Abstract

A theory of usual (positive) refraction of partially coherent electromagnetic beams has been developed recently. In this Letter, we discuss the theory of negative refraction of a partially coherent electromagnetic beam. We show that negative refraction can produce change in spatial coherence of such a beam.

© 2013 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).
  3. A list of related important references can be found in [15].
  4. Z. Tong and O. Korotkova, Opt. Lett. 35, 175 (2010).
    [CrossRef]
  5. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2004).
  6. M. Lahiri and E. Wolf, Phys. Rev. A 86, 043815 (2012).
    [CrossRef]
  7. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  8. Another definition of the degree of coherence of electromagnetic beams has been proposed [16]. For our purpose, it is immaterial which of the definitions is used.
  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  10. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
    [CrossRef]
  11. T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
    [CrossRef]
  12. O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
    [CrossRef]
  13. H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
    [CrossRef]
  14. F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, J. Opt. Soc. Am. A 25, 1016 (2008).
    [CrossRef]
  15. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
    [CrossRef]
  16. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
    [CrossRef]

2012 (1)

M. Lahiri and E. Wolf, Phys. Rev. A 86, 043815 (2012).
[CrossRef]

2010 (1)

2008 (1)

2005 (2)

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

2004 (3)

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef]

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
[CrossRef]

2001 (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, J. Opt. Soc. Am. A 25, 1016 (2008).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Friberg, A. T.

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, J. Opt. Soc. Am. A 25, 1016 (2008).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2004).

Korotkova, O.

Z. Tong and O. Korotkova, Opt. Lett. 35, 175 (2010).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

Lahiri, M.

M. Lahiri and E. Wolf, Phys. Rev. A 86, 043815 (2012).
[CrossRef]

Mandel, L.

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

Milonni, P. W.

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef]

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Ramírez-Sánchez, V.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Salem, M.

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, J. Opt. Soc. Am. A 25, 1016 (2008).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Setälä, T.

Shirai, T.

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef]

Tervo, J.

Tong, Z.

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef]

Wolf, E.

M. Lahiri and E. Wolf, Phys. Rev. A 86, 043815 (2012).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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

J. Opt. A (2)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

M. Lahiri and E. Wolf, Phys. Rev. A 86, 043815 (2012).
[CrossRef]

Science (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (6)

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).

A list of related important references can be found in [15].

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2004).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Another definition of the degree of coherence of electromagnetic beams has been proposed [16]. For our purpose, it is immaterial which of the definitions is used.

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

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Figures (3)

Fig. 1.
Fig. 1.

Negative refraction of a monochromatic plane wave.

Fig. 2.
Fig. 2.

Modulus of the spectral degree of coherence |η| of the transmitted beam, at two fixed points on the interface, plotted against the angle of incidence θi (in degree) for n2=1.5 and n2=2. The solid curve shows the dependence of |η| of the incident beam on θi, at the same pair of points.

Fig. 3.
Fig. 3.

Dependence of |η| of the transmitted beams (dotted lines) on ρ (in meters) for n2=1.5 and n2=2 when θi=60°. The solid curve represents the dependence of |η| of the incident beam on ρ.

Equations (5)

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

Wlm(r1,r2;ω)=El*(r1;ω)Em(r2;ω).
η(r1,r2;ω)TrW(r1,r2;ω)TrW(r1,r1;ω)TrW(r2,r2;ω),
E0v(t)E0v(i)=2n1cosθin1cosθi+μ1|μ2||n2|2n12sin2θi,
E0h(t)E0h(i)=2n1|n2|cosθiμ1|μ2||n2|2cosθi+n1|n2|2n12sin2θi.
sinθt=|n1|sgn(n1)|n2|sgn(n2)sinθi,

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