Abstract

We show that, for 3D random electromagnetic fields that are created by optical systems from a partially polarized plane wave, two different definitions of the 3D degree of polarization proposed in literature have a monotonic one-to-one correspondence, thus providing the same information about the field’s polarization state. Examples of 3D fields obeying this result are the evanescent wave generated in total internal reflection, the tightly focused beam, and the far field scattered from an electric point dipole.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).
  2. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
    [CrossRef]
  3. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
    [CrossRef]
  4. A. Luis, Opt. Commun. 253, 10 (2005).
    [CrossRef]
  5. Ph. Réfrégier and F. Goudail, J. Opt. Soc. Am. A 23, 671 (2006).
    [CrossRef]
  6. M. Dennis, J. Opt. Soc. Am. A 24, 2065 (2007).
    [CrossRef]
  7. G. S. Agarwal, J. Mod. Opt. 52, 651 (2005).
    [CrossRef]
  8. C. Brosseau and A. Dogariu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2006), Vol. 49, p. 315.
    [CrossRef]
  9. J. J. Gil, Eur. Phys. J.: Appl. Phys. 40, 1 (2007).
    [CrossRef]
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  11. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).
  12. B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
    [CrossRef]
  13. K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005).
    [CrossRef]

2007 (2)

M. Dennis, J. Opt. Soc. Am. A 24, 2065 (2007).
[CrossRef]

J. J. Gil, Eur. Phys. J.: Appl. Phys. 40, 1 (2007).
[CrossRef]

2006 (1)

2005 (4)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

A. Luis, Opt. Commun. 253, 10 (2005).
[CrossRef]

G. S. Agarwal, J. Mod. Opt. 52, 651 (2005).
[CrossRef]

K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005).
[CrossRef]

2002 (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, J. Mod. Opt. 52, 651 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).

Brosseau, C.

C. Brosseau and A. Dogariu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2006), Vol. 49, p. 315.
[CrossRef]

Dennis, M.

Dogariu, A.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

C. Brosseau and A. Dogariu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2006), Vol. 49, p. 315.
[CrossRef]

Ellis, J.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Friberg, A. T.

K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Gil, J. J.

J. J. Gil, Eur. Phys. J.: Appl. Phys. 40, 1 (2007).
[CrossRef]

Goudail, F.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Kaivola, M.

K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Lindfors, K.

Luis, A.

A. Luis, Opt. Commun. 253, 10 (2005).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Ponomarenko, S.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Réfrégier, Ph.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Setälä, T.

K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Shevchenko, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Wolf, E.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).

Eur. Phys. J.: Appl. Phys. (1)

J. J. Gil, Eur. Phys. J.: Appl. Phys. 40, 1 (2007).
[CrossRef]

J. Mod. Opt. (1)

G. S. Agarwal, J. Mod. Opt. 52, 651 (2005).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

A. Luis, Opt. Commun. 253, 10 (2005).
[CrossRef]

Phys. Rev. E (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Proc. R. Soc. London (1)

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Other (4)

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 1999).

C. Brosseau and A. Dogariu, in Progress in Optics, E.Wolf, ed. (Elsevier, 2006), Vol. 49, p. 315.
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

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

Illustration of the geometry and notation used in the discussion of total internal reflection. The evanescent wave decays exponentially away from the medium.

Fig. 2
Fig. 2

Depiction of a high-NA focusing system. The geometry and variables are discussed in the text.

Fig. 3
Fig. 3

Illustration of the geometry and quantities related to the plane-wave scattering from an electric point dipole.

Equations (14)

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

ϕ i j ( r , ω ) = E i * ( r , ω ) E j ( r , ω ) , ( i , j ) = ( x , y , z ) ,
P 3 2 ( r , ω ) = 3 2 [ tr Φ 3 2 ( r , ω ) tr 2 Φ 3 ( r , ω ) 1 3 ] ,
Φ 3 ( r , ω ) = U Φ 3 ( r , ω ) U = diag ( λ 1 , λ 2 , λ 3 ) ,
P 3 ( r , ω ) = ( λ 1 λ 2 ) 2 + ( λ 1 λ 3 ) 2 + ( λ 2 λ 3 ) 2 2 ( λ 1 + λ 2 + λ 3 ) .
Φ 3 ( r , ω ) = M * ( r , ω ) Φ 2 ( ω ) M T ( r , ω ) ,
P 3 , 2 D 2 ( r , ω ) = 3 2 [ λ 1 2 + λ 2 2 ( λ 1 + λ 2 ) 2 1 3 ] .
P E ( r , ω ) = λ 1 λ 2 λ 1 + λ 2 + λ 3 .
P E , 2 D ( r , ω ) = λ 1 λ 2 λ 1 + λ 2 ,
P 3 , 2 D 2 ( r , ω ) = 3 4 P E , 2 D 2 ( r , ω ) + 1 4 .
M ( r , ω ) = ( i t p n ̃ 2 sin 2 θ i 1 0 0 t s t p n ̃ sin θ i 0 ) e i n 1 k 0 sin θ i x γ z ,
M ( r , ω ) = i k 0 2
× ( I 0 ( r , ω ) + I 2 ( r , ω ) cos 2 ϕ I 2 ( r , ω ) sin 2 ϕ I 2 ( r , ω ) sin 2 ϕ I 0 ( r , ω ) I 2 ( r , ω ) cos 2 ϕ 2 i I 1 ( r , ω ) cos ϕ 2 i I 1 ( r , ω ) sin ϕ ) .
M ( r , ω ) = μ 0 ω 2 α 0 ( ω ) e i k 0 r 4 π r
× ( 1 sin 2 θ cos 2 ϕ 1 2 sin 2 θ sin 2 ϕ 1 2 sin 2 θ sin 2 ϕ 1 sin 2 θ sin 2 ϕ 1 2 sin 2 θ cos ϕ 1 2 sin 2 θ sin ϕ ) ,

Metrics