Abstract

Coupled photonic oscillators and resonators are sensitive to unavoidable nanoscale disorder, and localization in periodic structures induced by disorder leads eventually to a complete collapse of the bandwidth, which is generally considered problematic for device applications. Here, we investigate the dependence of bandwidth collapse on the interresonator coupling coefficient, a parameter controllable by lithography or device operation.

© 2011 Optical Society of America

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  1. F. Xia, L. Sekaric, and Y. Vlasov, Nat. Photon. 1, 65 (2007).
    [CrossRef]
  2. M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photon. 2, 741 (2008).
    [CrossRef]
  3. M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa, F. Xia, Y. A. Vlasov, and S. Mookherjea, Opt. Express 18, 26505 (2010).
    [CrossRef] [PubMed]
  4. V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
    [CrossRef]
  5. S. Mookherjea and A. Oh, Opt. Lett. 32, 289 (2007).
    [CrossRef] [PubMed]
  6. D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).
    [CrossRef]
  7. M. A. Popovic, T. Barwicz, E. P. Ippen, and F. X. Kärtner, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.
  8. S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, Nat. Photon. 2, 90 (2008).
    [CrossRef]
  9. J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
    [CrossRef]
  10. L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
    [CrossRef] [PubMed]
  11. P. Markoš and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-handed Materials (Princeton University, 2008), Chap. 7.
  12. C.-S. Deng, H. Xu, and L. Deych, Opt. Express 19, 6923 (2011).
    [CrossRef] [PubMed]
  13. M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa, F. Xia, D. K. Gifford, and S. Mookherjea, Opt. Lett. 35, 3030 (2010).
    [CrossRef] [PubMed]
  14. M. L. Cooper and S. Mookherjea, IEEE Photon. Technol. Lett. 23, 872 (2011).
    [CrossRef]
  15. F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
    [CrossRef] [PubMed]
  16. J. R. Ong, M. L. Cooper, G. Gupta, W. M. J. Green, S. Assefa, F. Xia, and S. Mookherjea, Opt. Lett. 36, 2964 (2011).
    [CrossRef] [PubMed]

2011 (4)

M. L. Cooper and S. Mookherjea, IEEE Photon. Technol. Lett. 23, 872 (2011).
[CrossRef]

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

C.-S. Deng, H. Xu, and L. Deych, Opt. Express 19, 6923 (2011).
[CrossRef] [PubMed]

J. R. Ong, M. L. Cooper, G. Gupta, W. M. J. Green, S. Assefa, F. Xia, and S. Mookherjea, Opt. Lett. 36, 2964 (2011).
[CrossRef] [PubMed]

2010 (3)

2008 (3)

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photon. 2, 741 (2008).
[CrossRef]

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).
[CrossRef]

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, Nat. Photon. 2, 90 (2008).
[CrossRef]

2007 (3)

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

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

S. Mookherjea and A. Oh, Opt. Lett. 32, 289 (2007).
[CrossRef] [PubMed]

2004 (1)

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Ashili, S. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Assefa, S.

Astratov, V. N.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Bandaru, P. R.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, Nat. Photon. 2, 90 (2008).
[CrossRef]

Barwicz, T.

M. A. Popovic, T. Barwicz, E. P. Ippen, and F. X. Kärtner, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Cooper, M. L.

Deng, C.-S.

Deych, L.

Dignam, M. M.

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Ferrari, C.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Franchak, J. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Fussell, D. P.

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Gifford, D. K.

Green, W. M. J.

Gupta, G.

Hughes, S.

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Ippen, E. P.

M. A. Popovic, T. Barwicz, E. P. Ippen, and F. X. Kärtner, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.

Kärtner, F. X.

M. A. Popovic, T. Barwicz, E. P. Ippen, and F. X. Kärtner, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.

Kuramochi, E.

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photon. 2, 741 (2008).
[CrossRef]

Lodahl, P.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Markoš, P.

P. Markoš and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-handed Materials (Princeton University, 2008), Chap. 7.

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Mookherjea, S.

Morichetti, F.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photon. 2, 741 (2008).
[CrossRef]

Oh, A.

Ong, J. R.

Park, J. S.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, Nat. Photon. 2, 90 (2008).
[CrossRef]

Popovic, M. A.

M. A. Popovic, T. Barwicz, E. P. Ippen, and F. X. Kärtner, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.

Samarelli, A.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Sapienza, L.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Schneider, M. A.

Sekaric, L.

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

Smolka, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Sorel, M.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Markoš and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-handed Materials (Princeton University, 2008), Chap. 7.

Stobbe, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Tanabe, T.

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photon. 2, 741 (2008).
[CrossRef]

Thyrrestrup, H.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Vlasov, Y.

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

Vlasov, Y. A.

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Xia, F.

Xu, H.

Yang, S. H.

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, Nat. Photon. 2, 90 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. L. Cooper and S. Mookherjea, IEEE Photon. Technol. Lett. 23, 872 (2011).
[CrossRef]

Nat. Commun. (1)

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, Nat. Commun. 2, 296 (2011).
[CrossRef] [PubMed]

Nat. Photon. (3)

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

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photon. 2, 741 (2008).
[CrossRef]

S. Mookherjea, J. S. Park, S. H. Yang, and P. R. Bandaru, Nat. Photon. 2, 90 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

D. P. Fussell, S. Hughes, and M. M. Dignam, Phys. Rev. B 78, 144201 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Science (1)

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Other (2)

P. Markoš and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-handed Materials (Princeton University, 2008), Chap. 7.

M. A. Popovic, T. Barwicz, E. P. Ippen, and F. X. Kärtner, in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.

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Figures (3)

Fig. 1
Fig. 1

(A) Coupled-resonator optical waveguide using directly coupled silicon microring resonators [3]. (b) Measurements show that, in longer resonator chains, not only is the peak transmission reduced because of loss, but the transmission bandwidth decreases because of disorder effects. (c) Random matrix model of a resonator chain was used to calculate the Lyapunov coefficient (inverse of the localization length) near the band edge [11]. The fitted line shape is used to propose Δ ω ( N ) in the text.

Fig. 2
Fig. 2

Examples of bandwidth scaling with number of resonators: (a)–(d) were experimentally measured at wavelengths of 1528.8, 1549.4, 1570.6, and 1599.9 nm , with | κ | 2 = 0.362 , 0.454, 0.557 and 0.692, respectively; (e)–(g) were obtained from simulations with | κ | 2 = 0.0974 , 0.334, and 0.856, and error bars indicate variations over 16 Monte Carlo iterations. Solid curves are fitted using the equation for Δ ω given in the text, and N crit is defined as the number of resonators where the fitted line crosses the horizontal axis, zero bandwidth.

Fig. 3
Fig. 3

N crit = | 2 π κ / σ | 2 on the vertical axis should vary linearly with | κ | 2 , the horizontal axis. Data from measurements are shown with blue squares, and those from ab initio transfer matrix simulations are shown with green circles. The fitted dashed curve gives disorder strength σ 2 = 0.080 , in close agreement with the assumption made in the simulations, σ 2 = 0.075 .

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