Abstract

Starting from the vector angular spectrum of the electromagnetic beam, the analytical vectorial structure of the radially polarized beams (RPBs) is presented. The energy flux distributions of the RPBs are demonstrated. The physical pictures of the RPBs are well illustrated from the vectorial structure. This particular electromagnetic field is entirely transverse magnetic, and on axis it only has a longitudinal (z) electric-field component (i.e., no transverse electric field and no magnetic field at all on axis).

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Appl. Phys. B 72, 109 (2001).
  2. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  3. C. Varin and M. Piché, Appl. Phys. B 74, S83 (2002).
    [CrossRef]
  4. Y. I. Salamin, Opt. Lett. 32, 90 (2007).
    [CrossRef]
  5. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
    [CrossRef]
  6. K. T. Gahagan and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 16, 533 (1999).
    [CrossRef]
  7. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
    [CrossRef] [PubMed]
  8. A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000).
    [CrossRef]
  9. V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
    [CrossRef]
  10. S. C. Tidwell, D. H. Ford, and W. D. Kimura, Appl. Opt. 29, 2234 (1990).
    [CrossRef] [PubMed]
  11. N. Passilly, R. de S. Denis, and K. Aït-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, J. Opt. Soc. Am. A 22, 984 (2005).
    [CrossRef]
  12. A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, J. Phys. D 32, 2871 (1999).
    [CrossRef]
  13. K. Yonezawa, Y. Kozawa, and S. Sato, Opt. Lett. 31, 2151 (2006).
    [CrossRef] [PubMed]
  14. I. Moshe, S. Jackel, A. Meir, Y. Lumer, and E. Leibush, Opt. Lett. 32, 47 (2007).
    [CrossRef]
  15. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 285 (2002).
    [CrossRef]
  16. U. Levy, C.-H. Tsai, L. Pang, and Y. Fainman, Opt. Lett. 29, 1718 (2004).
    [CrossRef] [PubMed]
  17. R. Martínez-Herrero, P. M. Mejías, S. Bosch, and A. Carnicer, J. Opt. Soc. Am. A 18, 1678 (2001).
    [CrossRef]
  18. P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, Prog. Quantum Electron. 26, 65 (2002).
    [CrossRef]
  19. H. M. Guo, J. B. Chen, and S. L. Zhuang, Opt. Express 14, 2095 (2006).
    [CrossRef] [PubMed]
  20. G. Q. Zhou, Opt. Lett. 31, 2616 (2006).
    [CrossRef] [PubMed]
  21. Y. I. Salamin, Opt. Lett. 31, 2619 (2006).
    [CrossRef] [PubMed]
  22. A. A. Tovar, Opt. Lett. 15, 2705 (1998).
  23. D. M. Deng, J. Opt. Soc. Am. B 23, 1228 (2006).
    [CrossRef]
  24. M.Abramowitz and I.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

2007 (2)

2006 (5)

2005 (1)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2002 (3)

C. Varin and M. Piché, Appl. Phys. B 74, S83 (2002).
[CrossRef]

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, Prog. Quantum Electron. 26, 65 (2002).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 285 (2002).
[CrossRef]

2001 (3)

R. Martínez-Herrero, P. M. Mejías, S. Bosch, and A. Carnicer, J. Opt. Soc. Am. A 18, 1678 (2001).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Appl. Phys. B 72, 109 (2001).

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

2000 (1)

A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000).
[CrossRef]

1999 (3)

V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
[CrossRef]

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, J. Phys. D 32, 2871 (1999).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 16, 533 (1999).
[CrossRef]

1998 (1)

A. A. Tovar, Opt. Lett. 15, 2705 (1998).

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

1990 (1)

Appl. Opt. (1)

Appl. Phys. B (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Appl. Phys. B 72, 109 (2001).

C. Varin and M. Piché, Appl. Phys. B 74, S83 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

J. Phys. D (3)

A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000).
[CrossRef]

V. G. Niziev and A. V. Nesterov, J. Phys. D 32, 1455 (1999).
[CrossRef]

A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, J. Phys. D 32, 2871 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

Phys. Rev. Lett. (3)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, Prog. Quantum Electron. 26, 65 (2002).
[CrossRef]

Other (1)

M.Abramowitz and I.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

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 (1)

Fig. 1
Fig. 1

Energy flux distribution of the RPB in the plane (a)–(c) z = 10 λ and (d)–(f) z = 100 λ versus x λ and y λ . The parameters are chosen as (a) and (d) n = 0 , (b) and (e) n = 1 , (c) and (f) n = 2 . For all plots σ = 1 π ( w 0 = 0.5 λ ) .

