Abstract

We propose a new scheme for buffering optical signals in two-ring resonator system that has a larger delay-bandwidth product than those achievable in single-ring and two-ring configurations of the optical analog of electromagnetically-induced transparency (EIT).

© 2008 Optical Society of America

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References

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  1. F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature 1, 65 (2007).
    [PubMed]
  2. J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical delay lines," J. Opt. Soc. B 26, 1665-1673 (2004).
    [CrossRef] [PubMed]
  3. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Polymer microring coupled-resonator optical waveguides," IEEE J. Lightwave. Technol. 24,1843-1849 (2006).
    [CrossRef] [PubMed]
  4. L. B. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonator," Opt. Lett. 29, 626 (2004).
    [CrossRef] [PubMed]
  5. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency," Phys. Rev. Lett. 93, 233903 (2004).
    [CrossRef] [PubMed]
  6. M. F. Yanik and S. Fan, "Stopping and storing light coherently," Phys. Rev. A 71, 013803 (2005).
    [CrossRef] [PubMed]
  7. Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high capacity optical delay lines," Phys. Rev. E 68, 066616 (2003).
    [CrossRef] [PubMed]
  8. F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 89, 041122 (2006).
    [CrossRef] [PubMed]
  9. Q. Xu, S. Sandhu, M. L.  Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental Realization of an on-Chip All-Optical Analogue to Electromagnetically Induced Transparency," Phys. Rev. Lett. 96, 123901 (2006).
    [CrossRef] [PubMed]
  10. Q. Xu, J. Shakya, and M. Lipson, "Direct Measurement of tunable optical delay on chip to electromagnetically induced transparency," Opt. Express 14, 6463 (2006).
    [CrossRef] [PubMed]
  11. Q. Xu, P. Dong, and M. Lipson, "Breaking the delay-bandwidth limit in a photonic structure," Nature 3, 406 (2007).
    [PubMed]
  12. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
    [CrossRef] [PubMed]
  13. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
    [CrossRef] [PubMed]
  14. S. E. Harris, "Electromagnetically induced transparency," Physics Today 50, 36-42 (1997).
    [CrossRef] [PubMed]
  15. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594-596 (1999).
    [CrossRef] [PubMed]
  16. P. C. Ku, C. J. Chang-Hasnain, and S. L. Chuang, "Variable semiconductor all-optical buffers," Electron. Lett. 38, 1581-1583 (2002).
    [CrossRef] [PubMed]
  17. J. Kim, S. L. Chuang, P. C. Ku, and C. J. Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter. 16, S3727-S3735 (2004).
    [CrossRef] [PubMed]
  18. S. W. Chang, and S. L. Chuang, "Slow light based on population oscillation in quantum dots with inhomogeneous broadening," Phys. Rev. B 72, 235330 (2005).
    [CrossRef] [PubMed]
  19. S. W. Chang, P. K. Kondratko, H. Su, and S. L. Chuang, "Slow light based on coherent population in quantum dots at room temperature," IEEE J. Quantum Electron. 43, 196-205 (2007).
    [CrossRef] [PubMed]
  20. J. B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis," J. Opt. Soc. Am. B 22, 1062-1074 (2005).
    [CrossRef] [PubMed]
  21. M. Först, J. Niehusmann, T. Plötzing, J. Bolten, T. Wahlbrink, C. Moormann, A, and H. Kurz, "High-speed all-optical switching in ion-implanted silicon-on-insulator microring resoantors," Opt. Lett. 29, 2861 (2004).
  22. J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh-quality-factor silicon-on-insulator microring resonator," Opt. Lett. 29, 2861 (2004).
    [CrossRef] [PubMed]
  23. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Talliert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, "Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography," IEEE Photon. Technol. Lett. 16, 1328 (2004).
    [CrossRef] [PubMed]
  24. L. Y. Mario, S. Darmawan, and M. K. Chin, "Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching," Opt. Express. 14, 12770 -12781 (2006).
    [CrossRef] [PubMed]
  25. L. Y. Mario, D. C. S. Lim and M. K. Chin, "Proposal of ultranarrow passband using two coupled rings," IEEE. Photon. Technol. Lett 19, 1688 (2007).
    [CrossRef] [PubMed]

2007

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature 1, 65 (2007).
[PubMed]

