Abstract

Photonic crystal ring resonators (PhCRR) combine the features of ring resonators with the slow-light effects present in photonic crystal waveguides, resulting in better mode confinement and increased light-matter interaction. When the resonator modes are near the photonic band edge, this enhancement is maximized. However, for this to be useful it is necessary to design the resonator so that these modes are at a desired wavelength. We introduce a design prescription, based on a theoretical analysis of the mode spectrum of PhCRRs, that maximizes these effects at a given wavelength. We test the procedure using numerical simulations, finding a good agreement between the design objectives and the simulated mode structures. We also consider the effects of disorder on the device.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Slow light in mass-produced, dispersion-engineered photonic crystal ring resonators

Kathleen McGarvey-Lechable, Tabassom Hamidfar, David Patel, Luhua Xu, David V. Plant, and Pablo Bianucci
Opt. Express 25(4) 3916-3926 (2017)

Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal

Damian Goldring, Uriel Levy, Ido E. Dotan, Alexander Tsukernik, Mark Oksman, Idan Rubin, Yaara David, and David Mendlovic
Opt. Express 16(8) 5585-5595 (2008)

Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide

Nobuyuki Matsuda, Takumi Kato, Ken-ichi Harada, Hiroki Takesue, Eiichi Kuramochi, Hideaki Taniyama, and Masaya Notomi
Opt. Express 19(21) 19861-19874 (2011)

References

  • View by:
  • |
  • |
  • |

  1. B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [Crossref]
  2. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
    [Crossref] [PubMed]
  3. D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
    [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, 1081–1084 (2004).
    [Crossref] [PubMed]
  5. M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q = 1.2 million,” Opt. Express 17, 14098–14103 (2009).
    [Crossref] [PubMed]
  6. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
    [Crossref]
  7. M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
    [Crossref] [PubMed]
  8. T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
    [Crossref] [PubMed]
  9. T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
    [Crossref]
  10. J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
    [Crossref] [PubMed]
  11. D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express 15, 3156–3168 (2007).
    [Crossref] [PubMed]
  12. J. Y. Lee and P. M. Fauchet, “Slow-light dispersion in periodically patterned silicon microring resonators,” Opt. Lett. 37, 58–60 (2012).
    [Crossref] [PubMed]
  13. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
    [Crossref]
  14. J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
    [Crossref]
  15. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  16. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008), 2nd ed.
  17. Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
    [Crossref] [PubMed]
  18. M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystal Guiding (Cambridge University, 2008).
    [Crossref]
  19. D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Medlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express 16, 5585–5595 (2008).
    [Crossref] [PubMed]
  20. T. P. White, L. O’Faolain, J. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16, 17076–17081 (2008).
    [Crossref] [PubMed]
  21. L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
    [Crossref]
  22. N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
    [Crossref]
  23. L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15, 13129–13138 (2007).
    [Crossref]
  24. A. Petrov, M. Krause, and M. Eich, “Backscattering and disorder limits in slow light photonic crystal waveguides,” Opt. Express 17, 8676–8684 (2009).
    [Crossref] [PubMed]
  25. J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
    [Crossref]
  26. T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
    [Crossref]

2013 (3)

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
[Crossref]

2012 (3)

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

J. Y. Lee and P. M. Fauchet, “Slow-light dispersion in periodically patterned silicon microring resonators,” Opt. Lett. 37, 58–60 (2012).
[Crossref] [PubMed]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

2011 (2)

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
[Crossref] [PubMed]

2010 (2)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[Crossref]

2009 (3)

2008 (4)

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
[Crossref]

D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Medlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express 16, 5585–5595 (2008).
[Crossref] [PubMed]

T. P. White, L. O’Faolain, J. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16, 17076–17081 (2008).
[Crossref] [PubMed]

2007 (3)

2004 (2)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

2001 (1)

1997 (1)

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Adachi, J.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

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, 1081–1084 (2004).
[Crossref] [PubMed]

Andreani, L. C.

Baba, T.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

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, 1081–1084 (2004).
[Crossref] [PubMed]

Beausoleil, R. G.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

Beggs, D. M.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

Bianucci, P.

