Abstract

We present the theoretical concept of an optical isolator based on resonance splitting in a silicon ring resonator covered with a magneto-optical polymer cladding. For this task, a perturbation method is derived for the modes in the cylindrical coordinate system. A polymer magneto-optical cladding causing a 0.01 amplitude of the off- diagonal element of the dielectric tensor is assumed. It is shown that the derived resonance splitting of the clockwise and counterclockwise modes increases for smaller ring radii. For the ring with a radius of approximately 1.5μm, a 29GHz splitting is demonstrated. An integrated optical isolator with a 10μm geometrical footprint is proposed based on a critically coupled ring resonator.

© 2010 Optical Society of America

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  1. H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, J. Opt. Soc. Am. B 22, 240 (2005).
    [CrossRef]
  2. J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
    [CrossRef]
  3. N. Kono, K. Kakihara, K. Saitoh, and M. Koshiba, Opt. Express 15, 7737 (2007).
    [CrossRef] [PubMed]
  4. Z. Wang and S. Fan, Opt. Lett. 30, 1989 (2005).
    [CrossRef] [PubMed]
  5. W. Smigaj, J. Romero-Vivas, B. Gralak, L. Magdenko, B. Dagens, and M. Vanwolleghem, Opt. Lett. 35, 568(2010).
    [CrossRef] [PubMed]
  6. M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
    [CrossRef]
  7. H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
    [CrossRef]
  8. R. L. Espinola, T. Izuhara, M.-C. Tsai, R. M. Osgood, Jr., and H. Dötsch, Opt. Lett. 29, 941 (2004).
    [CrossRef] [PubMed]
  9. P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
    [CrossRef]
  10. G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
    [CrossRef]
  11. P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
    [CrossRef]
  12. F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
    [CrossRef]
  13. A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.
  14. S. Fan and Z. Wang, J. Magn. Soc. Jpn. 30, 641 (2006).
    [CrossRef]
  15. V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
    [CrossRef]
  16. H. Piller and R. F. Potter, Phys. Rev. Lett. 9, 203 (1962).
    [CrossRef]
  17. J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
    [CrossRef]
  18. Computer Simulation Technology, www.cst.com.
  19. M. Krause, H. Renner, and E. Brinkmeyer, IEEE J. Sel. Top. Quantum Electron. 12, 1359 (2006).
    [CrossRef]
  20. A. Yariv, Electron. Lett. 36, 321 (2000).
    [CrossRef]

2010 (2)

W. Smigaj, J. Romero-Vivas, B. Gralak, L. Magdenko, B. Dagens, and M. Vanwolleghem, Opt. Lett. 35, 568(2010).
[CrossRef] [PubMed]

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

2009 (2)

F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
[CrossRef]

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

2008 (1)

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

2007 (1)

2006 (4)

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

S. Fan and Z. Wang, J. Magn. Soc. Jpn. 30, 641 (2006).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, IEEE J. Sel. Top. Quantum Electron. 12, 1359 (2006).
[CrossRef]

2005 (2)

2004 (1)

2000 (2)

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

1997 (1)

V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
[CrossRef]

1992 (1)

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

1984 (1)

J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
[CrossRef]

1962 (1)

H. Piller and R. F. Potter, Phys. Rev. Lett. 9, 203 (1962).
[CrossRef]

Abe, M.

F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
[CrossRef]

Araoka, F.

F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
[CrossRef]

Bahlmann, N.

Boyd, J.

V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
[CrossRef]

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, IEEE J. Sel. Top. Quantum Electron. 12, 1359 (2006).
[CrossRef]

Dagens, B.

DeBrabander, G.

V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
[CrossRef]

Doorsselaere, K. V.

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

Dötsch, H.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, J. Opt. Soc. Am. B 22, 240 (2005).
[CrossRef]

R. L. Espinola, T. Izuhara, M.-C. Tsai, R. M. Osgood, Jr., and H. Dötsch, Opt. Lett. 29, 941 (2004).
[CrossRef] [PubMed]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

Eich, M.

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

Espinola, R. L.

Fan, S.

S. Fan and Z. Wang, J. Magn. Soc. Jpn. 30, 641 (2006).
[CrossRef]

Z. Wang and S. Fan, Opt. Lett. 30, 1989 (2005).
[CrossRef] [PubMed]

Ferrera, M.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Foerier, S.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Gangopadhyay, P.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

Gerhardt, R.

Gralak, B.

Hammer, M.

Hampe, J.

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

Harnagea, C.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Hertel, P.

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, J. Opt. Soc. Am. B 22, 240 (2005).
[CrossRef]

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

Hosaka, T.

J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
[CrossRef]

Hwang, J.-Y.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Izuhara, T.

Jalas, D.

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

Kakihara, K.

Koeckelberghs, G.

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

Kono, N.

Koshiba, M.

Krause, M.

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

M. Krause, H. Renner, and E. Brinkmeyer, IEEE J. Sel. Top. Quantum Electron. 12, 1359 (2006).
[CrossRef]

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Linzon, Y.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Lopez-Santiago, A.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

Luhrmann, B.

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

Magdenko, L.

Morandotti, R.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Naghski, D.

V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
[CrossRef]

Noda, J.

J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
[CrossRef]

Norwood, R. A.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

Osgood, R. M.

