Abstract

The Q-factor of an optical resonance device determines the width of its transmission resonances. For this reason, in sensing applications of optical resonators, it is commonly assumed that the Q-factor fully determines resonator sensitivity. Practically, the latter is not exactly correct. In this Letter, the parameters responsible for the sensitivity of resonance devices (i.e., the steepness and the sharpness of the transmission resonance) are analyzed. It is shown that, for given intrinsic losses of a single ring resonator sensor, the slope of the resonance is largest if its extinction ratio is 9.5dB, while the resonance is sharpest if its extinction ratio is 6dB. For a sensor consisting of several identical ring resonators coupled to a bus waveguide, the largest slope and sharpness parameters correspond to the extinction ratios of 9dB and 4.5dB, respectively. The determined optimum parameters can be achieved by tuning the coupling between the resonator rings and the waveguide.

© 2007 Optical Society of America

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References

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2006

M. Sumetsky, Y. Dulashko, J. M. Fini, A. Hale, and D. J. DiGiovanni, J. Lightwave Technol. 24, 242 (2006).
[CrossRef]

C-Y. Chao, W. Fung, and L. J. Guo, IEEE J. Sel. Top. Quantum Electron. 12, 134 (2006).
[CrossRef]

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, IEEE J. Sel. Top. Quantum Electron. 12, 148 (2006).
[CrossRef]

2005

2004

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, IEEE J. Quantum Electron. 40, 726 (2004).
[CrossRef]

O. Schwelb, J. Lightwave Technol. 22, 1380 (2004).
[CrossRef]

S. Ashkenazi, C.-Y. Chao, L. J. Guo, and M. O'Donnell, Appl. Phys. Lett. 85, 5418 (2004).
[CrossRef]

2002

2001

Appl. Opt.

Appl. Phys. Lett.

S. Ashkenazi, C.-Y. Chao, L. J. Guo, and M. O'Donnell, Appl. Phys. Lett. 85, 5418 (2004).
[CrossRef]

IEEE J. Quantum Electron.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, IEEE J. Quantum Electron. 40, 726 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

C-Y. Chao, W. Fung, and L. J. Guo, IEEE J. Sel. Top. Quantum Electron. 12, 134 (2006).
[CrossRef]

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, and B. B. Goldberg, IEEE J. Sel. Top. Quantum Electron. 12, 148 (2006).
[CrossRef]

J. Lightwave Technol.

Opt. Lett.

Phys. Rev. E

J. E. Heebner, R. W. Boyd, and Q. Park, Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Other

Equations and assume that the accuracy of measurement of the transmission power does not depend on the power magnitude.

In fact, introducing the attenuation constant α we have 1−τ=1−exp(−αL)≈αL and, therefore, γi≈αλ02/(2πn).

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Figures (2)

Fig. 1
Fig. 1

(a) Ring resonator, (b) SCISSOR.

Fig. 2
Fig. 2

(a) Left axis, relative enhancement of the maximum slope with the optimized resonance compared to the critical coupling resonance; right axis, ER of optimized resonances. (b) Shape of resonances for the condition of critical coupling (black), with maximum slope (red) and with maximum sharpness (blue).

Equations (12)

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S = d P d λ = max .
Θ = d 2 P d λ 2 d P d λ = 0 = max .
P = P 0 τ 2 2 r τ cos ( ϕ ) + r 2 1 2 r τ cos ( ϕ ) + r 2 τ 2 , ϕ = 2 π n L λ ,
P = P 0 ( λ λ 0 ) 2 + ( γ i γ c ) 2 ( λ λ 0 ) 2 + ( γ i + γ c ) 2 ,
γ i = ( 1 τ ) λ 0 2 2 π n L , γ c = ( 1 r ) λ 0 2 2 π n L .
R = 10 log [ ( γ e + γ i γ e γ i ) 2 ] .
Q = λ 0 2 ( γ i + γ c ) .
R = 10 log ( 9 ) = 9.54 dB .
R = 10 log ( 4 ) = 6.02 dB .
P N = P N ,
R N = 10 log [ ( 2 N + 1 ) 2 N ( 2 N 1 ) 2 N ] dB .
R N = 10 log [ ( 3 + 2 N 4 N 2 3 ) 2 N ( 3 2 N + 4 N 2 3 ) 2 N ] .

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