , c 1 = 1 , c 2 = i .

Fig. 3
Fig. 3

(a) Longitudinal and (b) azimuthal components of the Poynting vector versus the normalized radial coordinate for the Bessel beam of the order m = 1 and different phase offsets Δ ψ = ψ 2 ψ 1 . Parameters: ε = 1.0 , μ = 1.0 , q k = 0.9 .

Fig. 4
Fig. 4

Comparison of the longitudinal and azimuthal components of the Poynting vector for the Bessel beam of the order m = 3 . Parameters: ε = 1.0 , μ = 1.0 , q k = 0.9 , c 1 = 1 , c 2 = i .

Fig. 5
Fig. 5

Reflection of the Bessel beam from the circular aperture.

Equations (22)

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

( E ( r , t ) H ( r , t ) ) = ( E ( r , φ ) H ( r , φ ) ) exp ( i β z + i m φ i ω t ) ,
E r = 1 q 2 ( m μ k r H z + i β d E z d r ) ,
E φ = 1 q 2 ( m β r E z i μ k d H z d r ) ,
H r = 1 q 2 ( m ε k r E z + i β d H z d r ) , H φ = 1 q 2 ( m β r H z + i ε k d H z d r ) .
d 2 d r 2 ( E z H z ) + m r d d r ( E z H z ) + ( q 2 m 2 r 2 ) ( E z H z ) = 0 ,
H z = c 1 J m ( q r ) , E z = c 2 J m ( q r ) ,
E ( r ) = exp ( i m φ + i β z ) ( J m ( q r ) c 2 e z k μ q c 1 ( e z × b ) + β q c 2 b ) ,
H ( r ) = exp ( i m φ + i β z ) ( J m ( q r ) c 1 e z + β q c 1 b + k ε q c 2 ( e z × b ) ) ,
β 2 = k 2 ε μ q 2 , b = i J m ( q r ) e r m q r J m ( q r ) e φ ,
J m ( q r ) = d J m d ( q r ) .
S = c 8 π ( k β q 2 ( μ c 1 2 + ε c 2 2 ) ( J m 2 + m 2 q 2 r 2 J m 2 ) 2 m q 3 r ( β 2 + k 2 ε μ ) Im ( c 1 c 2 * ) J m J m ) e z + c 8 π ( m k q 2 r ( μ c 1 2 + ε c 2 2 ) J m 2 2 β q Im ( c 1 c 2 * ) J m J m ) e φ .
J m = 1 2 ( J m 1 J m + 1 ) , m J m q r = 1 2 ( J m 1 + J m + 1 ) ,
S = c 8 π ( k β 2 q 2 ( μ c 1 2 + ε c 2 2 ) ( J m 1 2 + J m + 1 2 ) β 2 + k 2 ε μ 2 q 2 Im ( c 1 c 2 * ) ( J m 1 2 J m + 1 2 ) ) e z + c r 32 π m ( k ( μ c 1 2 + ε c 2 2 ) ( J m 1 + J m + 1 ) 2 2 β Im ( c 1 c 2 * ) ( J m 1 2 J m + 1 2 ) ) e φ .
J m ( q r ) = 2 π q r cos ( q r π 4 m π 2 ) ;
S = c k β 8 π 2 q 3 r ( ( μ c 1 2 + ε c 2 2 ) ( 1 ( 1 ) m sin ( 2 q r ) ) e z ( 1 ) m + 1 2 q Im ( c 1 c 2 * ) β cos ( 2 q r ) e φ ) .
S c 16 π q 2 ( k β ( μ c 1 2 + ε c 2 2 ) ( β 2 + k 2 ε μ ) Im ( c 1 c 2 * ) ) J m 1 2 ( q r ) e z .
sin ( Δ ψ ) < a , a = k β ( μ c 1 2 + ε c 2 2 ) ( β 2 + k 2 ε μ ) c 1 c 2 .
π + arcsin ( a ) < Δ ψ < 2 π arcsin ( a ) .
P = 0 S ( r ) r d r = c k β 8 π q 2 ( μ c 1 2 + ε c 2 2 ) 0 J m 1 2 r d r e z + c 8 π ( m k q 2 ( μ c 1 2 + ε c 2 2 ) 0 J m 2 d r 2 β q Im ( c 1 c 2 * ) 0 J m J m r d r ) e φ .
0 J m 2 d x 0 J m J m x d x = x J m 2 x = 0 J m 2 d x ,
m k ( μ c 1 2 + ε c 2 2 ) 2 m k ε μ c 1 c 2 2 β c 1 c 2 sin ( Δ ψ ) .
Z 2 π Z G = λ 2 ( q k ) 2 ,

Metrics