## 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]:

*I*represents the signal at output of the tapered fiber at the non resonant wavelength (i.e. it represents the input signal) and

_{ip}*I*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 (

_{wg}*θ*) of the waveguide signal respectively. The ring down time (

*τ*) is given by Eq. (2). 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
(|Δ2*θ*|) 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]

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