Abstract

A new formalism is developed for diffraction-free vector beams in free space. The solutions of Maxwell’s equations are separated into two polarization modes, TE and TM. We discuss the validity of the method by applying it to a particular solution, the vectorial Bessel beam of order m.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Beth, Phys. Rev. 50, 115 (1936).
    [CrossRef]
  2. K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
    [CrossRef]
  3. Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555(1995).
  4. Y. Z. Yu and W. B. Dou, Prog. Electromagn. Res. Lett. 5, 57 (2008).
    [CrossRef]
  5. R. Martínez-Herrero and P. M. Mejías, Opt. Express 18, 7965 (2010).
  6. G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
    [CrossRef]
  7. C. Li, Phys. Rev. A 80, 063814 (2009).
  8. I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
    [CrossRef]
  9. J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1999).
  10. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  11. G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

2011 (1)

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

2010 (1)

2009 (1)

C. Li, Phys. Rev. A 80, 063814 (2009).

2008 (2)

G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
[CrossRef]

Y. Z. Yu and W. B. Dou, Prog. Electromagn. Res. Lett. 5, 57 (2008).
[CrossRef]

2002 (1)

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

1995 (1)

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555(1995).

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1936 (1)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Arfken, G.

G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

Arlt, J.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beth, R. A.

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

Bouchal, Z.

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555(1995).

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Dholakia, K.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Dou, W. B.

Y. Z. Yu and W. B. Dou, Prog. Electromagn. Res. Lett. 5, 57 (2008).
[CrossRef]

Garcés-Chávez, V.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1999).

Li, C.

C. Li, Phys. Rev. A 80, 063814 (2009).

Martínez-Herrero, R.

Mejías, P. M.

Molina-Terriza, G.

G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
[CrossRef]

Olivík, M.

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555(1995).

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Weber, H. J.

G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yu, Y. Z.

Y. Z. Yu and W. B. Dou, Prog. Electromagn. Res. Lett. 5, 57 (2008).
[CrossRef]

J. Mod. Opt. (1)

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555(1995).

J. Opt. (1)

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

J. Opt. B (1)

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Opt. Express (1)

Phys. Rev. (1)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Phys. Rev. A (3)

G. Molina-Terriza, Phys. Rev. A 78, 053819 (2008).
[CrossRef]

C. Li, Phys. Rev. A 80, 063814 (2009).

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Prog. Electromagn. Res. Lett. (1)

Y. Z. Yu and W. B. Dou, Prog. Electromagn. Res. Lett. 5, 57 (2008).
[CrossRef]

Other (2)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1999).

G. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995).

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.


Equations (21)

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

Et=ikt2[kztEzωz^×tBz],
Bt=ikt2[kztBz+ωc2z^×tEz].
E(x,y,z)TM=eikzz[ikzkt2tEz+Ezz^],
B(x,y,z)TM=eikzz[iωkt2c2z^×tEz]
E(x,y,z)TE=eikzz[ωikt2z^×tBz],
B(x,y,z)TE=eikzz[ikzkt2tBz+Bzz^].
(t2+kt2)(Ez,Bz)=0.
S(x,y,z)TM=ωkzϵ02kt4[ikt2kzEztEz*+|tEz|2z^],
S(x,y,z)TE=ωkz2μ0kt4[ikt2kzBz*tBz+|tBz|2z^].
jTM=ωkzϵ02c2kt4[kt2kzEzLt,orbEz*+|tEz|2r×z^],
jTE=ωkz2μ0c2kt4[kt2kzBz*Lt,orbBz+|tBz|2r×z^].
jzTM=ωϵ02c2kt2Ez(Lt,orbEz*)·z^,
jzTE=ω2μ0c2kt2Bz*(Lt,orbBz)·z^.
t[Jme±imϕ]=kte±imϕ2[ρ^J±iϕ^J+],
STMRe=|E0|2ωϵ04kt[JmJ+ϕ^+kzkt(Jm12+Jm+12)z^].
jzTM=mωϵ0|E0|22c2kt2Jm2(ktρ).
jzTE=mω|B0|22μ0c2kt2Jm2(ktρ).
UTM=ϵ0ω22kt2c2A|Ez|2da+ϵ04kt4(kz2+ω2c2)CEz*Ezρdl.
CEz*Ezρdl=|E0|2πktRJm(ktR)[Jm1(ktR)Jm+1(ktR)],
JzTM,TEU=mω.
PzTE,TMU=kzω

Metrics