Abstract

The volume current method is used to estimate analytically the scattering losses that are due to boundary corrugations and surface roughness in microdisk and ring resonators. The harmonic components of boundary imperfections either phase match the unguided continuum or lead to tunneling radiation. Phase-matched radiation can contribute significant loss and is only weakly dependent on disk radius. In high-index contrast devices the longitudinal electric field component is thus responsible for most of the radiation.

© 1996 Optical Society of America

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References

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  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  2. A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
    [CrossRef]
  3. Z. Zhang, D. Chu, S. Wu, S. Ho, W. Bi, C. Tu, R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
    [CrossRef] [PubMed]
  4. B. E. Little, S. T. Chu, H. A. Haus, in LEOS 8th Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1995), paper WDM 2.3.
  5. M. Kuznetsov, H. A. Haus, IEEE J. Quantum Electron. QE-19, 1501 (1983).
  6. H. Abromawitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

1995 (1)

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

1993 (1)

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

1992 (1)

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

1983 (1)

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

Abromawitz, H.

H. Abromawitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Bi, W.

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

Chu, D.

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

Chu, S. T.

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

Glass, J. L.

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

Haus, H. A.

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

B. E. Little, S. T. Chu, 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, R. Tiberio, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Kuznetsov, M.

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

Levi, A. F.

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

Levi, A. F. J.

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

Little, B. E.

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

Logan, R. A.

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

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

McCall, S. L.

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

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

Pearton, S. J.

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

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

Slusher, R. E.

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

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

Stegun, I.

H. Abromawitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Tiberio, R.

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

Tu, C.

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

Wu, S.

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

Zhang, Z.

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

Appl. Phys. Lett. (2)

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

A. F. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, R. A. Logan, Appl. Phys. Lett. 62, 561 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Phys. Rev. Lett. (1)

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

Other (2)

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

H. Abromawitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

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Figures (2)

Fig. 1
Fig. 1

(a) Disk resonator reduced to two dimensions by the effective-index method. (b) Locally, at the disk edge, the situation resembles a straight waveguide with local decay constant α in the cladding. The relative magnitudes of the transverse, Eρ, and longitudinal, Eϕ, electric fields are shown.

Fig. 2
Fig. 2

Loss-limited quality factor Q, normalized to the perturbation corrugation depth h, as a function of corrugation period Λ. Disk radius R is a parameter. h is the radial depth of the sinusoidal perturbation (in micometers). The phase-matched radiation region contains those values of Λ that match the continuum,βkno < 2π/Λ < β + kno, and that depend on R. The overall Q value for a shape that comprises several harmonics with different depths is Q−1 = ∑mQm−1.

Equations (9)

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k n e J n + 1 ( k n e R ) = ( α n e 2 n o 2 + β ) J n ( k n e R ) ,
J ϕ = o ω E ϕ a m A ¯ δ n 2 δ ( r R ) δ ( z ) exp [ + j ( m n ) ϕ ] ,
S r ( r , ϕ , θ ) = C 2 R 2 r 2 J N 2 ( k n o R cos θ ) ,
P ^ rad = 1 2 π R S r r 2 cos θ d θ d ϕ ,
C 2 = k 4 A ¯ 2 E ϕ 2 n o c o δ n 4 a m 2 8 , N = n m = R ( β Ω ) .
P ^ rad = C 2 R π 1 / 2 γ 1 / 2 J N 2 ( k n o R ) ,
γ = 1 2 + k n o R J N ( k n o R ) J N ( k n o R ) .
P ^ rad = 4 C 2 k π n o cos 1 ( β Ω k n o ) .
Q = ω P g v g P ^ rad k n e P g P ^ rad

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