J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
[Crossref]

Bowers, J. E.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

Busch, K.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Cheben, P.

Chu, S.

Chu, S. T.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

Clarke, E.

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

Coles, R. J.

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

Combrie, S.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

David, Y.

De Rossi, A.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Dotan, I. E.

Duchesne, D.

Eich, M.

Fan, X.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

Fauchet, P. M.

Feisst, A.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Ferrera, M.

Fiorentino, M.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

Foresi, J.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Fox, A. M.

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

Gaeta, A. L.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

Gao, J.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Geppert, T.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Glatthaar, R.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Goldring, D.

Hahn, P.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Hamachi, Y.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

Haus, H.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Huffaker, D. L.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Hugonin, J. P.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Ishikura, N.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

Jamois, C.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Janz, S.

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008), 2nd ed.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008), 2nd ed.

Kawasaki, T.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

Krause, M.

Krauss, T. F.

Kuipers, L.

Laine, J.-P.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Lalanne, P.

Lambrecht, A.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Lee, J. Y.

Lee, P.-T.

T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
[Crossref]

Lehoucq, G.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Levy, U.

Li, J.

Liang, B.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Liang, D.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

Lipson, M.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Little, B.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Little, B. E.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q = 1.2 million,” Opt. Express 17, 14098–14103 (2009).
[Crossref] [PubMed]

Loncar, M.

Lu, T.-W.

T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
[Crossref]

Luxmoore, I. J.

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

Mazoyer, S.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008), 2nd ed.

Medlovic, D.

Meldrum, A.

J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
[Crossref]

Melloni, A.

Mendlovic, D.

Morandotti, R.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q = 1.2 million,” Opt. Express 17, 14098–14103 (2009).
[Crossref] [PubMed]

Mori, D.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

Morichetti, F.

Moss, D. J.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q = 1.2 million,” Opt. Express 17, 14098–14103 (2009).
[Crossref] [PubMed]

O’Brien, D.

O’Faolain, L.

Oksman, M.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

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, 1081–1084 (2004).
[Crossref] [PubMed]

Park, Y.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

Pasquazi, A.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

Peccianti, M.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q = 1.2 million,” Opt. Express 17, 14098–14103 (2009).
[Crossref] [PubMed]

Pergande, D.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Petrov, A.

Quan, Q.

Razzari, L.

Rhein, A. V.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Rodríguez, J. R.

J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
[Crossref]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

Rubin, I.

Sasaki, H.

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

Schilling, J.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Schmitteckert, P.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Schulz, S. A.

Schweizer, S.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Settle, M. D.

Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

Skorobogatiy, M.

M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystal Guiding (Cambridge University, 2008).
[Crossref]

Spasenovic, M.

Srinivasan, S.

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Tsai, W.-C.

T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
[Crossref]

Tsukernik, A.

Veinot, J. G. C.

J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
[Crossref]

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Wasley, N. A.

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

Wehrspohn, R. B.

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

White, T. P.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008), 2nd ed.

Wong, C. W.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Wu, T.-Y.

T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
[Crossref]

Xavier, S.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Xu, D.-X.

Xu, X.

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Yang, J.

M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystal Guiding (Cambridge University, 2008).
[Crossref]

Yuan, X.

Zhu, H.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

Anal. Chim. Acta (1)

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620, 8–26 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

T.-W. Lu, W.-C. Tsai, T.-Y. Wu, and P.-T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102, 051103 (2013).
[Crossref]

J. R. Rodríguez, J. G. C. Veinot, P. Bianucci, and A. Meldrum, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008).
[Crossref]

N. A. Wasley, I. J. Luxmoore, R. J. Coles, E. Clarke, and A. M. Fox, “Disorder-limited photon propagation and anderson-localization in photonic crystal waveguides,” Appl. Phys. Lett. 101, 051116 (2012).
[Crossref]

Comput. Phys. Comm. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Comm. 181, 687–702 (2010).
[Crossref]

IEEE J. Select. Topics Quantum Electron. (1)

