Abstract

We theoretically derive the polarization-resolved intensity distribution of a TM-polarized fundamental Gaussian beam reflected by an air–glass plane interface at Brewster incidence. The reflected beam has both a dominant (TM) and a cross-polarized (TM) component, carried by a TEM10 and a TEM01 Hermite–Gaussian spatial mode, respectively. Remarkably, we find that the TE-mode power scales quadratically with the angular spread of the incident beam and is comparable to the TM-mode power. Experimental confirmations of the theoretical results are also presented.

© 2009 Optical Society of America

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References

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  1. D. Brewster, Philos. Trans. R. Soc. London 105, 125 (1815).
    [CrossRef]
  2. Y. Fainman and J. Shamir, Appl. Opt. 23, 3188 (1984).
    [CrossRef] [PubMed]
  3. A. Kőházi-Kis, Opt. Commun. 253, 28 (2005).
    [CrossRef]
  4. Q. Li and R. J. Vernon, IEEE Trans. Antennas Propag. 54, 3449 (2006).
    [CrossRef]
  5. W. Nasalski, Opt. Commun. 197, 217 (2001).
    [CrossRef]
  6. W. Nasalski and Y. Pagani, J. Opt. A 8, 21 (2006).
  7. K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  8. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef] [PubMed]
  9. Throughout this Letter we use the symbols “⋅” and “×” to denote the ordinary scalar and vector products in R3, respectively.
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, 1995).
  11. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2003).
  12. R. F. Gragg, Am. J. Phys. 56, 1092 (1988).
    [CrossRef]
  13. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  14. I. H. Deutsch and J. C. Garrison, Phys. Rev. A 43, 2498 (1991).
    [CrossRef] [PubMed]
  15. A. Aiello, M. Merano, and J. P. Woerdman, arXiv:0903.1950v1 [Phys. Opt.] (2009).
  16. R. Simon, E. C. G. Sudarshan, and N. Mukunda, Appl. Opt. 26, 1589 (1987).
    [CrossRef] [PubMed]
  17. W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
    [CrossRef]

2008 (1)

2006 (3)

W. Nasalski and Y. Pagani, J. Opt. A 8, 21 (2006).

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Q. Li and R. J. Vernon, IEEE Trans. Antennas Propag. 54, 3449 (2006).
[CrossRef]

2005 (1)

A. Kőházi-Kis, Opt. Commun. 253, 28 (2005).
[CrossRef]

2001 (1)

W. Nasalski, Opt. Commun. 197, 217 (2001).
[CrossRef]

1994 (1)

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

1991 (1)

I. H. Deutsch and J. C. Garrison, Phys. Rev. A 43, 2498 (1991).
[CrossRef] [PubMed]

1988 (1)

R. F. Gragg, Am. J. Phys. 56, 1092 (1988).
[CrossRef]

1987 (1)

1984 (1)

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

1815 (1)

D. Brewster, Philos. Trans. R. Soc. London 105, 125 (1815).
[CrossRef]

Aiello, A.

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef] [PubMed]

A. Aiello, M. Merano, and J. P. Woerdman, arXiv:0903.1950v1 [Phys. Opt.] (2009).

Bliokh, Y. P.

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2003).

Brewster, D.

D. Brewster, Philos. Trans. R. Soc. London 105, 125 (1815).
[CrossRef]

Deutsch, I. H.

I. H. Deutsch and J. C. Garrison, Phys. Rev. A 43, 2498 (1991).
[CrossRef] [PubMed]

Erikson, W. L.

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

Fainman, Y.

Garrison, J. C.

I. H. Deutsch and J. C. Garrison, Phys. Rev. A 43, 2498 (1991).
[CrossRef] [PubMed]

Gragg, R. F.

R. F. Gragg, Am. J. Phys. 56, 1092 (1988).
[CrossRef]

Koházi-Kis, A.

