Whispering gallery mode sensors: erratum

Matthew R. Foreman; Jon D. Swaim; Frank Vollmer

doi:10.1364/AOP.7.000632

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.

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 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 $ε_{h}$ is missing from Eqs. (6) and (9), which should read

\frac{δ ω}{ω_{0}} \approx - \frac{\int_{V_{p}} [ε_{p} (r) - ε_{h}] E^{†} (r) \cdot E^{'} (r) d r}{2 \int_{V} ε (r) E^{†} (r) \cdot E^{'} (r) d r} \approx - \frac{Re [α]}{2} \frac{f ε_{h} {| E (r_{p}) |}^{2}}{\int_{V} ε (r) {| E (r) |}^{2} d r},

and

\frac{δ γ_{abs}}{ω_{0}} \approx Im [α] ε_{h} \frac{{| E (r_{p}) |}^{2}}{\int_{V} ε (r) {| E (r) |}^{2} d r},

respectively, where

ε_{p}

and

ε_{h}

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

ε_{0}

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).

References

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M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015).
[Crossref]
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]
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]
Y.-F. Xiao, State Key Lab for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China (personal communication, 2015).