Abstract

This erratum corrects errors in the expressions for βTMD and fitted form of IHRS and a consequent data point in Fig. 4 of a recent Letter [Opt. Lett. 42, 5018 (2017) [CrossRef]  ]. It also supplies data for the reference compound para-nitroaniline (pNA). The correction to βTMD improves experimental agreement from 46% to within 21% of independent scissors-corrected density functional theory (DFT) calculations. Central findings from the original Letter remain intact.

© 2018 Optical Society of America

Equation (2) on page 5019 in Ref. [1] contained an extraneous Beer–Lambert correction factor, eσ. Calculation of the orientation-averaged first hyperpolarizability, β, for tungsten disulfide (WS2), a transition metal dichalcogenide (TMD), from hyper Rayleigh scattering (HRS) data should instead use

βTMD=αTMDFpNAαpNATTMDβpNA,
where αi is the linear slope of IHRS versus number density (Ni), and F and T are field correction factors. Removing the Beer–Lambert correction factor decreased the derived magnitudes of βTMD, χ(2), and χxxx(2) by a factor of 1.84 in the Letter [1].

The expression for fitted form of IHRS in the Fig. 2 caption and in paragraph 5 on page 5019 in Ref. [1] is missing two No terms for TMD to clarify absolute versus relative αi. Its correct form is

IHRS=(αTMDNo)(N/No)e(σTMDNo)(N/No)+IHRSo,
where a relative concentration ratio (N/No) was introduced to normalize number densities for TMD and pNA. “Stock” number densities for TMD and pNA were No=9.62×1012cm3 and 6.02×1020cm3, respectively. Reference pNA was dissolved in methanol, for which FpNA((nmethanol2ω)2+23)6=3.93. The fitted value for (αpNANo) was 2.02 in Fig. 2. Fitted αi values regressed from data in Fig. 2 were accurate and remain as reported in Ref. [1].

The corrected β value is 2.66±0.13×1025esu. Subsequently, the corrected bulk-like second-order nonlinear susceptibilities, χ(2) and χxxx(2), are 150±7 and 250±12pmV1, respectively, using a mean WS2 flake volume of 1455nm3. Figure 1 is the corrected Fig. 4 from Ref. [1], which summarizes published measured and calculated χxxx(2) for monolayer WS2 [2,3]. The corrected HRS-measured value differs from the scissors-corrected (ΔSCI) DFT value by 21%, rather than 46% as reported in the original Letter [1]. The central findings and conclusions of the original Letter remain intact.

 figure: Fig. 1.

Fig. 1. Updated Fig. 4 from Ref. [1]. χ(2) for WS2 via (i) DFT calculations (black dashed) with and without scissors correction (ΔSCI) and (ii) measured values by HRS (this work; blue) and microscopy with a Green’s function calculation (red and green).

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Funding

National Science Foundation (NSF) (EEC-1260301, GRFP to G.T.F., GRFP to J.R.D.); University of Arkansas Foundation; Walton Charitable Foundation; Swiss SEFRI (C15.0041); French-Switzerland Interreg Program (NANOFIMT); Army Research Laboratory (ARL) (Cooperative Agreement W911NF-17-2-0057).

Acknowledgment

This study was performed in the context of the European COST Action MP1302 Nanospectroscopy. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation, Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

REFERENCES

1. G. T. Forcherio, J. Riporto, J. R. Dunklin, Y. Mugnier, R. Le Dantec, L. Bonacina, and D. K. Roper, Opt. Lett. 42, 5018 (2017). [CrossRef]  

2. C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014). [CrossRef]  

3. C. Y. Wang and G. Y. Guo, J. Phys. Chem. C 119, 13268 (2015). [CrossRef]  

References

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  1. G. T. Forcherio, J. Riporto, J. R. Dunklin, Y. Mugnier, R. Le Dantec, L. Bonacina, and D. K. Roper, Opt. Lett. 42, 5018 (2017).
    [Crossref]
  2. C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
    [Crossref]
  3. C. Y. Wang and G. Y. Guo, J. Phys. Chem. C 119, 13268 (2015).
    [Crossref]

2017 (1)

2015 (1)

C. Y. Wang and G. Y. Guo, J. Phys. Chem. C 119, 13268 (2015).
[Crossref]

2014 (1)

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Bonacina, L.

Crespi, V.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Dunklin, J. R.

Elías, A. L.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Forcherio, G. T.

Guo, G. Y.

C. Y. Wang and G. Y. Guo, J. Phys. Chem. C 119, 13268 (2015).
[Crossref]

Janisch, C.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Le Dantec, R.

Liu, Z.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Ma, D.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Mehta, N.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Mugnier, Y.

Perea-López, N.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Riporto, J.

Roper, D. K.

Terrones, M.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

Wang, C. Y.

C. Y. Wang and G. Y. Guo, J. Phys. Chem. C 119, 13268 (2015).
[Crossref]

Wang, Y.

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

J. Phys. Chem. C (1)

C. Y. Wang and G. Y. Guo, J. Phys. Chem. C 119, 13268 (2015).
[Crossref]

Opt. Lett. (1)

Sci. Rep. (1)

C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Sci. Rep. 4, 5530 (2014).
[Crossref]

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Figures (1)

Fig. 1.
Fig. 1. Updated Fig. 4 from Ref. [1]. χ ( 2 ) for WS 2 via (i) DFT calculations (black dashed) with and without scissors correction ( Δ SCI ) and (ii) measured values by HRS (this work; blue) and microscopy with a Green’s function calculation (red and green).

Equations (2)

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β TMD = α TMD F pNA α pNA T TMD β pNA ,
I HRS = ( α TMD N o ) ( N / N o ) e ( σ TMD N o ) ( N / N o ) + I HRS o ,

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