Abstract

We demonstrate that a photonic lattice with short- and long-range harmonic modulations of the refractive index facilitates formation of flat photonic bands and leads to slow propagation of light. The system can be considered a coupled-resonator optical waveguide (CROW): photonic bands with abnormally small dispersion are created due to the interaction of long-lived states in the cavity regions via weak coupling across tunneling barriers. Unlike previous CROW implementations, the proposed structures can be fabricated with interference photolithography (holography), sidestepping the issue of resonator-to-resonator fluctuation of the system parameters. The proposed holography-based approach enables fabrication of arrays with a large number of coupled optical resonators, which is necessary for practical applications.

© 2007 Optical Society of America

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References

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  2. P. W. Milonni, Fast Light, Slow Light and Left Handed Light (Institute of Physics, 2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 3870 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
    [CrossRef]

2006 (1)

2005 (3)

See J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photon. News 16(2), 36 (2005) and references therein.
[CrossRef]

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

2004 (2)

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

2002 (1)

2001 (3)

M. Bayindir, S. Tanriseven, and E. Ozbay, Appl. Phys. A 72, 117 (2001).
[CrossRef]

M. Bayindir, C. Kural, and E. Ozbay, J. Opt. A 3, 184 (2001).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Appl. Phys. 90, 3905 (2001).
[CrossRef]

2000 (1)

Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 3870 (2000).

1999 (1)

1998 (2)

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Phys. Soc. Jpn. 67, 3414 (1998).
[CrossRef]

1996 (1)

J. M. Benedickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[CrossRef]

1994 (1)

1976 (1)

D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
[CrossRef]

Altug, H.

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Bayindir, M.

M. Bayindir, S. Tanriseven, and E. Ozbay, Appl. Phys. A 72, 117 (2001).
[CrossRef]

M. Bayindir, C. Kural, and E. Ozbay, J. Opt. A 3, 184 (2001).
[CrossRef]

Belmonte, M.

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

Benedickson, J. M.

J. M. Benedickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Bertino, M. F.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Della Valle, G.

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

DeRose, G. A.

Dowling, J. P.

J. M. Benedickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Du, Y.

Gadipalli, R. R.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Galzerano, G.

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

Guha, S.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

He, J.-L.

Hofstadter, D. R.

D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
[CrossRef]

Janner, D.

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

Kawaguchi, T.

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

Kitahara, H.

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

Koda, T.

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Appl. Phys. 90, 3905 (2001).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Phys. Soc. Jpn. 67, 3414 (1998).
[CrossRef]

Kural, C.

M. Bayindir, C. Kural, and E. Ozbay, J. Opt. A 3, 184 (2001).
[CrossRef]

Laporta, P.

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

Lee, R. K.

Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 3870 (2000).

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Leventis, N.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Liao, J.

Liu, Z.-W.

Longhi, S.

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

Martin de Sterke, C.

Milonni, P. W.

P. W. Milonni, Fast Light, Slow Light and Left Handed Light (Institute of Physics, 2005).

Ming, N.-B.

Miyashital, J.

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

Modinos, A.

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

Ohtaka, K.

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Appl. Phys. 90, 3905 (2001).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Phys. Soc. Jpn. 67, 3414 (1998).
[CrossRef]

Ozbay, E.

M. Bayindir, S. Tanriseven, and E. Ozbay, Appl. Phys. A 72, 117 (2001).
[CrossRef]

M. Bayindir, C. Kural, and E. Ozbay, J. Opt. A 3, 184 (2001).
[CrossRef]

Paloczi, G.

See J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photon. News 16(2), 36 (2005) and references therein.
[CrossRef]

Poladian, L.

Poon, J.

See J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photon. News 16(2), 36 (2005) and references therein.
[CrossRef]

Poon, J. K. S.

Qin, Y.-Q.

Scalora, M.

J. M. Benedickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[CrossRef]

Scherer, A.

Scheuer, J.

See J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photon. News 16(2), 36 (2005) and references therein.
[CrossRef]

Shimada, R.

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Appl. Phys. 90, 3905 (2001).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Phys. Soc. Jpn. 67, 3414 (1998).
[CrossRef]

Sipe, J. E.

Sotiriou-Leventis, C.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, Photonic Band Gap Materials (Kluwer, 1996).

Stefanou, N.

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

Story, J. G.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Takeda, M. W.

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

Tanriseven, S.

M. Bayindir, S. Tanriseven, and E. Ozbay, Appl. Phys. A 72, 117 (2001).
[CrossRef]

Tokuhiro, A. T.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Ueta, T.

