Abstract

A Bragg-reflection-based ring resonator is proposed and analyzed. Closed-form expressions for the field and dispersion curves for radial Bragg gratings and photonic bandgap crystals are derived. The required gratings exhibit a chirped period and a varying index profile. Small bending radii and strong control over the resonator dispersion are possible by the Bragg confinement. Large free spectral range and low radiation loss are predicted theoretically.

© 2003 Optical Society of America

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References

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  1. A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
    [CrossRef]
  2. B. E. Little, Opt. Lett. 23, 1570 (1998).
    [CrossRef]
  3. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
    [CrossRef]
  4. A. Yariv, Opt. Lett. 27, 936 (2002).
    [CrossRef]
  5. M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
    [CrossRef]
  6. L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
    [CrossRef]

2002 (2)

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

A. Yariv, Opt. Lett. 27, 936 (2002).
[CrossRef]

1999 (1)

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

1998 (1)

1975 (1)

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Djaloshinski, L.

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

Harris, J. H.

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Little, B. E.

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

Orenstein, M.

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

Yariv, A.

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

A. Yariv, Opt. Lett. 27, 936 (2002).
[CrossRef]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Heiblum and J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

L. Djaloshinski and M. Orenstein, IEEE J. Quantum Electron. 35, 737 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Yariv, IEEE Photon. Technol. Lett. 14, 483 (2002).
[CrossRef]

Opt. Lett. (2)

Other (1)

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Bragg-reflection-based ring resonator. A, Reflection by annular Bragg gratings. B, Realization with an inhomogeneous hole density PBC.

Fig. 2
Fig. 2

Refractive-index profile in (A) the U,V plane and in (B) the ρ,θ plane.

Fig. 3
Fig. 3

Refractive index of an annular defect waveguide confined to a triangular PBC and the equivalent structure.

Fig. 4
Fig. 4

Field profile in A, the U,V plane and in B, the ρ,θ plane. neqmin=0.1, neqmax=0.1037, Ucent=-1309.4, b=15.

Equations (12)

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1ρρρEρ+1ρ22Eθ2+k02n2ρE=0,
ρ=R expU/R, θ=V/R,
2EU2+2EV2+k02neq2UE=0,
U=R lnρ/R, V=θR, nρ=neqρR/ρ.
EU,V=E¯UexpiβV,
βtriang PBC=k02eq,0-lπ/b21/2, l=1,2,3,,
Δneql2=1bb/2b/2neq2-eq,0exp-il2πbVdV=i2πlneqmax2-neqmin2exp-ilπ-1,
WBragg=sb/l, s=1,2,3,.
E¯U=E0 cosπbU-UcentU-Ucentb2E0 cosπbU-Ucentexp-κ1U-Ucent-b2U-Ucentb2E0 cosπbU-Ucentexpκ1U-Ucent+b2U-Ucent-b2,
βR=k02neqmin2-lπ/b1/2R=m, m=1,2,3,.
FSR=dvdm=c2neqminv2-cl/b21/22neqmin2Rπv,
FSRc2nDefectπρDefect,

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