Abstract

An InP-based Mach–—Zehnder interferometer combined with a metamaterial layer consisting of a split-ring resonator array was constructed to measure the complex permeability of the metamaterial. At a wavelength of 1.5 μm, the metamaterial showed non-unity relative permeability induced by magnetic interaction with propagating light in the device. This method of measurement would be useful to determine constitutive parameters in such waveguide-based photonic devices, allowing us to design photonic integrated circuits that make use of metamaterials.

© 2012 Optical Society of America

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  1. S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
    [CrossRef]
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    [CrossRef]
  3. W. Cai, U. K. Chettiar, H. K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Opt. Express 15, 3333 (2007).
    [CrossRef]
  4. M. S. Rill, C. E. Kriegler, M. Thiel, G. von Freymann, S. Linden, and M. Wegener, Opt. Lett. 34, 19 (2009).
    [CrossRef]
  5. C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
    [CrossRef]
  6. G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.
  7. K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (4)

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, Opt. Express 19, 3973 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, S. Myoga, N. Nishiyama, and S. Arai, Opt. Lett. 36, 2327 (2011).
[CrossRef]

2010 (1)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
[CrossRef]

2009 (3)

2007 (3)

2006 (1)

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Adamo, G.

G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.

Amemiya, T.

T. Amemiya, T. Shindo, D. Takahashi, S. Myoga, N. Nishiyama, and S. Arai, Opt. Lett. 36, 2327 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

Arai, S.

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, S. Myoga, N. Nishiyama, and S. Arai, Opt. Lett. 36, 2327 (2011).
[CrossRef]

Atwater, H. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, Science 316(5823), 430 (2007).
[CrossRef]

Bratkovsky, A. M.

Brueck, S. R.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

Brueck, S. R. J.

Burger, S.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Cai, W.

Chaturvedi, P.

Chettiar, U. K.

Cho, D. J.

Coldren, L. A.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Dani, K. M.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, Opt. Express 19, 3973 (2011).
[CrossRef]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

De Angelis, F.

G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.

de Silva, V. C.

Di Fabrizio, E.

G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.

Dionne, J. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, Science 316(5823), 430 (2007).
[CrossRef]

Dolling, G.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Drachev, V. P.

Enkrich, C.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Guzzon, R. S.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Ishikawa, A.

Johansson, L.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Kawata, S.

Kildishev, A. V.

Klein, M. W.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Koschny, T.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Kriegler, C. E.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
[CrossRef]

M. S. Rill, C. E. Kriegler, M. Thiel, G. von Freymann, S. Linden, and M. Wegener, Opt. Lett. 34, 19 (2009).
[CrossRef]

Krishnamachari, U.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Ku, Z.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, Opt. Express 19, 3973 (2011).
[CrossRef]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, Science 316(5823), 430 (2007).
[CrossRef]

Linden, S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
[CrossRef]

M. S. Rill, C. E. Kriegler, M. Thiel, G. von Freymann, S. Linden, and M. Wegener, Opt. Lett. 34, 19 (2009).
[CrossRef]

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

MacDonald, K. F.

G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.

Myoga, S.

Nicholes, S. C.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Nishiyama, N.

T. Amemiya, T. Shindo, D. Takahashi, S. Myoga, N. Nishiyama, and S. Arai, Opt. Lett. 36, 2327 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

Norberg, E. J.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Ponizovskaya, E.

Prasankumar, R. P.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, Opt. Express 19, 3973 (2011).
[CrossRef]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

Rill, M. S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
[CrossRef]

M. S. Rill, C. E. Kriegler, M. Thiel, G. von Freymann, S. Linden, and M. Wegener, Opt. Lett. 34, 19 (2009).
[CrossRef]

Ristic, S.

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

Schmidt, F.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Shalaev, V. M.

Shen, Y. R.

Shindo, T.

T. Amemiya, T. Shindo, D. Takahashi, S. Myoga, N. Nishiyama, and S. Arai, Opt. Lett. 36, 2327 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

Soukoulis, C. M.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Takahashi, D.

T. Amemiya, T. Shindo, D. Takahashi, S. Myoga, N. Nishiyama, and S. Arai, Opt. Lett. 36, 2327 (2011).
[CrossRef]

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

Tanaka, T.

Taylor, A. J.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, Opt. Express 19, 3973 (2011).
[CrossRef]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

Thiel, M.

Upadhya, P. C.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. J. Brueck, Opt. Express 19, 3973 (2011).
[CrossRef]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

von Freymann, G.

Wang, F.

Wang, S. Y.

Wegener, M.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
[CrossRef]

M. S. Rill, C. E. Kriegler, M. Thiel, G. von Freymann, S. Linden, and M. Wegener, Opt. Lett. 34, 19 (2009).
[CrossRef]

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

Wu, W.

Yuan, H. K.

Zhang, X.

Zheludev, N. I.

G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.

Zhou, J.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Amemiya, T. Shindo, D. Takahashi, N. Nishiyama, and S. Arai, IEEE J. Quantum Electron. 47, 736 (2011).
[CrossRef]

IEEE J. Sel. Topics. Quantum Electron. (2)

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 12, 1097 (2006).
[CrossRef]

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Topics. Quantum Electron. 16, 367 (2010).
[CrossRef]

J. Lightw. Technol. (1)

L. A. Coldren, S. C. Nicholes, L. Johansson, S. Ristic, R. S. Guzzon, E. J. Norberg, and U. Krishnamachari, J. Lightw. Technol. 29, 554 (2011).
[CrossRef]

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

Nano Lett. (1)

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, Nano Lett. 37, 3565 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Science (1)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, Science 316(5823), 430 (2007).
[CrossRef]

Other (1)

G. Adamo, K. F. MacDonald, F. De Angelis, E. Di Fabrizio, and N. I. Zheludev, in Proceedings of 23rd Annual Meeting of the IEEE Photonics Society (2010), paper WM2.

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Figures (4)

Fig. 1.
Fig. 1.

(a) GaInAsP/InP waveguide with SRR array and (b) Mach–Zehnder interferometer consisting of GaInAsP/InP waveguides and SRR array attached on one arm.

Fig. 2.
Fig. 2.

SRRs and arms of MZI: (a) oblique view of four-cut SRRs and (c) two arms, observed with SEM. One arm has an SRR array. Three-dimensional views of (b) four-cut SRR and (d) two-cut SRR.

Fig. 3.
Fig. 3.

Output intensity in devices with four-cut SRRs (blue lines), two-cut SRRs (red lines), and without SRRs (black lines) as a function of wavelength, measured for (a) straight ridge waveguides and (b) MZIs.

Fig. 4.
Fig. 4.

Measured relative permeability (real and imaginary parts) of SRR array on MZI waveguide, plotted as a function of frequency.

Tables (1)

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Table 1. All Parameters Used in the Experiment

Equations (1)

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x2Ex+y2Ex+(k02εxμzμzμyβ2)Ex=0

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