Abstract

We study circular grating resonators (CGRs) which are formed by a central defect surrounded by concentric rings composing a grating and which display perfect azimuthal modal-symmetry. Because of their radial symmetry they exhibit a complete band gap for a minimal index contrast. However, as is the case for all 2D resonators their quality factors are limited by vertical losses. To reduce the vertical losses we introduce a chirp of the grating period by reducing it towards the central defect. The chirped CGRs exhibit drastically improved quality factors of up to tens of millions with a modal volume of a few cubic wavelengths.

© 2009 Optical Society of America

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  1. J. Niehusmann, A. Vorckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh quality-factor silicon-on-insulator microringresonator," Opt. Lett. 29(24), 2861-2863 (2004), http://ol.osa.org/abstract.cfm?URI=ol-29-24-2861.
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    [CrossRef]
  4. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
    [CrossRef]
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  6. C. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83(8), 1527-1529 (2003), http://link.aip.org/link/?APL/83/1527/1.
    [CrossRef]
  7. A. Nitkowski, L. Chen, and M. Lipson, "Cavity-enhanced on-chip absorption spectroscopy using microring resonators," Opt. Express 16(16), 930-936 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-16-11930.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  19. Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.
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    [CrossRef]

2009 (1)

2008 (3)

A. Nitkowski, L. Chen, and M. Lipson, "Cavity-enhanced on-chip absorption spectroscopy using microring resonators," Opt. Express 16(16), 930-936 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-16-11930.

Y. Tanaka, T. Asano, and S. Noda, "Design of Photonic Crystal Nanocavity With Q-Factor of ∼ 109," J. Lightwave Technol. 26(11), 1532-1539 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 11,095-11,102 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-15-11095.

2007 (2)

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

X. Sun, J. Scheuer, and A. Yariv, "Optimal Design and Reduced Threshold in Vertically Emitting Circular Bragg Disk Resonator Lasers," IEEE J. Sel.Top. in Quantum Electron. 13(2), 359-366 (2007).
[CrossRef]

2006 (1)

2005 (2)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435(7040), 325-327 (2005), http://dx.doi.org/10.1038/nature03569.
[CrossRef]

D. Chang, J. Scheuer, and A. Yariv, "Optimization of circular photonic crystal cavities- beyond coupled mode theory," Opt. Express 13(23), 9272-9279 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-23-9272.
[CrossRef]

2004 (4)

J. Niehusmann, A. Vorckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh quality-factor silicon-on-insulator microringresonator," Opt. Lett. 29(24), 2861-2863 (2004), http://ol.osa.org/abstract.cfm?URI=ol-29-24-2861.
[CrossRef]

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
[CrossRef]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

2003 (1)

C. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83(8), 1527-1529 (2003), http://link.aip.org/link/?APL/83/1527/1.
[CrossRef]

2002 (1)

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

2001 (2)

S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8(3), 173-190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=oe-8-3-173.
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78(22), 3388-3390 (2001), http://link.aip.org/link/?APL/78/3388/1.
[CrossRef]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
[CrossRef]

Asano, T.

Y. Tanaka, T. Asano, and S. Noda, "Design of Photonic Crystal Nanocavity With Q-Factor of ∼ 109," J. Lightwave Technol. 26(11), 1532-1539 (2008).
[CrossRef]

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

Bachtold, W.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
[CrossRef]

Bauer, C.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Bermel, P.

Bolivar, P. H.

Bolten, J.

Bona, G.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

Burr, G. W.

Chang, D.

Chao, C.

C. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83(8), 1527-1529 (2003), http://link.aip.org/link/?APL/83/1527/1.
[CrossRef]

Chen, L.

A. Nitkowski, L. Chen, and M. Lipson, "Cavity-enhanced on-chip absorption spectroscopy using microring resonators," Opt. Express 16(16), 930-936 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-16-11930.

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Erni, D.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78(22), 3388-3390 (2001), http://link.aip.org/link/?APL/78/3388/1.
[CrossRef]

Farjadpour, A.

Forst, M.

G¨otzinger, S.

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Giessen, H.

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Guo, L. J.

C. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83(8), 1527-1529 (2003), http://link.aip.org/link/?APL/83/1527/1.
[CrossRef]

Hagino, H.

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Henschel, W.

Ibanescu, M.

Jebali, A.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31(20), 2972-2974 (2006), http://ol.osa.org/abstract.cfm?URI=ol-31-20-2972.
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78(22), 3388-3390 (2001), http://link.aip.org/link/?APL/78/3388/1.
[CrossRef]

Johnson, S.

Johnson, S. G.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31(20), 2972-2974 (2006), http://ol.osa.org/abstract.cfm?URI=ol-31-20-2972.
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78(22), 3388-3390 (2001), http://link.aip.org/link/?APL/78/3388/1.
[CrossRef]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Kley, E. B.

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Kuramochi, E.

M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 11,095-11,102 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-15-11095.

Kurz, H.

Lipson, M.

