Abstract

We present a phase-sensitive near-field study of speckle fields from photonic crystals in the presence of disorder. We observe phase singularities (vortices) and analyze their statistical properties and screening effects. The experimental results show a clear polarization dependence, not only in their morphological parameters but also in their spatial distribution.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
    [CrossRef]
  2. M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
    [CrossRef]
  3. S. Zhang and A. Z. Genack, Phys. Rev. Lett. 99, 203901 (2007).
    [CrossRef]
  4. W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
    [CrossRef] [PubMed]
  5. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
    [CrossRef] [PubMed]
  6. N. Shvartsman and I. Freund, Phys. Rev. Lett. 72, 1008(1994).
    [CrossRef] [PubMed]
  7. M. R. Dennis, Proc. SPIE 4403, 13 (2001).
    [CrossRef]
  8. M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
    [CrossRef]
  9. M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
    [CrossRef] [PubMed]
  10. B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
    [CrossRef] [PubMed]
  11. P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
    [CrossRef]
  12. P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
    [CrossRef] [PubMed]
  13. V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 92, 253902 (2004).
    [CrossRef] [PubMed]
  14. P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
    [CrossRef]
  15. B. I. Halperin, in Physics of Defects (North Holland, 1981).
  16. I. Freund, J. Opt. Soc. Am. A 11, 1644 (1994).
    [CrossRef]
  17. A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901(2003).
    [CrossRef] [PubMed]
  18. C. Liu and S.-H. Park, Opt. Lett. 30, 1602 (2005).
    [CrossRef] [PubMed]
  19. V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
    [CrossRef] [PubMed]

2010 (1)

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

2009 (1)

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

2007 (1)

S. Zhang and A. Z. Genack, Phys. Rev. Lett. 99, 203901 (2007).
[CrossRef]

2005 (2)

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

C. Liu and S.-H. Park, Opt. Lett. 30, 1602 (2005).
[CrossRef] [PubMed]

2004 (1)

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 92, 253902 (2004).
[CrossRef] [PubMed]

2003 (2)

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901(2003).
[CrossRef] [PubMed]

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

2002 (1)

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

2001 (1)

M. R. Dennis, Proc. SPIE 4403, 13 (2001).
[CrossRef]

2000 (3)

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

1999 (1)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
[CrossRef]

1994 (2)

I. Freund, J. Opt. Soc. Am. A 11, 1644 (1994).
[CrossRef]

N. Shvartsman and I. Freund, Phys. Rev. Lett. 72, 1008(1994).
[CrossRef] [PubMed]

1986 (1)

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Aliev, F.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Apalkov, V. M.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 92, 253902 (2004).
[CrossRef] [PubMed]

Apostol, A.

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901(2003).
[CrossRef] [PubMed]

Baba, T.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Balistreri, M. L. M.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Bertone, J. F.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
[CrossRef]

Burresi, M.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Cazayous, M.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Colocci, M.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Colvin, V. L.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
[CrossRef]

Dennis, M. R.

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

M. R. Dennis, Proc. SPIE 4403, 13 (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

Dogariu, A.

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901(2003).
[CrossRef] [PubMed]

Emiliani, V.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Engelen, R. J. P.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Freund, I.

N. Shvartsman and I. Freund, Phys. Rev. Lett. 72, 1008(1994).
[CrossRef] [PubMed]

I. Freund, J. Opt. Soc. Am. A 11, 1644 (1994).
[CrossRef]

Genack, A. Z.

S. Zhang and A. Z. Genack, Phys. Rev. Lett. 99, 203901 (2007).
[CrossRef]

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Halperin, B. I.

B. I. Halperin, in Physics of Defects (North Holland, 1981).

Hanson, S. G.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Hu, B.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

Hwang, K. S.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
[CrossRef]

Intonti, F.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

Jiang, P.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
[CrossRef]

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

Korterik, J. P.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Kuipers, L.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Lagendijk, A.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Liu, C.

Miyamoto, Y.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Mori, D.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

OHolleran, K.

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

Opheij, A.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Padgett, M. J.

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

Park, S.-H.

Pnini, R.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Raikh, M. E.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 92, 253902 (2004).
[CrossRef] [PubMed]

Sebbah, P.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Shapiro, B.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 92, 253902 (2004).
[CrossRef] [PubMed]

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef] [PubMed]

Shvartsman, N.

N. Shvartsman and I. Freund, Phys. Rev. Lett. 72, 1008(1994).
[CrossRef] [PubMed]

Takeda, M.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

van Hulst, N. F.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

van Oosten, D.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

Wang, W.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

Wiersma, D. S.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang and A. Z. Genack, Phys. Rev. Lett. 99, 203901 (2007).
[CrossRef]

Chem. Mater. (1)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, Chem. Mater. 11, 2132 (1999).
[CrossRef]

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

Nature Phys. (1)

M. R. Dennis, R. P. King, B. Jack, K. OHolleran, and M. J. Padgett, Nature Phys. 6, 118 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Phys. Rev. Lett. (10)

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef] [PubMed]

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 92, 253902 (2004).
[CrossRef] [PubMed]

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901(2003).
[CrossRef] [PubMed]

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef] [PubMed]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef] [PubMed]

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef] [PubMed]

S. Zhang and A. Z. Genack, Phys. Rev. Lett. 99, 203901 (2007).
[CrossRef]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, Phys. Rev. Lett. 94, 103902 (2005).
[CrossRef] [PubMed]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

N. Shvartsman and I. Freund, Phys. Rev. Lett. 72, 1008(1994).
[CrossRef] [PubMed]

Proc. R. Soc. A (2)

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 456, 2059(2000).
[CrossRef]

Proc. SPIE (1)

M. R. Dennis, Proc. SPIE 4403, 13 (2001).
[CrossRef]

Other (1)

B. I. Halperin, in Physics of Defects (North Holland, 1981).

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

(a) Schematic representation of the setup. The inset (I) shows a scanning electron microscope image of the near-field probe. (b) Example of the electric field amplitude distribution collected by the near-field microscope at λ = 1442 nm . The white dots in correspondence of the zero val ues of the field amplitude correspond to vortice positions. (c), (d) Phase map and the map of the zero lines of the real part and the imaginary part of the field are presented, respectively, in correspondence to region indicated by the square in (a). (e) Map of the integrated charge correlation function C Q obtained from the experiential data. (f) Angular average of C Q ( Δ r ) compared with the calculated expression.

Fig. 2
Fig. 2

(a) Schematic representation of the geometry of the real/imaginary tangent plane: the angle that measures the orientation of the plane with respect to the x axes is ρ, while the slope of the plane is ϕ. (b)–(d) Vortex morphological parameters distributions for ρ, α, and a, respectively. The red curves in the graphs represent the expected behavior for such parameters for the isotropic random field case.

Fig. 3
Fig. 3

(a), (b) Real part of the spatial correlation function of the electric field for λ = 1442 nm and λ = 1562 nm , respectively. (c) The dotted black line in the graph reports the cut along the y direction of the real part of the spatial correlation function, while the dotted red (gray) line reports the imaginary part. The black straight line is the fit of the real part of the correlation function obtained considering the theory for random systems reported in [11]. (d) Same as (c) for the x direction. The black straight line is the expression of the real part of the correlation function considering a refractive index equal to 1.

Equations (2)

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

E ( r ) = A ( r ) exp i φ ( r ) = f Re ( r ) + i f Im ( r ) ,
C Q ( Δ r ) = 2 η < N + ( 0 ) [ N + ( Δ r ) N ( Δ r ) ] > δ ( Δ r ) ,

Metrics