R. L. Espinola, T. Izuhara, M.-C. Tsai, R. M. Osgood, Jr., and H. Dötsch, Opt. Lett. 29, 941 (2004).
[CrossRef] [PubMed]

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

Persoons, A.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

Petrov, A.

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

Peyghambarian, N.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

Pignolet, A.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Piller, H.

H. Piller and R. F. Potter, Phys. Rev. Lett. 9, 203 (1962).
[CrossRef]

Popkov, A. F.

Potter, R. F.

H. Piller and R. F. Potter, Phys. Rev. Lett. 9, 203 (1962).
[CrossRef]

Razzari, L.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, IEEE J. Sel. Top. Quantum Electron. 12, 1359 (2006).
[CrossRef]

Robijns, E.

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

Romero-Vivas, J.

Saitoh, K.

Sasaki, Y.

J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
[CrossRef]

Sekhar, M. C.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Smigaj, W.

Subramaniam, V.

V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
[CrossRef]

Sure, S.

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

Takezoe, H.

F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
[CrossRef]

Thomas, J.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

Tsai, M.-C.

Ulrich, R.

J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
[CrossRef]

Vangheluwe, M.

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

Vanwolleghem, M.

Verbiest, T.

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

Voorakaranam, R.

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

Wang, Z.

S. Fan and Z. Wang, J. Magn. Soc. Jpn. 30, 641 (2006).
[CrossRef]

Z. Wang and S. Fan, Opt. Lett. 30, 1989 (2005).
[CrossRef] [PubMed]

Wilkens, L.

Winkler, H. P.

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

Yamamoto, T.

F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
[CrossRef]

Yariv, A.

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

Ye, M.

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

Zaezjev, M.

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Zhuromskyy, O.

Appl. Phys. Express (1)

F. Araoka, M. Abe, T. Yamamoto, and H. Takezoe, Appl. Phys. Express 2, 011501 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dötsch, Appl. Phys. Lett. 76, 2158 (2000).
[CrossRef]

M. C. Sekhar, J.-Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, Appl. Phys. Lett. 94, 181916 (2009).
[CrossRef]

Electron. Lett. (2)

J. Noda, T. Hosaka, Y. Sasaki, and R. Ulrich, Electron. Lett. 20, 906 (1984).
[CrossRef]

A. Yariv, Electron. Lett. 36, 321 (2000).
[CrossRef]

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

M. Krause, H. Renner, and E. Brinkmeyer, IEEE J. Sel. Top. Quantum Electron. 12, 1359 (2006).
[CrossRef]

IEEE Trans. Magn. (1)

H. Dötsch, P. Hertel, B. Luhrmann, S. Sure, H. P. Winkler, and M. Ye, IEEE Trans. Magn. 28, 2979 (1992).
[CrossRef]

J. Lightwave Technol. (1)

V. Subramaniam, G. DeBrabander, D. Naghski, and J. Boyd, J. Lightwave Technol. 15, 990 (1997).
[CrossRef]

J. Magn. Soc. Jpn. (1)

S. Fan and Z. Wang, J. Magn. Soc. Jpn. 30, 641 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (1)

P. Gangopadhyay, R. Voorakaranam, A. Lopez-Santiago, S. Foerier, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, J. Phys. Chem. C 112, 8032 (2008).
[CrossRef]

Macromol. Rapid Commun. (1)

G. Koeckelberghs, M. Vangheluwe, K. V. Doorsselaere, E. Robijns, A. Persoons, and T. Verbiest, Macromol. Rapid Commun. 27, 1920 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

H. Piller and R. F. Potter, Phys. Rev. Lett. 9, 203 (1962).
[CrossRef]

Proc. SPIE (1)

P. Gangopadhyay, S. Foerier, G. Koeckelberghs, M. Vangheluwe, A. Persoons, T. Verbiest, and R. A. Norwood, Proc. SPIE 6331, 63310Z (2006).
[CrossRef]

Other (2)

A. Petrov, D. Jalas, M. Krause, J. Hampe, and M. Eich, in 7th International Conference on Group IV Photonics (GFP) (IEEE, 2010), paper P2.4.

Computer Simulation Technology, www.cst.com.

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Figures (3)

Fig. 1
Fig. 1

Logarithmic plot of the electric field amplitude in a ring with a 1 μm radius. Dark gray value denotes a high field strength.

Fig. 2
Fig. 2

Frequency splitting ( Δ f ) estimated with a perturbation method (solid curve) and with FIT (symbols) in comparison to the FWHM of the resonance.

Fig. 3
Fig. 3

Z component of the optical magnetic field amplitude at 193.72 THz for a 1.465 μm ring resonator coupled with a waveguide and excited from (a) port 1 and (b) port 2. (c) Resulting spectra.

Equations (4)

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

V = i ω 0 2 g ( r ) e z · [ E cw * × E cw ] d r ϵ | E cw | 2 d r ,
Δ ω = ω 0 | r g ( r , z ) [ E r * E φ E φ * E r ] d r d z r ϵ | E | 2 d r d z | ,
R eff = r ϵ | E | 2 d r d z ϵ | E | 2 d r d z .
Δ ω = ω 0 | g ( r , z ) [ E r * E φ E φ * E r ] d r d z ϵ | E | 2 d r d z + ( r R eff ) g ( r , z ) [ E r * E φ E φ * E r ] d r d z R eff ϵ | E | 2 d r d z | .

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