A. Nitkowski, L. Chen, and M. Lipson, "Cavity-enhanced on-chip absorption spectroscopy using microring resonators," Opt. Express 16(16), 930-936 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-16-11930.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435(7040), 325-327 (2005), http://dx.doi.org/10.1038/nature03569.
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
[CrossRef]

Mahrt, R. F.

S. Schonenberger, N. Moll, T. Stoferle, R. F. Mahrt, B. J. Offrein, S. Gotzinger, V. Sandoghdar, J. Bolten, T. Wahlbrink, T. Plotzing, M. Waldow, and M. Forst, "Circular Grating Resonators as Small Mode-Volume Microcavities for Switching," Opt. Express 17(8), 5953-5964 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-8-5953.
[CrossRef]

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Mekis, A.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78(22), 3388-3390 (2001), http://link.aip.org/link/?APL/78/3388/1.
[CrossRef]

Moll, N.

S. Schonenberger, N. Moll, T. Stoferle, R. F. Mahrt, B. J. Offrein, S. Gotzinger, V. Sandoghdar, J. Bolten, T. Wahlbrink, T. Plotzing, M. Waldow, and M. Forst, "Circular Grating Resonators as Small Mode-Volume Microcavities for Switching," Opt. Express 17(8), 5953-5964 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-8-5953.
[CrossRef]

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Niehusmann, J.

Nitkowski, A.

A. Nitkowski, L. Chen, and M. Lipson, "Cavity-enhanced on-chip absorption spectroscopy using microring resonators," Opt. Express 16(16), 930-936 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-16-11930.

Noda, S.

Y. Tanaka, T. Asano, and S. Noda, "Design of Photonic Crystal Nanocavity With Q-Factor of ∼ 109," J. Lightwave Technol. 26(11), 1532-1539 (2008).
[CrossRef]

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

Notomi, M.

M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 11,095-11,102 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-15-11095.

Offrein, B. J.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
[CrossRef]

Plotzing, T.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435(7040), 325-327 (2005), http://dx.doi.org/10.1038/nature03569.
[CrossRef]

Rodriguez, A.

Roundy, D.

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Sandoghdar, V.

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Scherf, U.

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Scheuer, J.

X. Sun, J. Scheuer, and A. Yariv, "Optimal Design and Reduced Threshold in Vertically Emitting Circular Bragg Disk Resonator Lasers," IEEE J. Sel.Top. in Quantum Electron. 13(2), 359-366 (2007).
[CrossRef]

D. Chang, J. Scheuer, and A. Yariv, "Optimization of circular photonic crystal cavities- beyond coupled mode theory," Opt. Express 13(23), 9272-9279 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-23-9272.
[CrossRef]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435(7040), 325-327 (2005), http://dx.doi.org/10.1038/nature03569.
[CrossRef]

Schnabel, B.

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

Schonenberger, S.

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Song, B.

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

Stoferle, T.

Sun, X.

X. Sun, J. Scheuer, and A. Yariv, "Optimal Design and Reduced Threshold in Vertically Emitting Circular Bragg Disk Resonator Lasers," IEEE J. Sel.Top. in Quantum Electron. 13(2), 359-366 (2007).
[CrossRef]

Takahashi, Y.

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

Tanaka, Y.

Y. Tanaka, T. Asano, and S. Noda, "Design of Photonic Crystal Nanocavity With Q-Factor of ∼ 109," J. Lightwave Technol. 26(11), 1532-1539 (2008).
[CrossRef]

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

Taniyama, H.

M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 11,095-11,102 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-15-11095.

Vorckel, A.

Wahlbrink, T.

Waldow, M.

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435(7040), 325-327 (2005), http://dx.doi.org/10.1038/nature03569.
[CrossRef]

Yariv, A.

X. Sun, J. Scheuer, and A. Yariv, "Optimal Design and Reduced Threshold in Vertically Emitting Circular Bragg Disk Resonator Lasers," IEEE J. Sel.Top. in Quantum Electron. 13(2), 359-366 (2007).
[CrossRef]

D. Chang, J. Scheuer, and A. Yariv, "Optimization of circular photonic crystal cavities- beyond coupled mode theory," Opt. Express 13(23), 9272-9279 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-23-9272.
[CrossRef]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Appl. Phys. Lett. (3)

N. Moll, R. F. Mahrt, C. Bauer, H. Giessen, B. Schnabel, E. B. Kley, and U. Scherf, "Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser," Appl. Phys. Lett. 80(5), 734-736 (2002), http://link.aip.org/link/?APL/80/734/1.
[CrossRef]

C. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83(8), 1527-1529 (2003), http://link.aip.org/link/?APL/83/1527/1.
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, "Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap," Appl. Phys. Lett. 78(22), 3388-3390 (2001), http://link.aip.org/link/?APL/78/3388/1.
[CrossRef]

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

X. Sun, J. Scheuer, and A. Yariv, "Optimal Design and Reduced Threshold in Vertically Emitting Circular Bragg Disk Resonator Lasers," IEEE J. Sel.Top. in Quantum Electron. 13(2), 359-366 (2007).
[CrossRef]

J. Appl. Phys. (1)

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96(6), 3043-3049 (2004), http://link.aip.org/link/?JAP/96/3043/1.
[CrossRef]