D. Liang, M. Fiorentino, S. Srinivasan, J. E. Bowers, and R. G. Beausoleil, “Low threshold electrically-pumped hybrid silicon microring lasers,” IEEE J. Select. Topics Quantum Electron. 17, 1528–1533 (2011).
[Crossref]

J. Lightwave Technol. (1)

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Nat. Commun. (1)

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

Nat. Photon. (1)

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photon. 7, 597–607 (2013).
[Crossref]

Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Opt. Express (9)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express 15, 3156–3168 (2007).
[Crossref] [PubMed]

L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15, 13129–13138 (2007).
[Crossref]

D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Medlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express 16, 5585–5595 (2008).
[Crossref] [PubMed]

T. P. White, L. O’Faolain, J. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16, 17076–17081 (2008).
[Crossref] [PubMed]

A. Petrov, M. Krause, and M. Eich, “Backscattering and disorder limits in slow light photonic crystal waveguides,” Opt. Express 17, 8676–8684 (2009).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q = 1.2 million,” Opt. Express 17, 14098–14103 (2009).
[Crossref] [PubMed]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[Crossref]

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. (1)

T. Baba, J. Adachi, N. Ishikura, Y. Hamachi, H. Sasaki, T. Kawasaki, and D. Mori, “Dispersion-controlled slow light in photonic crystal waveguides,” Proc. Jpn. Acad. Ser. B. Phys. Biol. Sci. 85, 443–453 (2009).
[Crossref] [PubMed]

Proc. SPIE (1)

T. Geppert, S. Schweizer, J. Schilling, C. Jamois, A. V. Rhein, D. Pergande, R. Glatthaar, P. Hahn, A. Feisst, A. Lambrecht, and R. B. Wehrspohn, “Photonic crystal gas sensors,” Proc. SPIE 5511, 61–70 (2004).
[Crossref]

Sci. Rep. (1)

J. Gao, S. Combrie, B. Liang, P. Schmitteckert, G. Lehoucq, S. Xavier, X. Xu, K. Busch, D. L. Huffaker, A. De Rossi, and C. W. Wong, “Strongly coupled slow-light polaritons in one-dimensional disordered localized states,” Sci. Rep. 3, 1994 (2013).
[Crossref] [PubMed]

Other (2)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008), 2nd ed.

M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystal Guiding (Cambridge University, 2008).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 a) Geometry of the PhCRR under study. Black corresponds to a high-refractive index material and white to the background medium. b) Geometry of the straight periodic waveguide used to approximate the ring resonator.
Fig. 2
Fig. 2 (a) Representative dispersion relation for a periodically patterned waveguide.The greyed area above the dashed light-line corresponds to leaky modes. The inset shows three waveguide unit cells with the computed Hz field for the first band. (b) The group velocity dispersion, for the first band of a periodically patterned waveguide with a = 397.3 nm. (c) The group index for the same waveguide as in (b).
Fig. 3
Fig. 3 Dispersion relation (plotted over a shifted Brillouin cell) for the lowest band of the periodically patterned waveguide. The vertical lines represent some of the allowed values of the wavevector kx for a ring with an even (panel a) or odd (panel b) number of holes. The horizontal lines illustrate how to graphically find the resonant frequencies of the modes.
Fig. 4
Fig. 4 (a) Magnetic field spectrum of the resonant modes in the designed PhCRR (black, see text for parameters) and an equivalent standard RR (red) when excited by a broadband pulse. (b) Hz distributions for each one of the labeled modes in panel a).
Fig. 5
Fig. 5 (a) Q-factor as a function of the mode resonant wavelength. The crosses and circles correspond to the cases without and with surface roughness, respectively. (b) Q-factor versus artificially introduced geometrical disorder.
Fig. 6
Fig. 6 Hz field distributions for the fundamental mode of a ring with a random variation on the hole radius. The label identifies the average deviation from the nominal hole radius.

Equations (6)

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

H z ( x , y ) = H 0 ( y ) e i k x x .
k x R = m , m ,
Na = 2 π R .
m BE = N 2 .
H z e i m BE + p R x + e i m BE p R x = 2 e i π a x cos ( 2 π p Na x ) .
H z 2 e i π a x cos [ ( 2 p + 1 ) π Na x ] .

Metrics