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Whispering gallery mode sensors: erratum

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Abstract

We present an erratum to correct inadvertent typographical errors in our paper [Adv. Opt. Photon. 7, 168 (2015) [CrossRef]  ] and to update Fig. 7 therein following a revised version from the original authors.

© 2015 Optical Society of America

Figure 7 in our article [1] was reprinted from the supplementary material of [2]. The original authors of this article, however, issued a subsequent erratum [3] in which this figure was corrected. More recently, further modifications have been made to the original figure regarding the origin of the limiting noise source on the mode shift modality [4]. The updated version of the figure is shown here in Fig. 1, whereby it can be seen that the analysis of Shao et al. shows that for a mode of given Q, the mode-broadening detection modality can outperform both mode shift and mode-splitting type schemes, but does not necessarily do so.

 figure: Figure 1

Figure 1 Comparison of the theoretical detection limit for spherical polystyrene nanoparticles in air using different WGM detection modalities: resonance shifts (blue), mode broadening (red), and mode splitting (green). [Shao et al., Adv. Mater. 26, 991 (2014) [3]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.]

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Additionally, we have found some inadvertent typographical errors. Specifically, we note that by virtue of the definition of the polarizability in Eq. (7), a factor of εh is missing from Eqs. (6) and (9), which should read

δωω0Vp[εp(r)εh]E(r)·E(r)dr2Vε(r)E(r)·E(r)drRe[α]2fεh|E(rp)|2Vε(r)|E(r)|2dr,
and
δγabsω0Im[α]εh|E(rp)|2Vε(r)|E(r)|2dr,
respectively, where εp and εh denote the relative electric permittivity of the particle and host medium and ε(r) denotes the relative permittivity distribution before any perturbation. All other quantities are as defined in the original article. The factor of ε0 should also be dropped from Eq. (10).

References

1. M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015). [CrossRef]  

2. L. Shao, X.-F. Jiang, X.-C. Yu, B.-B. Li, W. R. Clements, F. Vollmer, W. Wang, Y.-F. Xiao, and Q. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013). [CrossRef]  

3. L. Shao, X.-F. Jiang, X.-C. Yu, B.-B. Li, W. R. Clements, F. Vollmer, W. Wang, Y.-F. Xiao, and Q. Gong, “Errata: detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 26, 991 (2014). [CrossRef]  

4. Y.-F. Xiao, State Key Lab for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China (personal communication, 2015).

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Figures (1)

Figure 1
Figure 1 Comparison of the theoretical detection limit for spherical polystyrene nanoparticles in air using different WGM detection modalities: resonance shifts (blue), mode broadening (red), and mode splitting (green). [Shao et al., Adv. Mater. 26, 991 (2014) [3]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.]

Equations (2)

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δ ω ω 0 V p [ ε p ( r ) ε h ] E ( r ) · E ( r ) d r 2 V ε ( r ) E ( r ) · E ( r ) d r Re [ α ] 2 f ε h | E ( r p ) | 2 V ε ( r ) | E ( r ) | 2 d r ,
δ γ abs ω 0 Im [ α ] ε h | E ( r p ) | 2 V ε ( r ) | E ( r ) | 2 d r ,
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