Abstract

High-Q traveling-wave-resonators can enter a regime in which even minute scattering amplitudes associated with either bulk or surface imperfections can drive the system into the so-called strong modal coupling regime. Resonators that enter this regime have their coupling properties radically altered and can mimic a narrowband reflector. We experimentally confirm recently predicted deviations from criticality in such strongly coupled systems. Observations of resonators that had Q>108 and modal coupling parameters as large as 30 were shown to reflect more than 94% of an incoming optical signal within a narrow bandwidth of 40 MHz.

© 2002 Optical Society of America

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References

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  1. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, Opt. Lett. 18, 191 (1993).
    [CrossRef]
  2. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, J. Opt. Soc. Am. B 17, 1051 (2000).
    [CrossRef]
  3. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  4. J. C. Knight, G. Chueng, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997).
    [CrossRef] [PubMed]
  5. D. Weiss, V. Sandoghar, J. Hare, and V. Lefevre-Seguin, Opt. Lett. 20, 1835 (1995).
    [CrossRef] [PubMed]
  6. The doublet structure is not completely symmetric because the associated orthogonal pair of standing waves probes different regions of the sphere's surface.
  7. The resonator–waveguide distance with respect to the critical point is DX∝lnK.
  8. H. Mabuchi and H. Kimble, Opt. Lett. 19, 749 (1994).
    [CrossRef] [PubMed]
  9. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, Singapore, 1996).
  10. S. Goetzinger, O. Benson, and V. Sandoghar, Opt. Lett. 27, 80 (2002).
    [CrossRef]

2002

2000

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, J. Opt. Soc. Am. B 17, 1051 (2000).
[CrossRef]

1997

1995

1994

1993

Benson, O.

Birks, T. A.

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, Singapore, 1996).

Chang, R. K.

C. Swindal, D. H. Leach, R. K. Chang, and K. Young, Opt. Lett. 18, 191 (1993).
[CrossRef]

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, Singapore, 1996).

Chueng, G.

Goetzinger, S.

Gorodetsky, M. L.

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, J. Opt. Soc. Am. B 17, 1051 (2000).
[CrossRef]

Hare, J.

Haus, H.

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Ilchenko, V. S.

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, J. Opt. Soc. Am. B 17, 1051 (2000).
[CrossRef]

Jacques, F.

Kimble, H.

Knight, J. C.

Leach, D. H.

Lefevre-Seguin, V.

Mabuchi, H.

Pryamikov, A. D.

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, J. Opt. Soc. Am. B 17, 1051 (2000).
[CrossRef]

Sandoghar, V.

Swindal, C.

Weiss, D.

Young, K.

J. Opt. Soc. Am. B

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, J. Opt. Soc. Am. B 17, 1051 (2000).
[CrossRef]

Opt. Lett.

Other

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

The doublet structure is not completely symmetric because the associated orthogonal pair of standing waves probes different regions of the sphere's surface.

The resonator–waveguide distance with respect to the critical point is DX∝lnK.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, Singapore, 1996).

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Figures (3)

Fig. 1
Fig. 1

Spectral transmission Tt/s2 and reflection Rr/s2 properties6 of a 70µm sphere with Q0=1.2×108 and a modal coupling of Γ=10. Solid curve, fit from the model from Eqs. (1). Inset, microsphere coupled to a tapered fiber.

Fig. 2
Fig. 2

Transmission (stars) and reflection (diamonds) behavior for symmetric Δω=0 excitation relative to K (Ref. 7) for a mode with Q0=1.2×108 and a modal coupling of Γ=10. Solid curve, a theoretical fit with the model from Eqs. (1) and (2). The minimum T=0 occurs at KΓ and is accompanied by a maximum backreflection of 84%. Dotted–dashed curve, transmission for an ideal TWR in the absence of backscattering, where critical coupling occurs for K=1.

Fig. 3
Fig. 3

Experimentally observed and theoretically determined reflection at the critical point as a function of modal coupling Γ. Inset, transmission and reflection at the T=0 point for a mode with Γ=31. In this case 94% of the optical power is reflected. Note that the doublet structure is masked, because the lifetime of the mode is of the same order as the lifetime of the modal coupling process. However, the doublet structure is still evident in the spectrum, causing a flattened frequency response at resonance.

Equations (5)

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daCWdt=iΔωaCW-12τaCW+i2γaCCW+κs,daCCWdt=iΔωaCCW-12τaCCW+i2γaCW,
t=-s+κaCW,    r=κaCCW.
Kτ0/τex=1+Γ2.
Rcrit=Γ1+1+Γ22.
CaCWγ2+aCCWγ2aCWideal2=2Γ2+1+K22+1+K2Γ24Γ2+1+K22+Γ24Γ2+1+K2.

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