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Appl. Phys. 90, 3905 (2001).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Phys. Soc. Jpn. 67, 3414 (1998).
[CrossRef]

Vuckovic, J.

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Wang, H.-T.

Williams, C. G.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Xu, Y.

Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 3870 (2000).

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Yariv, A.

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, J. Lightwave Technol. 24, 1843 (2006).
[CrossRef]

See J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photon. News 16(2), 36 (2005) and references therein.
[CrossRef]

Y. Xu, R. K. Lee, and A. Yariv, J. Opt. Soc. Am. B 17, 3870 (2000).

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 2005).

Zhang, C.

Zhang, G.

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

Zhu, L.

Zhu, S.-N.

Zhu, Y.-Y.

Appl. Phys. A (1)

M. Bayindir, S. Tanriseven, and E. Ozbay, Appl. Phys. A 72, 117 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

M. F. Bertino, R. R. Gadipalli, J. G. Story, C. G. Williams, G. Zhang, C. Sotiriou-Leventis, A. T. Tokuhiro, S. Guha, and N. Leventis, Appl. Phys. Lett. 85, 6007 (2004).
[CrossRef]

H. Altug and J. Vuckovic, Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

J. Appl. Phys. (1)

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Appl. Phys. 90, 3905 (2001).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A (1)

M. Bayindir, C. Kural, and E. Ozbay, J. Opt. A 3, 184 (2001).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

J. Phys. Soc. Jpn. (2)

H. Kitahara, T. Kawaguchi, J. Miyashital, R. Shimada, and M. W. Takeda, J. Phys. Soc. Jpn. 73, 296 (2004).
[CrossRef]

R. Shimada, T. Koda, T. Ueta, and K. Ohtaka, J. Phys. Soc. Jpn. 67, 3414 (1998).
[CrossRef]

Opt. Lett. (1)

Opt. Photon. News (1)

See J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photon. News 16(2), 36 (2005) and references therein.
[CrossRef]

Phys. Rev. B (2)

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
[CrossRef]

Phys. Rev. E (2)

J. M. Benedickson, J. P. Dowling, and M. Scalora, Phys. Rev. E 53, 4107 (1996).
[CrossRef]

D. Janner, G. Galzerano, G. Della Valle, P. Laporta, S. Longhi, and M. Belmonte, Phys. Rev. E 72, 056605 (2005).
[CrossRef]

Other (3)

C. M. Soukoulis, Photonic Band Gap Materials (Kluwer, 1996).

P. W. Milonni, Fast Light, Slow Light and Left Handed Light (Institute of Physics, 2005).

P. Yeh, Optical Waves in Layered Media (Wiley, 2005).

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Figures (1)

Fig. 1
Fig. 1

(a) Photonic bandgap diagram (local PBG) of the dual-periodic photonic crystal lattice defined by Eq. (1) and shown in (b). We used ϵ 0 = 2.25 , Δ ϵ = 0.99 , N = 80 , and asymmetry parameter E 1 E 2 = 7.5 . A N and B N mark the frequencies of the foremost photonic bands on the long- and short-wavelength sides, respectively, of the compound PBG, which extends from A to B when N . (c) Calculated photonic band structure ( N = 80 ) . The A N band shows typical cosine dependence as in Eq. (1) dispersion (d). Plot (e) of the group velocity for the series of bands approaching the compound PBG shows the monotonic decrease (notice the logarithmic scale) toward the gap. As discussed in the text, we attribute this trend to (i) the decrease of the local group velocity inside the resonator regions and (ii) the decrease in tunneling coupling between the resonators. (f) Group velocity in the A N band shown in (d); the inset shows the distribution of intensity (over one period) for the band-edge frequency within the band A N .

Equations (5)

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

ω ( K ) = Ω [ 1 + κ cos ( K a ) ] .
n 2 ( x ) = ϵ ( x ) = ϵ 0 + Δ ϵ [ α cos ( k 1 x ) + β cos ( k 2 x ) ] 2 ,
[ q L 1 , E L 1 q L 2 , E L 2 q R 1 , E R 1 q R 2 , E R 2 ] = [ k 0 { sin ( θ 1 ) , 0 , cos ( θ 1 ) } , E 1 k 0 { sin ( θ 2 ) , 0 , cos ( θ 2 ) } , E 2 k 0 { sin ( θ 1 ) , 0 , cos ( θ 1 ) } , E 1 k 0 { sin ( θ 2 ) , 0 , cos ( θ 2 ) } , E 2 ] .
E ( ω , x ) = e ( ω , x ) × exp [ i K ( ω ) x ] ,
κ = Γ 2 Ω 1 Q .

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