Abstract

We demonstrate, for what is to our knowledge the first time, two-dimensional (2D) corrugated waveguides at optical wavelengths obtained by use of 2D colloidal crystals. We report experimental studies of light coupling into and out of the waveguide structure. The diffracted light shows interesting optical properties that exist only in such 2D grating structures. Field distribution of the fundamental mode in the structure is studied by use of a simplified model in our analysis. Potential applications of this type of structure are discussed.

© 1999 Optical Society of America

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  1. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  3. See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
    [CrossRef]
  4. See, for example, A. Yariv, Optical Electronics (Oxford University, New York, 1997)G. P. Agrawal and K. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).
  5. J. Joannopoulos, P. Villeneuve, and S. Fan, Nature 386, 143 (1997).
    [CrossRef]
  6. N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
    [CrossRef]
  7. G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
    [CrossRef]

1997 (1)

J. Joannopoulos, P. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

1994 (1)

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

1992 (1)

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1986 (1)

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

Alferness, R. C.

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

Buhl, L. L.

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

Denkov, N. D.

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Divino, M. D.

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

Fan, S.

J. Joannopoulos, P. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Ivanov, I. B.

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Joannopoulos, J.

J. Joannopoulos, P. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Joyner, C. H.

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

Kralchevsky, P. A.

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Lazarov, G. S.

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

Martyak, M. J. R.

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

Meade, R.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Nagayama, K.

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Nagayama, N.

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

Velev, O. D.

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Villeneuve, P.

J. Joannopoulos, P. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Winn, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yariv, A.

See, for example, A. Yariv, Optical Electronics (Oxford University, New York, 1997)G. P. Agrawal and K. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).

Yoshimura, H.

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

See, for example, R. C. Alferness, C. H. Joyner, M. D. Divino, M. J. R. Martyak, and L. L. Buhl, Appl. Phys. Lett. 49, 125 (1986)T. L. Koch, F. S. Choa, F. Heismann, and U. Koren, Electron. Lett. 25, 890 (1989).
[CrossRef]

J. Chem. Soc. Faraday Trans. (1)

G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994)O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997).
[CrossRef]

Langmuir (1)

N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992)Nature 361, 26 (1991).
[CrossRef]

Nature (1)

J. Joannopoulos, P. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Other (2)

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

See, for example, A. Yariv, Optical Electronics (Oxford University, New York, 1997)G. P. Agrawal and K. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup of the 2D corrugated waveguide with colloidal crystals. Inset: vector diagram for phase matching.

Fig. 2
Fig. 2

Far-field diffraction pattern of (a) polycrystalline and (b) single colloidal crystals upon a glass substrate.

Fig. 3
Fig. 3

(a) Intensity pattern of output light from a 2D corrugated waveguide with colloidal crystals and (b) phase-matching conditions for the pattern in space.

Fig. 4
Fig. 4

Index and mode profiles of the field in the 2D corrugated waveguide.

Equations (1)

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Kout,x=Kw+Kgcosϕ,Kout,y=Kw+Kgsinϕ,Kout,z=-2π/λ2-Kout,x2-Kout,y21/2.

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