Abstract

A side coupled adjacent resonators CROW (SC-CROW) structure is presented. The dispersion relation, group velocity and GVD are found numerically and analytically using a transfer matrix method. The structure shows fast and slow transmission of light. Zero group velocity is present at the ends of the Brillouin zone, but also in other parts of it. Infinite and finite SC-CROW structures show band gaps created by Bragg and ring resonances. Pulse propagation at slow group velocities is highly dispersive, but easier to manage at higher group velocities. The differences between SC-CROW, SCISSOR and CROW waveguides are studied in detail.

© 2009 Optical Society of America

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  2. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
    [CrossRef]
  3. T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
    [CrossRef]
  4. R. C. Polson, G. Levina, and Z. V. Vardeny, "Spectral analysis of polymer microring lasers," Appl. Phys. Lett. 76, 3858-3860 (2000).
    [CrossRef]
  5. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
    [CrossRef]
  6. J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
    [CrossRef]
  7. X. Fengnian, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).
  8. J. Heebner, P. Chak, S. Pereira, J. Sipe, and R. Boyd, "Distributed and localized feedback in microresonator sequences for linear and nonlinear optics," J. Opt. Soc. Am. B 21, 1818-1832 (2004).
    [CrossRef]
  9. J. Heebner, R. Boyd, and Q. Park, "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2002).
    [CrossRef]
  10. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
    [CrossRef]
  11. A. G. Yamilov, M. R. Herrera, and M. F. Bertino, "Slow-light effect in dual-periodic photonic lattice," J. Opt. Soc. Am. B 25, 599-608 (2008).
    [CrossRef]
  12. K. Sakoda, "Enhanced light amplification due to group velocity anomaly peculiar to two and three dimensional photonic crystals," Opt. Express 4, 167-176 (1999).
    [CrossRef] [PubMed]
  13. S. Nojima, "Enhancement of optical gain in two dimensional photonic crystal with active lattice points," Jpn. J. Appl. Phys. 37, 565-567 (1998).
    [CrossRef]
  14. S. Mookherjea, "Semiconductor coupled-resonator optical waveguide laser, "Appl. Phys. Lett. 84, 3265-3267 (2004).
    [CrossRef]
  15. P. Chak, J. S. Poon, and A. Yariv, "Optical bright and dark states in side-coupled resonator structures," Opt. Lett. 32, 1785-1787 (2007).
    [CrossRef] [PubMed]
  16. S. Ha et al., "Dispersionless tunneling of slow light in antisymmetric photonic crystal couplers," Opt. Express 16, 1104-1114 (2008).
    [CrossRef] [PubMed]
  17. K. Oda, N. Takato, and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 9, 728-736 (1991).
    [CrossRef]

2008

2007

2006

X. Fengnian, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).

2005

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
[CrossRef]

2004

2003

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

2002

2000

R. C. Polson, G. Levina, and Z. V. Vardeny, "Spectral analysis of polymer microring lasers," Appl. Phys. Lett. 76, 3858-3860 (2000).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

1999

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
[CrossRef]

K. Sakoda, "Enhanced light amplification due to group velocity anomaly peculiar to two and three dimensional photonic crystals," Opt. Express 4, 167-176 (1999).
[CrossRef] [PubMed]

1998

S. Nojima, "Enhancement of optical gain in two dimensional photonic crystal with active lattice points," Jpn. J. Appl. Phys. 37, 565-567 (1998).
[CrossRef]

1997

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

1994

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

1991

K. Oda, N. Takato, and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 9, 728-736 (1991).
[CrossRef]

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Bertino, M. F.

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Boyd, R.

Cao, W.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Chak, P.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Fengnian, X.

X. Fengnian, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Goldhar, J.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Ha, S.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Heebner, J.

Herrera, M. R.

Ho, P. T.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Ibrahim, T. A.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Kim, Y.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Lee, C. H.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Lee, R. K.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
[CrossRef]

Levina, G.

R. C. Polson, G. Levina, and Z. V. Vardeny, "Spectral analysis of polymer microring lasers," Appl. Phys. Lett. 76, 3858-3860 (2000).
[CrossRef]

Li, J.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Little, B. E.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Mookherjea, S.

S. Mookherjea, "Semiconductor coupled-resonator optical waveguide laser, "Appl. Phys. Lett. 84, 3265-3267 (2004).
[CrossRef]

Nojima, S.

S. Nojima, "Enhancement of optical gain in two dimensional photonic crystal with active lattice points," Jpn. J. Appl. Phys. 37, 565-567 (1998).
[CrossRef]

Oda, K.

K. Oda, N. Takato, and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 9, 728-736 (1991).
[CrossRef]

Paloczi, G. T.

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
[CrossRef]

Park, Q.

Pereira, S.

Polson, R. C.

R. C. Polson, G. Levina, and Z. V. Vardeny, "Spectral analysis of polymer microring lasers," Appl. Phys. Lett. 76, 3858-3860 (2000).
[CrossRef]

Poon, J. K. S.

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
[CrossRef]

Poon, J. S.

Sakoda, K.

Scalora, M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Scherer, A.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
[CrossRef]

Scheuer, J.

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
[CrossRef]

Sekaric, L.

X. Fengnian, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).

Sipe, J.

Takato, N.

K. Oda, N. Takato, and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 9, 728-736 (1991).
[CrossRef]

Toba, H.

K. Oda, N. Takato, and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 9, 728-736 (1991).
[CrossRef]

Vardeny, Z. V.

R. C. Polson, G. Levina, and Z. V. Vardeny, "Spectral analysis of polymer microring lasers," Appl. Phys. Lett. 76, 3858-3860 (2000).
[CrossRef]

Vlasov, Y.

X. Fengnian, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Xu, Y.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
[CrossRef]

Yamilov, A. G.

Yariv, A.

P. Chak, J. S. Poon, and A. Yariv, "Optical bright and dark states in side-coupled resonator structures," Opt. Lett. 32, 1785-1787 (2007).
[CrossRef] [PubMed]

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
[CrossRef]

Appl. Phys. Lett.

R. C. Polson, G. Levina, and Z. V. Vardeny, "Spectral analysis of polymer microring lasers," Appl. Phys. Lett. 76, 3858-3860 (2000).
[CrossRef]

S. Mookherjea, "Semiconductor coupled-resonator optical waveguide laser, "Appl. Phys. Lett. 84, 3265-3267 (2004).
[CrossRef]

IEEE J. Lightwave Technol.

K. Oda, N. Takato, and H. Toba, "A wide-FSR waveguide double-ring resonator for optical FDM transmission systems," IEEE J. Lightwave Technol. 9, 728-736 (1991).
[CrossRef]

J. Appl. Phys.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

J. Lightwave Technol.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

S. Nojima, "Enhancement of optical gain in two dimensional photonic crystal with active lattice points," Jpn. J. Appl. Phys. 37, 565-567 (1998).
[CrossRef]

Nat. Photonics

X. Fengnian, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).

Opt. Express

Opt. Lett

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett 24, 711-713 (1999).
[CrossRef]

Opt. Lett.

Opt. Photonics News

J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled resonator optical waveguides: towards slowing and storing of light," Opt. Photonics News 16, 36-40 (2005).
[CrossRef]

Photon. Technol. Lett.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, "Higher order filter response in coupled microring resonators," Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P. T. Ho, and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," Photon. Technol. Lett. 15, 36-38 (2003).
[CrossRef]

Supplementary Material (1)

» Media 1: MPG (3492 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

The SC-CROW structure. Unit cell length L=102µm, ring radius R=50µm.

Fig. 2.
Fig. 2.

Dispersion relations, group velocity and GVD for R=2.5µm, L=0.7πR, n=3.1. A) Weak coupling κ 1=κ 2=κ 3=0.2, B) Strong coupling κ 1=κ 2=κ 3=0.8.

Fig. 3.
Fig. 3.

The intensity of the filed in an infinite SC-CROW for κi =0.8, R=2.5µm, L=0.7πR, λ=1.537µm.

Fig. 4.
Fig. 4.

A two channel finite SC-CROW structures.

Fig. 5.
Fig. 5.

Transmission (A,B) and reflection (C,D) of the SC-CROW shown in Fig. 4. Light is injected in port 1. R=2.5µm, L=0.7πR, κ 1=κ 2=0.8, κ 3=0.2. A, B: Transmission of light in ports 1 and 4. C,D: Reflection in ports 1 and 4.

Fig. 6.
Fig. 6.

Pulse propagation in a 300 unit-cells SC-CROW with high coupling (κi =0.8). The pulse width is 1.5 ps λ=1.556µm (Media 1 - pulse propagation, same parameters).

Equations (6)

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

x ̲ n + 1 = [ x 1 x 8 ] n + 1 T = m · [ x 1 x 8 ] n T
m e i k eff L I = 0
Σ m = 0 4 c m ( ω ) cos ( m · k eff L ) = 0
V g = Σ m = 1 4 c m m L sin ( m k eff L ) Σ m = 1 4 d c m d ω cos ( m k eff L )
x ̲ out = m out m n m in x ̲ in
x ̲ in = [ a in 0 0 0 r 1 r 2 r 3 r 4 ] T x ̲ out = [ b 1 b 2 b 3 b 4 0 0 0 0 ] T

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