Q. Xu, P. Dong, and M. Lipson, "Breaking the delay-bandwidth limit in a photonic structure," Nature 3, 406 (2007).
[PubMed]

S. W. Chang, P. K. Kondratko, H. Su, and S. L. Chuang, "Slow light based on coherent population in quantum dots at room temperature," IEEE J. Quantum Electron. 43, 196-205 (2007).
[CrossRef] [PubMed]

L. Y. Mario, D. C. S. Lim and M. K. Chin, "Proposal of ultranarrow passband using two coupled rings," IEEE. Photon. Technol. Lett 19, 1688 (2007).
[CrossRef] [PubMed]

2006

L. Y. Mario, S. Darmawan, and M. K. Chin, "Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching," Opt. Express. 14, 12770 -12781 (2006).
[CrossRef] [PubMed]

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Polymer microring coupled-resonator optical waveguides," IEEE J. Lightwave. Technol. 24,1843-1849 (2006).
[CrossRef] [PubMed]

F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 89, 041122 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L.  Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental Realization of an on-Chip All-Optical Analogue to Electromagnetically Induced Transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Q. Xu, J. Shakya, and M. Lipson, "Direct Measurement of tunable optical delay on chip to electromagnetically induced transparency," Opt. Express 14, 6463 (2006).
[CrossRef] [PubMed]

2005

M. F. Yanik and S. Fan, "Stopping and storing light coherently," Phys. Rev. A 71, 013803 (2005).
[CrossRef] [PubMed]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef] [PubMed]

S. W. Chang, and S. L. Chuang, "Slow light based on population oscillation in quantum dots with inhomogeneous broadening," Phys. Rev. B 72, 235330 (2005).
[CrossRef] [PubMed]

J. B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis," J. Opt. Soc. Am. B 22, 1062-1074 (2005).
[CrossRef] [PubMed]

2004

M. Först, J. Niehusmann, T. Plötzing, J. Bolten, T. Wahlbrink, C. Moormann, A, and H. Kurz, "High-speed all-optical switching in ion-implanted silicon-on-insulator microring resoantors," Opt. Lett. 29, 2861 (2004).

J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh-quality-factor silicon-on-insulator microring resonator," Opt. Lett. 29, 2861 (2004).
[CrossRef] [PubMed]

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Talliert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, "Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography," IEEE Photon. Technol. Lett. 16, 1328 (2004).
[CrossRef] [PubMed]

J. Kim, S. L. Chuang, P. C. Ku, and C. J. Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter. 16, S3727-S3735 (2004).
[CrossRef] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef] [PubMed]

L. B. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonator," Opt. Lett. 29, 626 (2004).
[CrossRef] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency," Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical delay lines," J. Opt. Soc. B 26, 1665-1673 (2004).
[CrossRef] [PubMed]

2003

Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high capacity optical delay lines," Phys. Rev. E 68, 066616 (2003).
[CrossRef] [PubMed]

2002

P. C. Ku, C. J. Chang-Hasnain, and S. L. Chuang, "Variable semiconductor all-optical buffers," Electron. Lett. 38, 1581-1583 (2002).
[CrossRef] [PubMed]

1999

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594-596 (1999).
[CrossRef] [PubMed]

1997

S. E. Harris, "Electromagnetically induced transparency," Physics Today 50, 36-42 (1997).
[CrossRef] [PubMed]

Appl. Phys. Lett.

F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, "Coupled resonator optical waveguides based on silicon-on-insulator photonic wires," Appl. Phys. Lett. 89, 041122 (2006).
[CrossRef] [PubMed]

Electron. Lett.

P. C. Ku, C. J. Chang-Hasnain, and S. L. Chuang, "Variable semiconductor all-optical buffers," Electron. Lett. 38, 1581-1583 (2002).
[CrossRef] [PubMed]

IEEE J. Lightwave. Technol.