Equations (20)

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

E n 1 ( x , y , 0 ) = E n 1 x ( x , y , 0 ) e ̂ x + E n 1 y ( x , y , 0 ) e ̂ y ,
E n 1 x ( x , y , 0 ) = E 0 2 w 0 L n 1 ( 2 ρ 2 w 0 2 ) exp ( ρ 2 w 0 2 ) x ,
E n 1 y ( x , y , 0 ) = E 0 2 w 0 L n 1 ( 2 ρ 2 w 0 2 ) exp ( ρ 2 w 0 2 ) y ;
E n 1 ( r ) = + { E ̃ n 1 x ( p , q ) e ̂ x + E ̃ n 1 y ( p , q ) e ̂ y e ̂ z γ [ p × E ̃ n 1 x ( p , q ) + q E ̃ n 1 y ( p , q ) ] } exp ( i k m ) d p d q ,
E ̃ n 1 x ( p , q ) = 1 λ 2 + E n 1 x ( x , y , 0 ) exp ( i k v ) d x d y ,
= A p exp ( b 2 4 σ 2 ) L n 1 ( b 2 2 σ 2 ) ,
E ̃ n 1 y ( p , q ) = 1 λ 2 + E n 1 y ( x , y , 0 ) exp ( i k v ) d x d y ,
= A q exp ( b 2 4 σ 2 ) L n 1 ( b 2 2 σ 2 ) ,
E ( r ) = E TE ( r ) + E TM ( r ) ,
E TE ( r ) = + 1 b 2 [ q E ̃ x ( p , q ) p E ̃ y ( p , q ) ] × ( q e ̂ x p e ̂ y ) exp ( i k m ) d p d q ,
E TM ( r ) = + 1 b 2 [ p E ̃ x ( p , q ) + q E ̃ y ( p , q ) ] ( p e ̂ x + q e ̂ y b 2 γ e ̂ z ) exp ( i k m ) d p d q .
H ( r ) = H TE ( r ) + H TM ( r ) ,
H TE ( r ) = ϵ μ + 1 b 2 [ q E ̃ x ( p , q ) p E ̃ y ( p , q ) ] × ( p γ e ̂ x + q γ e ̂ y b 2 e ̂ z ) exp ( i k m ) d p d q ,
H TM ( r ) = ϵ μ + [ p E ̃ x ( p , q ) + q E ̃ y ( p , q ) ] × 1 b 2 γ ( q e ̂ x p e ̂ y ) exp ( i k m ) d p d q .
E n 1 ( r ) = E TM ( r ) ,
H n 1 ( r ) = H TM ( r ) .
E TM ( r ) = ( 1 ) n + 1 E 0 2 z R r 2 ( 1 i z R r ) 2 exp [ i k r c ( r ) ] { z 2 σ r P ( r ) × L n 1 [ Q ( r ) ] ( x e ̂ x + y e ̂ y ρ 2 z e ̂ z ) + i w 0 e ̂ z m = 0 n ( n + 1 ) ! ( n m ) ! m ! ( 1 ) m n ( 1 i z R r ) m L m + 1 [ c ( r ) ] } ,
H TM ( r ) = ϵ μ 2 i E 0 w 0 2 C ( r ) 16 r 7 exp [ i k r c ( r ) ] { ( 1 ) n × P ( r ) [ 4 z R 2 ρ 2 L n 1 2 [ Q ( r ) ] σ 3 ( 1 + z R 2 r 2 ) 2 + k C ( r ) [ 4 z R r 2 × ( n w 0 2 r 2 ) + 4 i r 3 ( r 2 ( n + 1 ) w 0 2 ) + 2 z R 3 ( ρ 2 + 2 z 2 ) + 2 i z R 2 r ( 2 w 0 2 + 3 ρ 2 + 2 z 2 ) ] [ σ ( i z R r + 1 ) ] L n 1 [ Q ( r ) ] ] + m = 0 n ( 1 ) m + 1 ( n + 1 ) ! ( n m ) ! m ! C ( r ) m 2 × [ w 0 [ k ( 4 z R 2 ρ 2 + 4 ( m 2 ) w 0 2 r 2 8 r 4 ) + 2 i r × ( 8 r 2 + ( m w 0 2 + 4 ρ 2 + 2 z 2 ) σ 2 ) ] C ( r ) × L m + 1 [ c ( r ) ] 2 z R C ( r ) σ ( 4 i r z 2 + 2 z R ( ρ 2 + 2 z 2 ) ) L m 1 [ c ( r ) ] ] } ( y e ̂ x x e ̂ y ) ,
E TM ( 0 , 0 , z ) = 2 E 0 w 0 e ̂ z m = 0 n π ( n + 1 ) ! ( 2 u ) m ( m + 1 ) ! ( n m ) ! m ! × m + 1 u m + 1 [ u exp ( k 2 4 u + z 2 u ) erfc ( z × u i k 2 u ) ] ,
H TM ( 0 , 0 , z ) = 0 ,

Metrics