Abstract

We incorrectly calculated the quality factor of the microcavity in our manuscript. Here, we provide a correct expression for the quality factor calculation. The technique presented, and the conclusions drawn in the paper remain unaffected.

© 2013 OSA

In section 2.1 of our manuscript [1], we incorrectly calculate the quality factor from the phase shift of the waveguide signal. The waveguide signal represents a coherent sum of the micro-cavity signal and the input signal rather than the incoherent sum. Therefore, the expressions in section 2.1 of [1] should be treated for fields instead of the intensity. From the detected phase shift (θ) of the waveguide signal, the correct expression for the phase shift of the microcavity signal coupled to the waveguide (tapered optical fiber) is given by Eq. (1) [ 2]:

ϕ=cos1[Iip(Iip+Iwg)+Iwg(3Iip+Iwg)cos2θ±2Iwgcos3θtan2θIipIwgIip2+Iwg22IipIwgcos2θ]
where Iip represents the signal at output of the tapered fiber at the non resonant wavelength (i.e. it represents the input signal) and Iwg represents the signal at output of the tapered fiber at the resonant wavelength. In the numerator of Eq.(1), + and − signs will be used for the detected negative (the case in [1]) and the positive phase shift (θ) of the waveguide signal respectively. The ring down time (τ) is given by Eq. (2).
tanϕ=ω2τ
where ω is the modulation frequency [1] and the factor of 2 comes from the fact that the expressions are derived by considering the coherent sum of the signals. The quality factor will then be calculated by using the Eq.(11) of [1].

Due to the updated analysis, the values on y axes of Fig. 3 and Fig. 5 in [1] will now represent the phase shift (|Δ2θ|) of the waveguide signal. After using the updated expressions, the values on the y axis of Fig. 4(a) in [1] will be reduced by a factor of approximately two.

The authors regret the error, which does not change the technique and the conclusions presented in [1].

Acknowledgments

The authors would like to thank Prof. Hans-Peter Loock at Queens University, Kingston, Canada for pointing us to this error.

References and links

1. M. I. Cheema, S. Mehrabani, A. A. Hayat, Y.-A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express 20, 9090–9098 (2012) [CrossRef]   [PubMed]  .

2. M. I. Cheema, “Towards optimal whispering gallery mode microcavity sensors: Novel techniques and analyses,” Ph.D. thesis, McGill University (2013). (To be published).

References

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  1. M. I. Cheema, S. Mehrabani, A. A. Hayat, Y.-A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express20, 9090–9098 (2012).
    [CrossRef] [PubMed]
  2. M. I. Cheema, “Towards optimal whispering gallery mode microcavity sensors: Novel techniques and analyses,” Ph.D. thesis, McGill University (2013). (To be published).

2012

Armani, A. M.

Cheema, M. I.

Hayat, A. A.

Kirk, A. G.

Mehrabani, S.

Peter, Y.-A.

Opt. Express

Other

M. I. Cheema, “Towards optimal whispering gallery mode microcavity sensors: Novel techniques and analyses,” Ph.D. thesis, McGill University (2013). (To be published).

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Equations (2)

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ϕ = cos 1 [ I i p ( I i p + I w g ) + I w g ( 3 I i p + I w g ) cos 2 θ ± 2 I w g cos 3 θ tan 2 θ I i p I w g I i p 2 + I w g 2 2 I i p I w g cos 2 θ ]
tan ϕ = ω 2 τ

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