Abstract

We report on the experimental observation of speckle formation from a transparent crystal formed by a random distribution of nonlinear domains. The angular distribution of second-harmonic light generated by a transparent strontium barium niobate crystal is measured for different diameters of the fundamental beam and crystal thicknesses. Distinct manifestations of speckle pattern formation are found in these experiments. By using a theoretical Green’s function formalism, we explain the reported observations as a result of the linear interference among the second-harmonic waves generated in all directions by each of the nonlinear domains forming the nonlinear crystal.

© 2011 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Controlling the diffused nonlinear light generated in random materials

Can Yao, Francisco J. Rodriguez, and Jordi Martorell
Opt. Lett. 37(10) 1676-1678 (2012)

Optical second-harmonic scattering from a non-diffusive random distribution of nonlinear domains

Jorge Bravo-Abad, Xavier Vidal, Jorge L. Domínguez Juárez, and Jordi Martorell
Opt. Express 18(13) 14202-14211 (2010)

Comparative analysis of ferroelectric domain statistics via nonlinear diffraction in random nonlinear materials

B. Wang, K. Switkowski, C. Cojocaru, V. Roppo, Y. Sheng, M. Scalora, J. Kisielewski, D. Pawlak, R. Vilaseca, H. Akhouayri, W. Krolikowski, and J. Trull
Opt. Express 26(2) 1083-1096 (2018)

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, J. Opt. Soc. Am. 66, 1145 (1976).
    [Crossref]
  2. M. P. Van Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
    [Crossref] [PubMed]
  3. P. E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
    [Crossref] [PubMed]
  4. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
    [Crossref]
  5. S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
    [Crossref]
  6. M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
    [Crossref] [PubMed]
  7. X. Vidal and J. Martorell, Phys. Rev. Lett. 97, 013902 (2006).
    [Crossref] [PubMed]
  8. J. Bravo-Abad, X. Vidal, J. L. Domínguez-Juárez, and J. Martorell, Opt. Express 18, 14202 (2010).
    [Crossref] [PubMed]
  9. A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
    [Crossref] [PubMed]
  10. T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
    [Crossref]

2010 (1)

2006 (1)

X. Vidal and J. Martorell, Phys. Rev. Lett. 97, 013902 (2006).
[Crossref] [PubMed]

2005 (1)

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

2004 (1)

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

2003 (1)

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[Crossref] [PubMed]

1998 (1)

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

1994 (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
[Crossref]

1985 (2)

M. P. Van Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[Crossref] [PubMed]

P. E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[Crossref] [PubMed]

1976 (1)

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
[Crossref]

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

Betzler, K.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[Crossref] [PubMed]

Bravo-Abad, J.

DeMattei, R. C.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

Domínguez-Juárez, J. L.

Feigelson, R. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
[Crossref]

Goodman, J. W.

Haidar, R.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

Isakov, D.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

Ivanov, N.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

Ivleva, L.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

Kawai, S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

Kupecek, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

Lagendijk, A.

M. P. Van Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[Crossref] [PubMed]

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
[Crossref]

Lee, H. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

Lemasson, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

Maret, G.

P. E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[Crossref] [PubMed]

Martorell, J.

Ogawa, T.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

Rosencher, E.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
[Crossref]

Tunyagi, A.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

Tunyagi, A. R.

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[Crossref] [PubMed]

Ulex, M.

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[Crossref] [PubMed]

Van Albada, M. P.

M. P. Van Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[Crossref] [PubMed]

Vidal, X.

Volk, T.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

Wöhlecke, M.

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

Wolf, P. E.

P. E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[Crossref]

J. Appl. Phys. (1)

T. Volk, D. Isakov, N. Ivanov, L. Ivleva, K. Betzler, A. Tunyagi, and M. Wöhlecke, J. Appl. Phys. 97, 074102 (2005).
[Crossref]

J. Opt. Soc. Am. (1)

Nature (2)

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[Crossref] [PubMed]

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, Nature 368, 436 (1994).
[Crossref]

Opt. Express (1)

Phys. Rev. Lett. (4)

M. P. Van Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[Crossref] [PubMed]

P. E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[Crossref] [PubMed]

X. Vidal and J. Martorell, Phys. Rev. Lett. 97, 013902 (2006).
[Crossref] [PubMed]

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[Crossref] [PubMed]

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 Speckle from the 532 nm wavelength SHG from a poled crystal detected with a CCD camera located at the focal plane of a 150 mm focal lens. Images taken using fundamental beam diameters of (a)  2 mm and (b)  4 mm . The inset on (b) shows the SHG speckle from a crystal with smaller domains. (c) Sequence when the crystal was rotated from 0 ° to 5 ° with respect to the incident beam. A 50 mm focal lens and 1 mm fundamental beam diameter were used in this case. (d) Intensity as a function of the angle of emission with respect to the fundamental beam. Inset: experimental scheme. (e) Intensity of the averaged speckle as a function of the crystal length obtained by translating the fundamental beam across a wedge-shaped crystal.
Fig. 2
Fig. 2 Simulated SHG intensity from 303 μm × 303 μm structures consisting of (a)  3 μm × 3 μm square domains when 2% of them are in a given polarization and (b)  1 μm × 1 μm square domains, 50% in each polarization. Examples of the structures are shown in the insets on the right, using white or black squares depending on the polarization. Left inset on (a): intensity fluctuations when the width of the structure is reduced to 75 μm . Left inset on (b): intensity at 5 ° from a similar composition of domains in which the length of the structure is changed. The result is averaged over 30 different random structures.
Fig. 3
Fig. 3 SHG intensity as a function of the angle of emission with respect to the fundamental beam in the direction (a) perpendicular and (b) parallel to the c axis. The thin lines correspond to the experimental data and the thick lines to the fittings with the theoretical model for cylindrical domains of 6 μm diameter and 580 μm length.

Equations (2)

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

E i ( 2 ω ) = ( 2 ω ) 2 e i | k ( 2 ω ) | r c 2 4 π r × V ( δ i , j k ^ i ( 2 ω ) k ^ j ( 2 ω ) ) ( χ j , k , l ( 2 ) E k ( ω ) E l ( ω ) ) e i Δ k · r d r ,
I ( 2 ω ) = 2 ω 4 n ( 2 ω ) [ χ z , z , z ( 2 ) ] 2 c 5 π 2 r 2 n ( ω ) 2 ε 0 [ I ( ω ) ] 2 h 2 L 4 × sinc 2 [ Δ k x L 2 ] sinc 2 [ Δ k y L 2 ] | i = 1 N e i ( Δ k x x i + Δ k y y i ) | 2 ,

Metrics