Abstract

We analyze fast- and slow-light transmission in a zigzag microring resonator chain. In the superluminal case, a new light-transmission effect is found whereby the input optical pulse is reproduced in an almost-simultaneous manner at the various system outputs. When the input carrier is tuned to a different frequency, the system permits to slow down the propagating optical signal. Between these two extreme cases, the relative delay can be tuned within a broad range. We propose, and analyze numerically, a laser-array configuration for the stable operation of active devices.

© 2009 Optical Society of America

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References

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2008 (3)

2007 (6)

J. B. Khurgin, Opt. Lett. 32, 133 (2007).
[CrossRef]

J. B. Khurgin, Opt. Lett. 32, 163 (2007).
[CrossRef]

F. Fraile-Pelaez and P. Chamorro-Posada, Opt. Express 15, 3177 (2007).
[CrossRef] [PubMed]

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

E. Parra and J. Lowell, Opt. Photonics News 18, 40 (2007).
[CrossRef]

R. W. Boyd and P. Narum, J. Mod. Opt. 54, 2403 (2007).
[CrossRef]

2006 (2)

S. Blair and K. Zheng, Opt. Express 14, 1064 (2006).
[CrossRef] [PubMed]

R. Boyd, D. J. Gauthier, and A. L. Gaeta, Opt. Photonics News 17, 18 (2006).
[CrossRef]

2005 (1)

J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photonics News 16, 36 (2005).
[CrossRef]

2002 (1)

J. Heebner and R. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

1991 (1)

M. Zirngibl, Electron. Lett. 27, 560 (1991).
[CrossRef]

Blair, S.

Boyd, R.

R. Boyd, D. J. Gauthier, and A. L. Gaeta, Opt. Photonics News 17, 18 (2006).
[CrossRef]

J. Heebner and R. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Boyd, R. W.

R. W. Boyd and P. Narum, J. Mod. Opt. 54, 2403 (2007).
[CrossRef]

Chamorro-Posada, P.

Ferrari, C.

Fraile-Pelaez, F.

Gaeta, A. L.

R. Boyd, D. J. Gauthier, and A. L. Gaeta, Opt. Photonics News 17, 18 (2006).
[CrossRef]

Gauthier, D. J.

R. Boyd, D. J. Gauthier, and A. L. Gaeta, Opt. Photonics News 17, 18 (2006).
[CrossRef]

Heebner, J.

J. Heebner and R. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Hoekstra, H. J. W. M.

Khurgin, J. B.

Li, Q.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, IEEE J. Sel. Top. Quantum Electron. 14, 706 (2008).
[CrossRef]

Liu, F.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, IEEE J. Sel. Top. Quantum Electron. 14, 706 (2008).
[CrossRef]

Lowell, J.

E. Parra and J. Lowell, Opt. Photonics News 18, 40 (2007).
[CrossRef]

Martinelli, M.

Melloni, A.

Morichetti, F.

Narum, P.

R. W. Boyd and P. Narum, J. Mod. Opt. 54, 2403 (2007).
[CrossRef]

Paloczi, G.

J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photonics News 16, 36 (2005).
[CrossRef]

Parra, E.

E. Parra and J. Lowell, Opt. Photonics News 18, 40 (2007).
[CrossRef]

Poon, J.

J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photonics News 16, 36 (2005).
[CrossRef]

Qiu, M.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, IEEE J. Sel. Top. Quantum Electron. 14, 706 (2008).
[CrossRef]

Roeloffzen, C. G. H.

Scheuer, J.

J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photonics News 16, 36 (2005).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Su, Y.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, IEEE J. Sel. Top. Quantum Electron. 14, 706 (2008).
[CrossRef]

Uranus, H. P.

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Yariv, A.

J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photonics News 16, 36 (2005).
[CrossRef]

Zhang, Z.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, IEEE J. Sel. Top. Quantum Electron. 14, 706 (2008).
[CrossRef]

Zheng, K.

Zhuang, L.

Zirngibl, M.

