Abstract

We study the coherence changes in partially coherent beams transmitted through binary metallic gratings. The interaction of Gaussian Schell-model beams with grating structures supporting surface plasmons is rigorously modeled using the Fourier modal method and the coherent mode representation of partially coherent fields. Our numerical results show that, by choosing suitable parameters for the grating, the degree of coherence of the beam can be significantly increased. The studied approach offers new possibilities to alter the coherence properties of fields using nanophotonic components.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef]
  2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
    [CrossRef]
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
    [CrossRef]
  4. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
    [CrossRef]
  5. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
    [CrossRef]
  6. N. Kuzmin, G. W. ‘t Hooft, E. R. Eliel, G. Gbur, H. F. Schouten, and T. D. Visser, Opt. Lett. 32, 445 (2007).
    [CrossRef]
  7. C. H. Gan, G. Gbur, and T. D. Visser, Phys. Rev. Lett. 98, 043908 (2007).
    [CrossRef]
  8. C. H. Gan and G. Gbur, Plasmonics 3, 111 (2008).
    [CrossRef]
  9. C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
    [CrossRef]
  10. J. Lindberg, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 23, 1349 (2006).
    [CrossRef]
  11. H. J. Hyvärinen, J. Turunen, and P. Vahimaa, Appl. Phys. B, 101, 273 (2010).
    [CrossRef]
  12. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  13. P. De Santis, F. Gori, G. Guattari, and C. Palma, J. Opt. Soc. Am. A 3, 1258 (1986).
    [CrossRef]
  14. D. Mendlovic, G. Shabtay, and A. W. Lohmann, Opt. Lett. 24, 361 (1999).
    [CrossRef]
  15. T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907 (2004).
    [CrossRef]
  16. A. S. Ostrovsky, G. Martínez-Niconoff, V. Arrizón, P. Martínez-Vara, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 17, 5257 (2009).
    [CrossRef]
  17. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [CrossRef]
  18. Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
    [CrossRef]
  19. M. J. Bastiaans, J. Opt. Soc. Am. A 1, 711 (1984).
    [CrossRef]
  20. P. Vahimaa and J. Tervo, J. Opt. A 6, S41 (2004).
    [CrossRef]
  21. J. Turunen, in Micro-Optics, Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, 1997).
  22. P. Vahimaa and J. Turunen, J. Opt. Soc. Am. A 14, 54 (1997).
    [CrossRef]
  23. J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
    [CrossRef]
  24. D. R. Lide, CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, 1984), p. E-370.
  25. http://www.crystran.co.uk/optical-materials/silica-glass-sio2 .

2012

C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
[CrossRef]

Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
[CrossRef]

2011

H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
[CrossRef]

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

2010

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, Appl. Phys. B, 101, 273 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

2009

2008

C. H. Gan and G. Gbur, Plasmonics 3, 111 (2008).
[CrossRef]

2007

2006

2004

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

2002

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

1999

1997

P. Vahimaa and J. Turunen, J. Opt. Soc. Am. A 14, 54 (1997).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

1986

1984

‘t Hooft, G. W.

Arrizón, V.

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Bastiaans, M. J.

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Carminati, R.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

Chen, Y.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

De Santis, P.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

Eliel, E. R.

Friberg, A. T.

Gan, C. H.

C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
[CrossRef]

C. H. Gan and G. Gbur, Plasmonics 3, 111 (2008).
[CrossRef]

C. H. Gan, G. Gbur, and T. D. Visser, Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Gbur, G.

C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
[CrossRef]

C. H. Gan and G. Gbur, Plasmonics 3, 111 (2008).
[CrossRef]

C. H. Gan, G. Gbur, and T. D. Visser, Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

N. Kuzmin, G. W. ‘t Hooft, E. R. Eliel, G. Gbur, H. F. Schouten, and T. D. Visser, Opt. Lett. 32, 445 (2007).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

Gori, F.

Greffet, J.-J.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

Gu, Y.

C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
[CrossRef]

Guattari, G.

Hyvärinen, H. J.

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, Appl. Phys. B, 101, 273 (2010).
[CrossRef]

Joulain, K.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Kaivola, M.

Korotkova, O.

Kuipers, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Kuzmin, N.

Lajunen, H.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

Lide, D. R.

D. R. Lide, CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, 1984), p. E-370.

Lindberg, J.

Lohmann, A. W.