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Polymer microring coupled-resonator optical waveguides," IEEE J. Lightwave. Technol. 24,1843-1849 (2006).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

S. W. Chang, P. K. Kondratko, H. Su, and S. L. Chuang, "Slow light based on coherent population in quantum dots at room temperature," IEEE J. Quantum Electron. 43, 196-205 (2007).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Talliert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, "Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography," IEEE Photon. Technol. Lett. 16, 1328 (2004).
[CrossRef] [PubMed]

IEEE. Photon. Technol. Lett

L. Y. Mario, D. C. S. Lim and M. K. Chin, "Proposal of ultranarrow passband using two coupled rings," IEEE. Photon. Technol. Lett 19, 1688 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

J. Opt. Soc. B

J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical delay lines," J. Opt. Soc. B 26, 1665-1673 (2004).
[CrossRef] [PubMed]

J. Phys. Condens. Matter.

J. Kim, S. L. Chuang, P. C. Ku, and C. J. Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter. 16, S3727-S3735 (2004).
[CrossRef] [PubMed]

Nature

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas," Nature 397, 594-596 (1999).
[CrossRef] [PubMed]

Q. Xu, P. Dong, and M. Lipson, "Breaking the delay-bandwidth limit in a photonic structure," Nature 3, 406 (2007).
[PubMed]

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature 1, 65 (2007).
[PubMed]

Opt. Express

Opt. Express.

L. Y. Mario, S. Darmawan, and M. K. Chin, "Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching," Opt. Express. 14, 12770 -12781 (2006).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

M. F. Yanik and S. Fan, "Stopping and storing light coherently," Phys. Rev. A 71, 013803 (2005).
[CrossRef] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 063804 (2004).
[CrossRef] [PubMed]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef] [PubMed]

Phys. Rev. B

S. W. Chang, and S. L. Chuang, "Slow light based on population oscillation in quantum dots with inhomogeneous broadening," Phys. Rev. B 72, 235330 (2005).
[CrossRef] [PubMed]

Phys. Rev. E

Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high capacity optical delay lines," Phys. Rev. E 68, 066616 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett.

Q. Xu, S. Sandhu, M. L.  Povinelli, J. Shakya, S. Fan, and M. Lipson, "Experimental Realization of an on-Chip All-Optical Analogue to Electromagnetically Induced Transparency," Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency," Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

Physics Today

S. E. Harris, "Electromagnetically induced transparency," Physics Today 50, 36-42 (1997).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

The schematic of the 2R1B structure, with two mutually coupled rings R1 and R2, where R1 is coupled to the waveguide bus The excited optical pathways are shown in the right inset.

Fig. 2.
Fig. 2.

(a). The transmission spectra for γ values varying from 1 to 2. (b). Close-up of the boxed area near δ 1=0. (c). The FDTD-simulated field distributions for γ=1 and (d). γ=2, where S, AS, and NR denote the symmetric, anti-symmetric and narrow resonance, respectively.

Fig. 3.
Fig. 3.

(a). The absorbance spectrum depends on the ratio Ω/Γ, displays a flat top shape when Ω/Γ~0.6. (b) The combinations of ( r 1, r 2) required to achieve the criterion Ω/Γ~0.6. In all cases, a 1=0.999.

Fig. 4.
Fig. 4.

(a). Different situations resulting from different values of r 1 or splitting-broadening ratio Ω/Γ. (b). Transparency and delay response for different loss parameters.

Fig. 5.
Fig. 5.

(a). The EIT spectrum and (b) The transparency and delay for two different EIT parameters.

Fig. 6.
Fig. 6.

Buffer schemes based on ring resonators: (a) the APF schemes based on one ring coupled to one waveguide bus and (b) three other schemes based on two mutually coupled rings coupled to one waveguide bus. Each scheme has its own signatures for transparency (T), modified round trip phase (δ), and phase response (φ). The dashed lines represent the location of the resonances.

Fig. 7.
Fig. 7.

Comparison of transparency and delay, between the proposed scheme with r 1=0.95 and r 2=0.999 (1), and the 10-ring CROW (2) with r WG =0.95 and r=0.999, and the EIT schemes with (3) r1=0. 9, a 1=0.88 and (4) r 1=0.96, a 1=0.95. The second ring for the EIT scheme is assumed lossless, for other cases a=0.999.

Fig. 8.
Fig. 8.

(a). Side by side comparison of propagation of bits in different structure lengths. Note that APF suffer more inter-symbol interference as N>40. (b) The comparison between the proposed scheme, APF, and CROW in a fixed 4(8) buffered RZ (NRZ) bits. The smaller the required number of modules, the larger is the delay-bandwidth product of the scheme

Tables (1)

Tables Icon

Table. 1. The parameter comparison between three schemes.