M. Zirngibl, Electron. Lett. 27, 560 (1991).
[CrossRef]

Electron. Lett. (1)

M. Zirngibl, Electron. Lett. 27, 560 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, IEEE J. Sel. Top. Quantum Electron. 14, 706 (2008).
[CrossRef]

J. Mod. Opt. (2)

R. W. Boyd and P. Narum, J. Mod. Opt. 54, 2403 (2007).
[CrossRef]

J. Heebner and R. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Nat. Photonics (1)

F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photonics 1, 65 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Opt. Photonics News (3)

J. Scheuer, G. Paloczi, J. Poon, and A. Yariv, Opt. Photonics News 16, 36 (2005).
[CrossRef]

R. Boyd, D. J. Gauthier, and A. L. Gaeta, Opt. Photonics News 17, 18 (2006).
[CrossRef]

E. Parra and J. Lowell, Opt. Photonics News 18, 40 (2007).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Geometry of the zig-zag microring resonator chain. Coupling regions are highlighted with dashed circles.

Fig. 2
Fig. 2

Amplitude transfer function and group delay for N = 5 and r g = 0.9 . (a) and (d) r = 0.1 ; (b) and (e) r = 0.9 . Solid, long dashed, short dashed, and dotted lines correspond to the first, second, third and fourth outputs, respectively, while the distinct fifth output is identified with small circles. Results shown in (c) and (f) satisfy condition (12).

Fig. 3
Fig. 3

(a) Proposed laser-array configuration. Gray circles correspond to vertically coupled microrings. (b) Normalized signal transmission. E ref is a reference signal corresponding to a delay of 10 τ 0 . (c) Output normalized peak amplitude, (d) relative delay of the signal peak, and (e) spectral signal to sidelobe ratio (SSLR).

Equations (12)

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H k ( Ω ) = ( 1 ) k exp ( j 2 ( k + 2 ) Ω d L ) r r g 2 exp ( 2 j Ω ) 1 g 2 r 2 exp ( 2 j Ω ) [ t 2 g exp ( j Ω ) 1 g 2 r 2 exp ( 2 j Ω ) ] k
H N ( Ω ) = ( 1 ) N exp ( j 2 ( N + 1 ) Ω d L ) [ t 2 g exp ( j Ω ) 1 g 2 r 2 exp ( j 2 Ω ) ] N .
τ g , k τ 0 = 2 ( k + 2 ) d L 2 g 2 ( cos ( 2 Ω ) g 2 ) 1 2 g 2 cos ( 2 Ω ) + g 4 + k + ( k + 1 ) 2 g 2 r 2 ( cos ( 2 Ω ) g 2 r 2 ) 1 2 g 2 r 2 cos ( 2 Ω ) + g 4 r 4
τ g , N τ 0 = 2 ( N + 1 ) d L + N ( 1 + 2 g 2 r 2 ( cos ( 2 Ω ) g 2 r 2 ) 1 2 g 2 r 2 cos ( 2 Ω ) + g 4 r 4 ) .
τ g , k τ 0 = 2 ( k + 2 ) d L + 1 + k + ( k + 1 ) 2 g 2 r 2 1 g 2 r 2 ,
τ g , N τ 0 = 2 ( N + 1 ) d L + N + N 2 g 2 r 2 1 g 2 r 2 ,
Δ τ g τ 0 = 2 d L + 1 + 2 g 2 r 2 1 g 2 r 2 .
τ g , k τ 0 = 2 ( k + 2 ) d L + 2 g 2 1 + g 2 + k ( k + 1 ) 2 g 2 r 2 1 + g 2 r 2
τ g , N τ 0 = 2 ( N + 1 ) d L + N ( 1 2 g 2 r 2 1 + g 2 r 2 ) .
τ g , k = τ r = τ 0 g 2 1 g 2 + 1 .
Δ τ g τ 0 = 2 d L + 1 2 g 2 r 2 1 + g 2 r 2 ,
r = g 1 g ( g + 1 ) .

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