Abstract

We study second-harmonic generation from gold split-ring resonators on a crystalline GaAs substrate. By systematically varying the relative orientation of the split-ring resonators with respect to the incident linear polarization of light and the GaAs crystallographic axes, we unambiguously identify a nonlinear contribution that originates specifically from the interplay of the local fields of the split-ring resonators and the bulk GaAs second-order nonlinear-susceptibility tensor. The experimental results are in good agreement with theoretical modeling.

© 2009 Optical Society of America

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2008 (5)

2007 (3)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, Opt. Express 15, 5238 (2007).
[CrossRef] [PubMed]

2006 (2)

2003 (1)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Brueck, S. R. J.

Canfield, B. K.

Decker, M.

Enkrich, C.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, Science 313, 502 (2006).
[CrossRef] [PubMed]

Fan, W.

Feth, N.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Hoyer, W.

Jin, J.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Kauranen, M.

Kim, E.

E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, Phys. Rev. B 78, 113102 (2008).
[CrossRef]

Kim, S.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Kim, S. W.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Kim, Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Kim, Y. J.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Klein, M. W.

Koch, S. W.

Kujala, S.

Linden, S.

Liu, J.

Molloy, K. J.

Moloney, J. V.

Niesler, F. B. P.

Osgood, R. M.

Panoiu, N. C.

Park, I. Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Shadrivov, I. V.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Shalaev, V. M.

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Shen, Y. R.

E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, Phys. Rev. B 78, 113102 (2008).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Svirko, Y.

Turunen, J.

Wang, F.

E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, Phys. Rev. B 78, 113102 (2008).
[CrossRef]

Wegener, M.

Wu, W.

E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, Phys. Rev. B 78, 113102 (2008).
[CrossRef]

Yu, Z.

E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, Phys. Rev. B 78, 113102 (2008).
[CrossRef]

Zeng, Y.

Zhang, S.

Zharov, A. A.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Nat. Photonics (1)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Nature (1)

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, Nature 453, 757 (2008).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (1)

E. Kim, F. Wang, W. Wu, Z. Yu, and Y. R. Shen, Phys. Rev. B 78, 113102 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Science (2)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, Science 313, 502 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, 2003).

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Figures (4)

Fig. 1
Fig. 1

Top, example of a measured normal-incidence reflectance spectrum (taken from the air side) of lithographically defined SRR on a crystalline GaAs substrate. Incident linear polarization is horizontal. The narrow gray area illustrates the exciting laser spectrum centered at 1.5 μ m wavelength. The sample corresponds to that in Fig. 3b; the electron micrograph on the right-hand side shows selected SRR from this sample. Bottom, same but theory.

Fig. 2
Fig. 2

(left) GaAs zinc-blende crystal structure and (right) schematic representation by a “checkerboard cube” (used in Fig. 3).

Fig. 3
Fig. 3

(a)–(c) SHG from three different samples: (a) (100) GaAs; (b) and (c) (110) GaAs. The orientation of the GaAs crystal (compare Fig. 2), SRR, and the incident horizontal linear polarization (unlettered arrow) is illustrated in the left column. Light impinges under normal incidence ( + z direction). SHG is detected into the forward direction (also + z ). The right column shows measured polar diagrams (dark, blue curves) of the emerging SHG signal, where the horizontal (vertical) axis with respect to the panel plane is the x ( y ) direction. The experiment in (b) can be directly compared with theory (light, red curve).

Fig. 4
Fig. 4

Snapshot of the local electric-field components underneath the SRR inside the GaAs for excitation at 1.5 μ m wavelength. All components are equally normalized to the incident electric-field amplitude in the GaAs. One unit cell of the SRR array is shown; the geometry corresponds to Fig. 3b.

Equations (2)

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P x ( 2 ) = ϵ 0 χ x , z , z ( 2 ) E z E z ϵ 0 χ x , y , y ( 2 ) E y E y ,
P y ( 2 ) = ϵ 0 χ y , x , y ( 2 ) E x E y ϵ 0 χ y , y , x ( 2 ) E y E x ,

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