J. Lightwave Technol. (1)

Nature (3)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432(7014), 200-203 (2004), http://dx.doi.org/10.1038/nature03119.
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435(7040), 325-327 (2005), http://dx.doi.org/10.1038/nature03569.
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431(7012), 1081-1084 (2004), http://dx.doi.org/10.1038/nature02921.
[CrossRef]

Opt. Express (6)

S. Schonenberger, N. Moll, T. Stoferle, R. F. Mahrt, B. J. Offrein, S. Gotzinger, V. Sandoghdar, J. Bolten, T. Wahlbrink, T. Plotzing, M. Waldow, and M. Forst, "Circular Grating Resonators as Small Mode-Volume Microcavities for Switching," Opt. Express 17(8), 5953-5964 (2009), http://www.opticsexpress.org/abstract.cfm?URI=oe-17-8-5953.
[CrossRef]

D. Chang, J. Scheuer, and A. Yariv, "Optimization of circular photonic crystal cavities- beyond coupled mode theory," Opt. Express 13(23), 9272-9279 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-23-9272.
[CrossRef]

M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 11,095-11,102 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-15-11095.

Y. Takahashi, H. Hagino, Y. Tanaka, B. Song, T. Asano, and S. Noda, "High-Q nanocavity with a 2-ns photon lifetime," Opt. Express 15(25), 17,206-17,213 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-25-17206.

S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8(3), 173-190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=oe-8-3-173.
[CrossRef]

A. Nitkowski, L. Chen, and M. Lipson, "Cavity-enhanced on-chip absorption spectroscopy using microring resonators," Opt. Express 16(16), 930-936 (2008), http://www.opticsexpress.org/abstract.cfm?URI=oe-16-16-11930.

Opt. Lett. (2)

Other (3)

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature Photon. 1(1), 65-71 (2007), http://dx.doi.org/10.1038/nphoton.2006.42.
[CrossRef]

K. Baumann, T. Stoferle, N. Moll, R. F. Mahrt, T. Wahlbrink, J. Bolten, T. Mollenhauer, C. Moormann, and U. Scherf, "Organic mixed-order photonic crystal lasers with ultrasmall footprint," Appl. Phys. Lett. 91(17), 171,108-3 (2007), http://link.aip.org/link/?APL/91/171108/1.

J. Scheuer, W. M. J. Green, G. A. DeRose, and A. Yariv, "Lasing from a circular Bragg nanocavity with an ultrasmall modal volume," Appl. Phys. Lett. 86(25), 251,101-3 (2005), http://link.aip.org/link/?APL/86/251101/1.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic top view of a CGR consisting of a central defect with a defect radius rc surrounded by concentric rings 1 to 7. (b) Cross section of the CGR where the duty cycle D is given by the ratio between the width of trench q and the grating period a (D=q/a). The height of the CGR is h. The CGR consists of Si as high-index material and is surrounded by SiO2 as low-index material.

Fig. 2.
Fig. 2.

(a) The quality factor Q, (b) the frequency ν, and (c) the modal volume Vm as a function of the defect radius rc for a CGR without chirp and an azimuthal order of m=0. The fixed geometric parameters are the duty cycle D=0.34 and the height h=0.85a. In (b), the lower band edge of the corresponding infinite linear grating is shown as dashed line.

Fig. 3.
Fig. 3.

(a) The quality factor Q, (b) the frequency ν, and (c) the modal volume Vm as a function of the shift of the first ring Δ1 for a chirped CGR and an azimuthal order of m=0. The fixed geometric parameters are the defect radius rc =1.60a, the duty cycle D=0.34, the height h=0.80a, and the decay constant Γ=0.88.

Fig. 4.
Fig. 4.

Effective local band edges for the optimum chirped configuration from Fig. 3 (m=0, rc =1.60a, D=0.34, h=0.80a, Δ1=-0.29, Γ=0.88). The lower (squares) and upper (circles) band edges are shown as function of the ring number N. The solid lines are single-exponential fits to the respective numerically calculated bands, which exhibit slight numerical noise due to aliasing effects resulting from finite grid resolution of the calculation. The resonance frequency (dotted line) of this CGR is ν=0.221c/a, and the lower and upper band edges (dashed lines) of the corresponding infinite periodic linear grating are shown for comparision.

Fig. 5.
Fig. 5.

Cross section of the electric field component Eφ at resonance for three different chirped CGRs where the shift of the first ring Δ1 is varied: (a) Δ1=-0.26a, which exhibits a Q=356000; (b) Δ1=-0.29a, which exhibits a Q=66200000, and (c) Δ1=-0.32,a which exhibits a Q=1270000. The other geometric parameters are the same as in Fig. 3 (m=0, rc =1.60a, D=0.34, h=0.80a, Γ=0.88)

Tables (1)

Tables Icon

Table 1. For three different azimuthal orders m the geometric parameters of the chirped CGRs are shown for which a maximized quality factor Q is achieved.

Equations (1)

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q N = Da Δ N and Δ N + 1 = Δ N Γ .

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