A. Kőházi-Kis, Opt. Commun. 253, 28 (2005).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Li, Q.

Q. Li and R. J. Vernon, IEEE Trans. Antennas Propag. 54, 3449 (2006).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, 1995).

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Merano, M.

A. Aiello, M. Merano, and J. P. Woerdman, arXiv:0903.1950v1 [Phys. Opt.] (2009).

Mukunda, N.

Nasalski, W.

W. Nasalski and Y. Pagani, J. Opt. A 8, 21 (2006).

W. Nasalski, Opt. Commun. 197, 217 (2001).
[CrossRef]

Pagani, Y.

W. Nasalski and Y. Pagani, J. Opt. A 8, 21 (2006).

Shamir, J.

Simon, R.

Singh, S.

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

Sudarshan, E. C. G.

Vernon, R. J.

Q. Li and R. J. Vernon, IEEE Trans. Antennas Propag. 54, 3449 (2006).
[CrossRef]

Woerdman, J. P.

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef] [PubMed]

A. Aiello, M. Merano, and J. P. Woerdman, arXiv:0903.1950v1 [Phys. Opt.] (2009).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2003).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, 1995).

Yu. Bliokh, K.

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Am. J. Phys. (1)

R. F. Gragg, Am. J. Phys. 56, 1092 (1988).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

Q. Li and R. J. Vernon, IEEE Trans. Antennas Propag. 54, 3449 (2006).
[CrossRef]

J. Opt. A (1)

W. Nasalski and Y. Pagani, J. Opt. A 8, 21 (2006).

Opt. Commun. (2)

W. Nasalski, Opt. Commun. 197, 217 (2001).
[CrossRef]

A. Kőházi-Kis, Opt. Commun. 253, 28 (2005).
[CrossRef]

Opt. Lett. (1)

Philos. Trans. R. Soc. London (1)

D. Brewster, Philos. Trans. R. Soc. London 105, 125 (1815).
[CrossRef]

Phys. Rev. A (2)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

I. H. Deutsch and J. C. Garrison, Phys. Rev. A 43, 2498 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (1)

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Other (4)

A. Aiello, M. Merano, and J. P. Woerdman, arXiv:0903.1950v1 [Phys. Opt.] (2009).

Throughout this Letter we use the symbols “⋅” and “×” to denote the ordinary scalar and vector products in R3, respectively.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, 1995).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2003).

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Figures (2)

Fig. 1
Fig. 1

Geometry of beam reflection at the air-medium interface; θ B is the Brewster angle.

Fig. 2
Fig. 2

Calculated and measured intensity transverse spatial profiles of the P- and the S-polarized modes of the reflected beam. The beam waist of the incident beam was w 0 = 34 μ m .

Equations (9)

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E I ( r ) = λ = 1 2 a λ ( k ) χ ̂ λ ( k ) d 2 k T ,
A ( k ) = e k T k 0 2 θ 0 2 e i k 0 d ( 1 k T k 0 2 ) 1 2 ,
χ ̂ λ ( k ) r λ ( k ) χ ̂ λ ( k ̃ ) ,
E I ( r ) E R ( r ) = λ = 1 2 a λ ( k ) r λ ( k ) χ ̂ λ ( k ̃ ) d 2 k T ,
I P ( r ) I 0 ( r ) = r P 2 + θ 0 u X + θ 0 2 ( v + p X 2 + q Y 2 ) ,
I S ( r ) I 0 ( r ) = θ 0 2 s Y 2 ,
p ( 1 + Z 2 ) = ( r P θ ) θ B 2 , s ( 1 + Z 2 ) = r S 2 n 2 θ B ,
I P ( r ) I 0 ( r ) = θ 0 2 p X 2 , I S ( r ) I 0 ( r ) = θ 0 2 s Y 2 ,
ρ = I S ( r ) d X d Y I P ( r ) d X d Y = ( r S n 1 r P θ ) θ = θ B 2 .

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