Additions and Corrections pubs.acs.org/journal/apchd5
Correction to Helical Plasmonic Nanostructures as Prototypical Chiral Near-Field Sources Martin Schaf̈ erling,* Xinghui Yin, Nader Engheta, and Harald Giessen ACS Photonics 2014, 1, 530−537, DOI: 10.1021/ph5000743 2 2 −2 resulting in |ECPL in | = 2 V m . When analyzing the helix structures, we always used linearly polarized illumination. Correspondingly, we should have used Exin for the normalization. However, we errornously performed the ̂ normalization with ECPL in , which leads to values for C that are a factor of 2 smaller than the correct values.
I
n our original publication, incorrect values for the normalization of the optical chirality have been mistakenly used. Due to this error, all calculated values of the normalized optical chirality are too small by a factor of 2. This does not, however, affect our finding that the proposed design with four intertwined helices is well-suited for the generation of strong optical chirality in an extended region. In fact, the response is even better than initially reported.
2. IMPLICATIONS OF THE RESULTS As discussed, all calculated values of C must be multiplied by a factor of 2 to obtain the correct results. This systematic error does not affect the distribution of optical chirality; only the absolute values have to be modified. This can simply be done by increasing all color bar labels in Figures 2, 4, 5, and 6 by a factor of 2. Additionally, the values on the y-axis in Figure 7 must be doubled as well because the error also affects the integrated values. The same changes must be performed for the written text. The small four-helix design reaches values down to −76 (instead of −38 as written originally), the optimized large four-helix design reaches −358 (instead of −179). Additionally, we can state that the expected averaged differential signal enhancement (discussion of Figure 7) exceeds 2 orders of magnitude. However, all these changes do not affect our conclusions of the manuscript. The working principle of the design stays unchanged, they even perform better than in our initial evaluation.
1. DETAILS OF THE NORMALIZATION The normalized optical chirality Ĉ is defined as (see eq 4 in original paper) Ĉ ≔
C + CCPL
(1)
Here, C+CPL is the optical chirality of a left-handed circularly polarized plane wave of the same frequency and power as the incident light. This means that we assume always circular polarization (which corresponds to the strongest possible optical chirality for plane waves) for the normalization, indepenently of the actual polarization of the incident light. Due to this choice, Ĉ can be interpreted as the enhancement of optical chirality for a given combination of plasmonic nanostructure and incident polarization compared to the best response that could be obtained without the nanostructure by optimizing only the polarization. The sign of Ĉ determines the handedness of the chiral near-fields. If we insert the definition of optical chirality (eq 2 in the original paper) and the optical chirality of left-handed circularly polarized light in eq 1, we obtain Ĉ = −
c Im(E*·B) |E in|2
3. CORRECTED FIGURES For convenience, we provide here the corrected figures of the original publication. Please note that only the values of the color bars or the corresponding axis have been changed.
(2)
Here, Ein denotes the electric field vector of the incident light, which can be arbitrarily polarized. In our single-structure simulations, the incident plane wave is given as x E in
⎛1 ⎞ ⎜ ⎟ = ⎜ 0 ⎟ V m −1 ⎝0⎠
(3)
for light polarized linearly in x-direction. This results in |Exin|2 = 1 V2 m−2. For incident circularly polarized light, the simulation uses ECPL in
⎛1⎞ ⎜ ⎟ = ⎜ ± i ⎟ V m −1 ⎝0⎠
Received: August 25, 2016
(4) © XXXX American Chemical Society
A
DOI: 10.1021/acsphotonics.6b00637 ACS Photonics XXXX, XXX, XXX−XXX
ACS Photonics
Additions and Corrections
Figure 5. Corrected Figure 5.
Figure 2. Corrected Figure 2
Figure 4. Corrected Figure 4. B
DOI: 10.1021/acsphotonics.6b00637 ACS Photonics XXXX, XXX, XXX−XXX
ACS Photonics
Additions and Corrections
Figure 6. Corrected Figure 6.
Figure 7. Corrected Figure 7.
C
DOI: 10.1021/acsphotonics.6b00637 ACS Photonics XXXX, XXX, XXX−XXX
