Abstract

We present a design of “ideal” optical delay lines (i.e., constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs. We present a simple formalism for deriving the time-domain coupling coefficients and convert these coefficients to field coupling coefficients of ring resonators. The reflecting CROWs possess a delay-bandwidth product of 0.5 per resonator, larger than that of any kind of transmitting CROW. In the presence of uniform gain, the gain enhanced by slow light propagation and the constant group delay result in efficient and dispersion-free amplifiers.

© 2012 Optical Society of America

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2011 (1)

2009 (1)

2008 (2)

2006 (1)

2005 (3)

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

J. B. Khurgin, Opt. Lett. 30, 513 (2005).
[CrossRef]

R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, J. Lightwave Technol. 23, 4046 (2005).
[CrossRef]

1999 (1)

1995 (1)

R. Orta, P. Savi, R. Tascone, and D. Trinchero, IEEE Photon. Technol. Lett. 7, 1447 (1995).
[CrossRef]

Belmonte, M.

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

Chang-Hasnain, C. J.

Della Valle, G.

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

Ferrari, C.

Galzerano, G.

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

Gomez-Iglesias, A.

Janner, D.

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

Khurgin, J. B.

Krauss, T. F.

Ku, P. C.

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.

Li, J.

Liu, H. C.

Longhi, S.

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

Martinelli, M.

Melloni, A.

Morichetti, F.

O’Faolain, L.

Orta, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, IEEE Photon. Technol. Lett. 7, 1447 (1995).
[CrossRef]

Savi, P.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, IEEE Photon. Technol. Lett. 7, 1447 (1995).
[CrossRef]

Scherer, A.

Tascone, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, IEEE Photon. Technol. Lett. 7, 1447 (1995).
[CrossRef]

Trinchero, D.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, IEEE Photon. Technol. Lett. 7, 1447 (1995).
[CrossRef]

Tucker, R. S.

Van, V.

White, T. P.

Xu, Y.

Yariv, A.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Spectra of reflection and group delay of an N=6 reflecting Bessel CROW. (b) Schematic drawing of a reflecting CROW. (c), (d) Reflecting CROWs based on ring resonators and grating-defect resonators, respectively.

Fig. 2.
Fig. 2.

(a) (left) CROW propagation band as a function of distance of an N=20 reflecting Bessel CROW. Red lines: Propagation distance for Δω/B=0, 1.4, and 2. (right) Group delay spectrum. (b) Field distribution along the CROW for Δω/B=0, 1.4, and 2.

Fig. 3.
Fig. 3.

(a–d) Spectra of reflection and group delay of N=6 reflecting Bessel CROWs based on ring resonators. (a) B=ωFSR·0.003. (b) B=ωFSR·0.003. (c), (d) B=ωFSR·0.003 with a uniform loss and gain of 1dB/cm respectively. (e),(f) N=10 reflecting Bessel CROWs with disorder of coupling coefficients. (e) κ4=1.05κ4. (f) κi=γiκi for all i.

Equations (3)

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A=[s+1τe1iκ1000iκ1siκ2000iκ2s·············siκN1····iκN1s]
R(s)=srsin=1μ12[A1]1,1=pNμ12pN1pN,
pN=(s+1τe1)pN1+κ12pN2,pN1=spN2+κ22pN3,p2=sp1+κN12,p1=s.

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