Mainguy, S.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

Mandel, L.

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

Martínez-Niconoff, G.

Martínez-Vara, P.

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Mendlovic, D.

Mulet, J.-P.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

Olvera-Santamaría, M. A.

Ostrovsky, A. S.

Palma, C.

Rickenstorff-Parrao, C.

Saastamoinen, T.

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
[CrossRef]

Schouten, H. F.

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Setälä, T.

Shabtay, G.

Shirai, T.

Tervo, J.

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

P. Vahimaa and J. Tervo, J. Opt. A 6, S41 (2004).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

Tong, Z.

Turunen, J.

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, Appl. Phys. B, 101, 273 (2010).
[CrossRef]

P. Vahimaa and J. Turunen, J. Opt. Soc. Am. A 14, 54 (1997).
[CrossRef]

J. Turunen, in Micro-Optics, Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, 1997).

Vahimaa, P.

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, Appl. Phys. B, 101, 273 (2010).
[CrossRef]

P. Vahimaa and J. Tervo, J. Opt. A 6, S41 (2004).
[CrossRef]

P. Vahimaa and J. Turunen, J. Opt. Soc. Am. A 14, 54 (1997).
[CrossRef]

Vartiainen, I.

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

Visser, T. D.

C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
[CrossRef]

C. H. Gan, G. Gbur, and T. D. Visser, Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

N. Kuzmin, G. W. ‘t Hooft, E. R. Eliel, G. Gbur, H. F. Schouten, and T. D. Visser, Opt. Lett. 32, 445 (2007).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Wolf, E.

T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907 (2004).
[CrossRef]

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

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

Appl. Phys. B

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, Appl. Phys. B, 101, 273 (2010).
[CrossRef]

J. Opt. A

P. Vahimaa and J. Tervo, J. Opt. A 6, S41 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1997).
[CrossRef]

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

C. H. Gan, G. Gbur, and T. D. Visser, Phys. Rev. Lett. 98, 043908 (2007).
[CrossRef]

Plasmonics

C. H. Gan and G. Gbur, Plasmonics 3, 111 (2008).
[CrossRef]

C. H. Gan, Y. Gu, T. D. Visser, and G. Gbur, Plasmonics 7, 313 (2012).
[CrossRef]

Proc. SPIE

J. Tervo, H. J. Hyvärinen, T. Saastamoinen, I. Vartiainen, and J. Turunen, Proc. SPIE 8171, 81710F (2011).
[CrossRef]

Rev. Mod. Phys.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Other

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

D. R. Lide, CRC Handbook of Chemistry and Physics, 64th ed. (CRC Press, 1984), p. E-370.

http://www.crystran.co.uk/optical-materials/silica-glass-sio2 .

J. Turunen, in Micro-Optics, Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, 1997).

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 (4)

Fig. 1.
Fig. 1.

Linear binary gold grating with period d, height h, and slit width c on a fused silica substrate.

Fig. 2.
Fig. 2.

(a) Transmission and (b) effective degree of coherence of a GSM beam as a function of grating period d and height h.

Fig. 3.
Fig. 3.

(a) Transmission and (b) effective degree of coherence of a GSM beam as a function of grating period d and the wavelength of the beam λ. The wavelength of surface plasmon at homogeneous gold–silica interface is plotted with a white line.

Fig. 4.
Fig. 4.

(a) Cross-spectral density, (c) the degree of coherence, and (e) the spreading upon propagation of the incident GSM beam, and the corresponding properties, (b), (d), and (f), respectively, of the beam transmitted through the grating.

Equations (8)

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

W(r1,r1,ω)=U*(r1,ω)U(r2,ω),
μ(r1,r2,ω)=W(r1,r2,ω)S(r1,ω)S(r2,ω).
μ¯2(ω)=DS(r1,ω)S(r2,ω)|μ(r1,r2,ω)|2d3r1d3r2DS(r1,ω)S(r2,ω)d3r1d3r2,
W(r1,r2,ω)=nλn(ω)ϕn*(r1,ω)ϕn(r2,ω),
DW(r1,r2,ω)ϕn(r1,ω)d3r1=λn(ω)ϕn(r2,ω).
Dϕm*(r,ω)ϕn(r,ω)d3r=δmn,
W(x1,x2,ω)=W0exp(x12+x22w02)exp[(x1x2)22σ02],
ksp=k0ε1ε2ε1+ε2,

Metrics