Abstract

Reflections that are due to random surface roughness in periodic structures such as dielectric rings and disks inherently phase match forward- and backward-propagating modes. Small reflections are thus considerably enhanced and may impair the performance of traveling-wave resonators. In addition, such contradirectional coupling leads to a splitting of the resonant peak. These effects are studied analytically.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  2. Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
    [CrossRef] [PubMed]
  3. B. E. Little, S. T. Chu, and H. A. Haus, in LEOS 8th Annual Meeting, (Institute of Electrical and Electronics Engineers, New York, 1995), paper WDM 2.3.
  4. G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, Opt. Lett. 21, 695 (1996).
    [CrossRef] [PubMed]
  5. B. E. Little and S. T. Chu, Opt. Lett. 21, 1390 (1996).
    [CrossRef] [PubMed]
  6. M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1501 (1983).
  7. C. Vassallo, Optical Waveguide Concepts (Elsevier, New York, 1991).

1996 (2)

1995 (1)

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

1983 (1)

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1501 (1983).

Arnold, S.

Bi, W.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Chu, D.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Chu, S. T.

B. E. Little and S. T. Chu, Opt. Lett. 21, 1390 (1996).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, and H. A. Haus, in LEOS 8th Annual Meeting, (Institute of Electrical and Electronics Engineers, New York, 1995), paper WDM 2.3.

Connolly, J.

Griffel, G.

Haus, H. A.

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1501 (1983).

B. E. Little, S. T. Chu, and H. A. Haus, in LEOS 8th Annual Meeting, (Institute of Electrical and Electronics Engineers, New York, 1995), paper WDM 2.3.

Ho, S.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Kuznetsov, M.

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1501 (1983).

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Little, B. E.

B. E. Little and S. T. Chu, Opt. Lett. 21, 1390 (1996).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, and H. A. Haus, in LEOS 8th Annual Meeting, (Institute of Electrical and Electronics Engineers, New York, 1995), paper WDM 2.3.

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Morris, N.

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Serpenguzel, A.

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Taskent, D.

Tiberio, R.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Tu, C.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts (Elsevier, New York, 1991).

Wu, S.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Zhang, Z.

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Kuznetsov and H. A. Haus, IEEE J. Quantum Electron. QE-19, 1501 (1983).

Opt. Lett. (2)

Phys. Rev. Lett. (1)

Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, and R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Other (2)

B. E. Little, S. T. Chu, and H. A. Haus, in LEOS 8th Annual Meeting, (Institute of Electrical and Electronics Engineers, New York, 1995), paper WDM 2.3.

C. Vassallo, Optical Waveguide Concepts (Elsevier, New York, 1991).

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 (3)

Fig. 1
Fig. 1

(a) Microring resonator channel-dropping filter. κ2 is the power coupled from the bus into the ring per pass, and R2 represents a lumped reflectivity that is due to the sidewall roughness distributed randomly around the ring. Ai are steady-state amplitudes of the forward mode at various coupling points. (b) Sidewall roughness of random amplitude rz about the ideal surface.

Fig. 2
Fig. 2

Normalized reflectivity due to sidewall roughness for the high-index contrast channel waveguide shown. The roughness correlation function is Ht=r2×expt2/Lc2. r is the rms value of the roughness depth, here measured in nanometers.

Fig. 3
Fig. 3

Wavelength response of a typical microring resonator filter using the channel guide depicted in the inset of Fig. 2 and a ring radius of R0=2.0 µm. κ=0.1 gives a Q of 8000 and a bandwidth of 0.2 nm.

Equations (9)

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

Jz=0ωδn2Ez exp-jβrzN-1hrzδyδx.
Ab=14N2VJzEz* exp-jβrzdV.
R2=C20L0Lrzr*zexp-j2βrz-zdzdz,
C2=0ωδn2hEz4N3-12.
R2=C2L0LHtexp-j2βrtdt.
R2L-1=C2πr2Lc exp-βrLc2,
A1=-jκsi+tkA6, A2=A1 exp-jθ, A3=-jRB3+tkA2, A4=A3 exp-jϕ/2-θ, A5=tkA4, A6=A5 exp-jϕ/2,
s0si=-jκ21-tk2A exp-jϕ,
A=tr-tk2 exp-jϕ1-trtk2 exp-jϕ.

Metrics