Abstract

The counterpropagating waves in a single traveling-wave cavity can be partially coupled by means of a small perturbation such as a notch. When it is side coupled to a waveguide, this single cavity yields a general second-order (Chebyshev) reflection response in the waveguide, which is useful for narrow-bandwidth reflecting applications. In a different application, the cavity amplifies small reflections induced by external perturbations, thus finding use in ultrafine sensing. Amplification factors as great as 1012 are predicted for the highest-Q microsphere resonators. The analytic theory of these devices is presented.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
    [CrossRef]
  2. R. Kazarinov, C. H. Henry, and A. Olsson, IEEE J. Quantum Electron. QE-23, 1419 (1987).
    [CrossRef]
  3. H. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
    [CrossRef]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:?Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  5. D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
    [CrossRef]
  6. B. E. Little, J.-P. Laine, and S. T. Chu, Opt. Lett. 22, 4 (1997).
    [CrossRef] [PubMed]
  7. B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
    [CrossRef]
  8. M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1505 (1983).
    [CrossRef]
  9. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), Chap.??1.
  10. S. T. Chu and S. K. Chaudhuri, J. Lightwave Technol. 7, 2033 (1989).
    [CrossRef]

1998

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

1997

B. E. Little, J.-P. Laine, and S. T. Chu, Opt. Lett. 22, 4 (1997).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

1991

H. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

1989

S. T. Chu and S. K. Chaudhuri, J. Lightwave Technol. 7, 2033 (1989).
[CrossRef]

1987

R. Kazarinov, C. H. Henry, and A. Olsson, IEEE J. Quantum Electron. QE-23, 1419 (1987).
[CrossRef]

1983

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1505 (1983).
[CrossRef]

Ackerman, D. A.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

Chaudhuri, S. K.

S. T. Chu and S. K. Chaudhuri, J. Lightwave Technol. 7, 2033 (1989).
[CrossRef]

Chu, S. T.

B. E. Little, J.-P. Laine, and S. T. Chu, Opt. Lett. 22, 4 (1997).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

S. T. Chu and S. K. Chaudhuri, J. Lightwave Technol. 7, 2033 (1989).
[CrossRef]

Dahbura, M. I.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Foresi, J. S.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

Haus, H.

H. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

Haus, H. A.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1505 (1983).
[CrossRef]

Henry, C. H.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

R. Kazarinov, C. H. Henry, and A. Olsson, IEEE J. Quantum Electron. QE-23, 1419 (1987).
[CrossRef]

Ippen, E. P.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:?Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Kazarinov, R.

R. Kazarinov, C. H. Henry, and A. Olsson, IEEE J. Quantum Electron. QE-23, 1419 (1987).
[CrossRef]

Kazarinov, R. F.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

Kimerling, L. C.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

Kistler, R. C.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

Kuo, C. Y.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

Kuznetsov, M.

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1505 (1983).
[CrossRef]

Lai, Y.

H. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

B. E. Little, J.-P. Laine, and S. T. Chu, Opt. Lett. 22, 4 (1997).
[CrossRef] [PubMed]

Little, B. E.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

B. E. Little, J.-P. Laine, and S. T. Chu, Opt. Lett. 22, 4 (1997).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), Chap.??1.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:?Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Olsson, A.

R. Kazarinov, C. H. Henry, and A. Olsson, IEEE J. Quantum Electron. QE-23, 1419 (1987).
[CrossRef]

Ripin, D. J.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

Shani, Y.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:?Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Appl. Phys. Lett.

D. A. Ackerman, M. I. Dahbura, Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and C. Y. Kuo, Appl. Phys. Lett. 58, 449 (1991).
[CrossRef]

IEEE J. Quantum Electron.

R. Kazarinov, C. H. Henry, and A. Olsson, IEEE J. Quantum Electron. QE-23, 1419 (1987).
[CrossRef]

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1505 (1983).
[CrossRef]

IEEE Photon. Technol. Lett.

B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling, E. P. Ippen, and D. J. Ripin, IEEE Photon. Technol. Lett. 10, 816 (1998).
[CrossRef]

J. Lightwave Technol.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

H. Haus and Y. Lai, J. Lightwave Technol. 9, 754 (1991).
[CrossRef]

S. T. Chu and S. K. Chaudhuri, J. Lightwave Technol. 7, 2033 (1989).
[CrossRef]

Opt. Lett.

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:?Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), Chap.??1.

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 (5)

Fig. 1
Fig. 1

(a) Narrow-bandwidth reflection filter with a notched-ring resonator. The notch partially couples forward and backward traveling-wave modes. (b) The notched-ring filter is equivalent to a second-order filter. The notch is equivalent to the gap, and its dimensions determine the type of second-order response produced.

Fig. 2
Fig. 2

Reflection response for a 20-nm-deep notch that yields a maximally flat response. The solid curve is for the numerical FDTD simulations, whereas the dashed curve is calculated from the analytic formulas. CMT, coupled-mode theory.

Fig. 3
Fig. 3

Reflection response for a 30-nm-deep notch. The solid curve is for the numerical FDTD simulations, whereas the dashed curve is calculated from the analytic formulas.

Fig. 4
Fig. 4

Electric field inside the notched-ring resonator with a 30-nm-deep notch. The wavelength corresponds to the larger-wavelength peak in Fig.  3. Note that there is a field null in the notch (compare with Fig.  5).

Fig. 5
Fig. 5

Electric field inside the notched-ring resonator with a 30-nm-deep notch. The wavelength corresponds to the shorter-wavelength peak in Fig.  3. Note that there is a field maximum in the notch, which is responsible for increased losses.

Equations (6)

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

Sr=jμ2μ1jΔω+μ2/22+μ12,
μ2=κ2vg2πR,  μ12=rnvg2πR2,
rn=-jωoEa24NΔzAnzΔrzexp-j2βzdz,
rn=ω0Ea2nco2-ne24Nβh=nco2-ncl2ne2d+2/γh1+γh,
h=γ+2Qvgnco2-ne2ω0πRne2d+2/γ-1.
Pr=4κ22rn2=4Qvgω0πR2rn2,

Metrics