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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25344–25345
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Nano-lens diffraction around a single heated nano particle: errata

Markus Selmke, Marco Braun, and Frank Cichos  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25344-25345 (2013)
http://dx.doi.org/10.1364/OE.21.025344


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Abstract

In our publication [Opt. Express, 20(7), 8055–8070 (2012)] a convergence issue resulted in a discrepancy between the relative photothermal signal of two models: the paraxial scalar diffraction model and the accurate vectorial generalized multilayer Lorenz-Mie scattering theory which served as a reference. The resolution yields the expected agreement.

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Discrepancy by a factor of order unity between the two models in Fig. (4) and the discussion following Eq. (21)

Unfortunately, the discretizations of the thermal lens scatterer n(r) used in the GLMT calculations of our article [1

1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

] were not carried out to large enough sizes, i.e. the outmost layer was not chosen sufficiently large as compared to the probing beam waist. As a result, in Fig. 4 of Ref. [1

1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

], and in the discussions based on these plots, an unexpected discrepancy by a factor of the order 𝒪 (1) was found between the results of the diffraction and the GLMT model. The problem resides in a convergence issue of the signal in the GLMT model [3

3. M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).

]: the thermal lens must be discretized up to a size of about rL > 5ω0, see Fig. 1. If this is done, the expected equivalence between both approaches is realized for weak and even moderate focusing, see the new Fig. 2 correcting former Fig. (4) of the article. This also corrects the discrepancy of Fig. (5) of Ref. [1

1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

], i.e. giving the same picture but without the scaling by a factor 1.6. Now, the solution to the paraxial approximation of the Helmholtz equation, i.e. Fresnel diffraction, and the exact solution for a focused beam which approximates the Gaussian beam (the Davis beam) match perfectly as they should. Expectedly, minor discrepancies remain for large numerical apertures or inverse apertures, see the new Fig. 2d).

Fig. 1 TL around a R = 10nm AuNP in PDSM (n0 = 1.46) with Δn = −3.60×10−2, wavelength λ = 635nm, beam-waist ω0 = 281nm. The graph shows the rel. transmitted power contributions of scattering (blue), extinction (red), and their sum (black), for a numerical detection aperture NAd = 0.75 at zp = −zR/2, plotted against the thermal lens cut-off radius normalized to the probing beam-waist rL0. The computed total detectable signal ΔPd saturates for a clipping size of the lens for rL ≈ 5ω0 [3].
Fig. 2 (correcting Fig. 4 of [1]) Comparison of the diffraction (black) and Gaussian GLMT model (red). Parameters used for calculations are detailed in the caption of Fig. 2 of the original article [1]. b) On-axis z-scan NAd = 0 of the rel. PT signal Φzp. The superimposed grey dashed curve is the approximation Eq. (1) of this errata. c) Scan for NAd = 0.75 (solid and dashed) and NAd = 0.3 (dashed solid and double-dashed solid). d) Scan with central beam stop (inverse aperture), i.e. NAd = [0.5, 0.75]. The semi-transparent curves corresponds to no central beam-stop, NAd = 0.75 from c)

Simplification of Eq. (7)

Eq. (7) of Ref. [1

1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

] is correct but can be simplified further to first order in the perturbation Δn/n0, see also Ref. [2

2. M. Selmke and F. Cichos, “Photothermal single particle Rutherford scattering microscopy,” Phys. Rev. Lett. 110, 103901 (2013). [CrossRef] [PubMed]

, 3

3. M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).

] on photonic Rutherford scattering:
Φ(zp)=2k0RΔnarctan(zp/zR)
(1)
This matches the accurate calculations well as seen in Fig. 2b) (gray dashed vs. black line).

Typo in Eq. (19)

Eq. (19) in Ref. [1

1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

] has a typo. The factor (−1)n should read (−1)n+1, i.e. the correct equation reads [3

3. M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).

]:
σinc,n=m=1nNmgmNnm+1gnm+1*θminθmax[ΣmΣnm+1(1)n+1ΔmΔnm+1]sin(θ)dθ,
(2)
where one may set θmin = 0. The calculations in Ref. [1

1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

] were all done using this correct equation. In view of practicability, we here also provide a more compact form [3

3. M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).

] for Gaussian (zero-order Davis) beams based on the Gaussian intensity profile:
σinc=π2ω02[eϑr(θmin)eϑr(θmax)],ϑr(θ)=2tan2(θ)θdiv2,θdiv=2kω0
(3)

References and links

1.

M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20(7), 8055–8070 (2012). [CrossRef] [PubMed]

2.

M. Selmke and F. Cichos, “Photothermal single particle Rutherford scattering microscopy,” Phys. Rev. Lett. 110, 103901 (2013). [CrossRef] [PubMed]

3.

M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(110.6820) Imaging systems : Thermal imaging
(180.5810) Microscopy : Scanning microscopy
(190.4870) Nonlinear optics : Photothermal effects
(260.1960) Physical optics : Diffraction theory
(350.4990) Other areas of optics : Particles
(050.1965) Diffraction and gratings : Diffractive lenses

ToC Category:
Physical Optics

History
Original Manuscript: October 8, 2013
Published: October 16, 2013

Citation
Markus Selmke, Marco Braun, and Frank Cichos, "Nano-lens diffraction around a single heated nano particle: errata," Opt. Express 21, 25344-25345 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25344


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References

  1. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express20(7), 8055–8070 (2012). [CrossRef] [PubMed]
  2. M. Selmke and F. Cichos, “Photothermal single particle Rutherford scattering microscopy,” Phys. Rev. Lett.110, 103901 (2013). [CrossRef] [PubMed]
  3. M. Selmke, “Photothermal single particle detection in theory & experiments,” Dissertation, Universität Leipzig, Institute for experimental physics I, (2013).

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