Equations (22)

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

N ST ( APF ) = τ Δ f = ( 1 + r ) π r 2 π < 1 ,
T = E T E IN 2 = r 1 a 1 τ 21 exp ( i δ 1 ) 1 a 1 r 1 τ 21 exp ( i δ 1 ) 2 ,
τ 21 = τ 21 exp ( i θ 21 ) = r 2 a 2 exp ( i δ 2 ) 1 a 2 r 2 exp ( i δ 2 )
T T exp ( i θ ) 2 = r 1 a exp ( i δ ) 1 ar 1 exp ( i δ ) 2 ,
θ = tan 1 ( ar 1 sin δ 1 ar 1 cos δ ) tan 1 ( a sin δ r 1 a cos δ )
δ = δ 1 θ 21 = δ 1 [ tan 1 ( a 2 sin δ 2 r 2 a 2 cos δ 2 ) tan 1 ( a 2 r 2 sin δ 2 1 a 2 r 2 cos δ 2 ) ]
τ D = ( 1 r 1 2 1 + r 1 2 2 r 1 cos δ ) ( 1 + γ 1 r 2 2 1 + r 2 2 2 r 2 cos δ 2 ) T 1 B 1 ( 1 + γ B 21 ) T 1 ,
B 1 = [ δ 1 2 + ( Δ 2 2 γ ) 2 ] B 1 ( 0 ) [ δ 1 2 + ( Δ 2 2 γ ) 2 ] + 4 Γ 2 [ δ 1 2 ( Ω γ 2 ) 2 ] 2 ,
Ω 1 = 2 cos 1 ( r 2 ) , Ω 2 = 2 cos 1 [ 1 2 ( 1 + r 2 ) ] .
τ D T 1 [ 4 r 1 ( 1 + r 1 ) 2 ] ( Γ Ω ) 2 B 1 ( 0 ) ,
N ST 4 π > 1
N ST 1 π < 1 .
exp ( i δ n ) = τ mn = [ r 2 exp ( i δ m ) ] [ 1 r 2 exp ( i δ m ) ] ,
cos [ 1 2 ( γ + 1 ) δ 1 ] = r 2 cos [ 1 2 ( γ 1 ) δ 1 ] .
Ω 1 = δ 1 + δ 1 = 2 cos 1 ( r 2 ) .
δ 1 ( NR ) = ( 2 m + 1 ) π , δ 1 ± = ± cos 1 [ 1 2 ( 1 + r 2 ) ] .
Ω 2 = 2 cos 1 [ 1 2 ( 1 + r 2 ) ] ,
B 1 = ( 1 r 1 2 ) ( 1 a 1 r 1 ) 2 + 4 a 1 r 1 sin 2 δ 2 ,
sin 2 δ 2 = [ cos ( γ + 1 ) δ 1 2 r 2 cos ( γ 1 ) δ 1 2 ] 2 1 + r 2 2 2 r 2 cos δ 2 .
B 1 ( 1 r 1 2 ) ( 1 a 1 r 1 ) 2 1 + 4 a 1 r 1 r 2 ( 1 a 1 r 1 ) 2 ( cos 1 2 ( γ + 1 ) δ 1 r 2 cos 1 2 ( γ 1 ) δ 1 ) 2 ( 1 r 2 ) 2 r 2 + δ 2 2 .
B 1 , γ = 1 = B 1 ( 0 ) 1 + 4 Δ 1 2 a 2 r 2 ( cos δ 1 r 2 ) 2 δ 2 2 + ( Δ 2 2 ) 2 ( δ 1 2 + ( Δ 2 2 ) 2 ) B 1 ( 0 ) ( δ 1 2 + ( Δ 2 2 ) 2 ) + 4 Γ 2 ( δ 1 2 ( Ω 1 2 ) ) 2
B 1 , γ = 2 = B 1 ( 0 ) 1 + 4 cos 2 δ 1 2 Δ 1 2 a 2 r 2 ( 2 cos δ 1 ( 1 + r 2 ) ) 2 γ 2 δ 1 2 + ( Δ 2 2 ) 2 ( δ 1 2 + ( Δ 2 2 γ ) 2 ) B 1 ( 0 ) ( δ 1 2 + ( Δ 2 2 γ ) 2 ) + 4 Γ 2 ( δ 1 2 ( Ω 2 2 ) ) 2

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