OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 10205–10206
« Show journal navigation

Boundary element method for surface nonlinear optics of nanoparticles: erratum

Jouni Mäkitalo, Saku Suuriniemi, and Martti Kauranen  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 10205-10206 (2013)
http://dx.doi.org/10.1364/OE.21.010205


View Full Text Article

Acrobat PDF (534 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report a correction to the numerical procedure, in which the source vector lacked a factor 1/2 and the integration in Eq. (19) was incorrect. The errors are inconsequential for the main results.

© 2013 OSA

The operators 𝒦l involve an integration over a strong singularity, so that the integral exists by means of the Cauchy principal value:
𝒦lf(r)=Vl[Gl(r,r)]×f(r)dS=12f(r)×nl+𝒦lf(r),
where
𝒦lf(r)=lima0VlD(r,a)[Gl(r,r)]×f(r)dS
where D(r, a) is a disk of radius a around r and it is assumed that the boundary ∂Vl is smooth. Thus the proper way to write Eqs. (7) and (8) of [1

1. J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011) [CrossRef] [PubMed]

] would be
(𝒟1J1S+𝒦1M1S𝒟2J2S𝒦2M2S)tan=12εSPnS,(𝒦1J1S+1η12𝒟1M1S+𝒦2J2S1η22𝒟2M2S)tan=i12ΩPS×n.
Although the Eqs. (7) and (8) are correct, the method of moments procedure should be applied to the operators involving the principal values. This was not noticed in the implementation of the numerical procedure. Consequently, the first two elements of the source vector b lacked a factor 1/2. This factor does not appear in the PMCHWT formulation for linear scattering due to the continuity of Etan and Htan.

Furthermore, there is a mistake in the source integral (19). For if PnS is constant in each triangle, the integral still vanishes for RWG functions. This may be overcome by first expanding SPnS in RWG basis as
SPnS=l=1Nplfl.
where pl can be obtained in the same way as bmn1 by integration by parts. Then the coefficients bmn2 can be computed directly as
bmn2=1εlplSmSlfmn×fldS,
where l runs over indices for which SmSl ≠ ∅. In [2

2. C. Forestiere, A. Capretti, and G. Miano, “Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles,” arXiv:1301.1880 [physics.optics] (2013)

], an alternative distributional approach / was presented for evaluating the coefficients bmn1 and bmn2.

Finally, we point out a curious observation, that these two mistakes very accurately cancelled each other out in the numerical results, as is apparent from the comparison to the multipole solution. In general this cancellation is not to be expected. Through use of the corrected expressions we verified the validity of the results in Fig. 5.

References and links

1.

J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express 19, 23386–23399 (2011) [CrossRef] [PubMed]

2.

C. Forestiere, A. Capretti, and G. Miano, “Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles,” arXiv:1301.1880 [physics.optics] (2013)

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.2620) Nonlinear optics : Harmonic generation and mixing
(240.4350) Optics at surfaces : Nonlinear optics at surfaces
(250.5403) Optoelectronics : Plasmonics
(290.5825) Scattering : Scattering theory
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 11, 2013
Published: April 16, 2013

Citation
Jouni Mäkitalo, Saku Suuriniemi, and Martti Kauranen, "Boundary element method for surface nonlinear optics of nanoparticles: erratum," Opt. Express 21, 10205-10206 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-10205


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Mäkitalo, S. Suuriniemi, and M. Kauranen, “Boundary element method for surface nonlinear optics of nanoparticles,” Opt. Express19, 23386–23399 (2011) [CrossRef] [PubMed]
  2. C. Forestiere, A. Capretti, and G. Miano, “Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles,” arXiv:1301.1880 [physics.optics] (2013)

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited