I often find that, when responding to reviewers, I learn quite a lot. Reviewer response letters often contain valuable information that does not make its way into the revised paper. Therefore, I thought it would be useful to make the reviewer responses for our latest paper “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips” public, in the spirit of “Transparent Peer Review” recently included as an option in Nature Communications.
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Dear Editors,
please find attached our revised manuscript entitled “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips” by Alessandro Tuniz and Markus A. Schmidt. We are grateful to the reviewers for making important points which have helped us to substantially improve the manuscript. In the list below you will find the reviewers’ comments in italic, and the changes in the manuscript in bold.
Reviewer 1:
R1.1: Looking at ref 34 and ref 31 and as the authors mentioned, it is now possible to integrate gold wire into fibers. Can the authors precise what typical length the existing techniques are able to reach without discontinuities? The study here shows that several tens of micrometer length is necessary to get efficient coupling, is it something now reachable?
This is a very good comment. Indeed, in Reference 31, Fig. 4(b), continuous gold nanowires with 500 nm diameters on the order of 50-60 μm were obtained using pressure-assisted melt filling, as shown in Fig. R1.
Fig. R1. Extract of Fig. 4(b) in Ref. [34]. (a) Schematic of the light scattering from a discontinuous gold nanowire located in a fibre-based plasmonic directional coupler. (b) Microscope side image (in reflection) of a representative section of the gold wire (diameter 510 nm).
This is well above the coupling length shown in Fig. 12(a) of our manuscript. We have expanded the relevant sentence in the manuscript (page 17, paragraph 2):
The Eigenmode approach reveals that η = 53% can be achieved for our example at z = Lc = 22μm, which is significantly shorter than the typical lengths of continuous 500 nm gold nanowires that can be integrated into fibers using pressure-assisted melt filling (approximately 50μm), see [34], Fig. 4(b).
R1.2a: I personally think that the part 2.1 can be a bit confusing notably for a non-initiate person. Is the modal amplitude “a” and “b” in equation (4) and (5) referring to the amplitude “a” of equation (2)?
The modal amplitudes ai in Eq. (4) are the same as in Eq. 2, taken at z=0. The modal amplitude in Eq. (5) are also modal amplitudes at a distance z>0. This is already described in the paper. For compactness, we use different letters (a and b) to describe the same physical quantity (modal amplitude) at different points (z=0 and z>0). We have defined a and b when appropriate.
R1.2b: What is the meaning of the dirac function in equation (4) and (5)?
The Dirac functions in Eq. 4 and 5 were a typographical error and have been removed. We thank the reviewer for pointing this out.
R1.2c: Also the authors can detail more how they reach equation (6).
This is obtained by considering a superposition of the Eigenmodes (including phase factors) in the dual core section and the respective modal amplitudes at a fixed position z, and taking the modulus squared. We have added the following sentence in the manuscript (page 7, paragraph 1):
To obtain the power fraction in either of the two waveguides, we superpose the evolved Eigenmodes (including phase factors) via the modal amplitudes, project the fields at a distance z of the dual waveguide system [Eqs. (1)-(2)] onto the appropriate isolated modes using orthonormality, and take the modulus squared. After some algebra we obtain a closed-form expression for the fraction of power in the projected waveguide at the (output) position z for each of the two waveguides.
R1.3a: In figure 5, the maximum of pointing vector or power in the core correspond to the minimum of power in the gold nanowire but the inverse is not true? Why is it the case?
This is an interesting observation. We can understand this difference in terms of the analytical equation describing the power transfer [Eq. (6)]. Let us consider for example the common case of two waveguides in the absence of loss (i.e. all imaginary parts are zero). In this case, the factor in front of sin function is zero, leading to no phase delay, so that, as the reviewer points out, the maximum power in one waveguide would correspond to a minimum in the other, and vice versa. However, in the presence of (lossy) metals as considered here, the imaginary part of the amplitudes leads to the term in front of the sin function being non-zero, leading to a phase delay, which in turn depends on whether you consider the dielectric (ai = bi) or plasmonic (ai ≠ bi) portion of the waveguide. In this case, Eq. (6) shows that there is a phase difference in the total oscillating function (intended as a superposition of sin and cos functions), depending on which waveguide you consider. We have added the following sentence in the paper to address this issue (page 11, paragraph 1):
This confirms that the superposition of the propagating (bounded) HEMs offers a straightforward pathway for analyzing the propagation characteristics of plasmonic/dielectric couplers with high degree of accuracy, greatly simplifying the design procedure with minimal simulation time, and providing additional physical insight. For example, the fact that the maximum SPP power transfer does not occur at the position where the power in the dielectric core is minimum [Fig. 5(b)] can be understood by inspecting Eq. (6), since in the presence of loss (non-zero imaginary field amplitudes), the power fractions in the dielectric (ai = bi) and plasmonic (ai ≠ bi) modes are phase-delayed.
R1.3b: To get background free nanofocusing device, will it not be preferable to cleave the fiber at a distance where the dielectric core contribution is minimum instead of plasmon contribution maximum?
This is an interesting question, which is worth investigating. Figure R2(a) shows the (normalized) Poynting vector magnitude at λ = 1550 nm, considering a cleave where the plasmon contribution is maximum (L=5.3μm), as shown in Fig. 7(b) of our submission. We have also repeated the calculation considering a cleave where the dielectric core contribution is minimum (L=8.5 μm), in Fig. R2(b), assuming the same input. We characterize the tip performance by considering the Poynting vector magnitude at a distance of 1 nm from the tip [vertical dotted lines in Fig. R2(a) and R2(b)], as shown in Fig. R2(c). We see that the delivery of power to the tip is orders of magnitude more efficient in the former case than the latter. Additionally, by re-normalizing to the maximum of each curve [Fig. R2(d)], we see that the background noise is also more pronounced in the latter case. As a result, it is preferable to cleave the fiber at the position where the transfer of energy to the plasmonic mode is maximum, as shown in our submission.
Fig. R2: Distribution of the Poynting vector magnitude for the planar superfocussing device (delivery mode operation) for two dielectric waveguide lengths [(a): L = 5.3 μm (“dielectric minimum”), (b): 8.5 μm (“plasmonic maximum”)]. The fundamental TM mode of the dielectric waveguide is incident from the left. (c) Poynting vector magnitude |S| at a distance of 1 nm from the nanotip, for L = 5.3 μm (blue) and L = 8.5 μm (green). (d) Same as (c), normalized to the maximum of each curve.
We have added the following sentence to address this (page 13-14, paragraph 1):
Note that we have selected a coupling section corresponding to the length where the energy transfer to the plasmonic mode is maximum, as opposed to where the power in the dielectric core is minimum. This choice was motivated by the observation that the latter results in orders of magnitude lower power delivery to the nanotip, accompanied by a relative increase in the background noise when the nanotip operates in light delivery mode.
R1.4: Can the authors mention the origin of the fast oscillations in figure 8?
The Reviewer is referring to fluctuations in delivery efficiency. These oscillations result from the fundamental propagating plasmon mode being reflected at the apex of the nanotip and the dielectric surface, which results in Fabry-Perot type resonances and was seen already in [P. Uebel te al. Appl. Phys. Lett. 103, 21101 (2013)]. We have added the following sentence to respond to this query (page 14, end of Section 3.1):
The fluctuations in delivery efficiency can be attributed to the fundamental plasmon mode being reflected at the apex and the base of the tip, forming Fabry-Perot type resonances [35].
R1.5: Comparing delivery spectrum in fig. 8 and collection spectrum in figure 10 a) (collection efficiency), I would expect by reciprocity both to have the same trend. Can the authors comment on that?
The mentioned difference is due to the inherently different excitation sources used in either case. In delivery mode, a forward-propagating waveguide mode is excited at the input. In collection mode, a point source is located in close proximity to the nanotip, with the collection performance being dependent on the orientation of the point dipole (see also the response to the next issue raised by the Reviewer, R1.6). We have added the following sentence to address this issue, also in response to R.1.6 (page 15-16, end of Section 3.2):
Note that the collection performance is dependent on the nature of the excitation source (e.g., relative orientation of dipole with respect to tip symmetry axis). For example, an x-oriented dipole placed at 1 nm distance from the tip has a collection efficiency of only 0.03 % at λ = 1.55 nm.
R1.6: An important point in nanoimaging using scanning near-field microscope when exciting and/or collecting with the tip is the contrast with the background (as already mentioned in 3)). Can the authors give and compare the collection efficiency they get when the dipole is right below the dielectric core at fixed z distance? What about a x oriented dipole?
We thank the Reviewer for this excellent comment. We have repeated the calculation for a dipole at the height of the dielectric core, and included the following sentence (page 16, end of Section 3.2):
Furthermore, when a z-oriented dipole is placed at a distance of x=250 nm (i.e., aligned with the central axis of the dielectric core, with the same z-position discussed so far) the collection performance is 0.015%, suggesting that direct coupling of a point source into the dielectric core is negligible compared to that via the gold nanotip.
With regards to the x-oriented dipole, see our response to Reviewer question R1.5.
Reviewer 2:
R2.1: I find the study to be quite interesting that will likely encourage experimentalists to play with such a hybrid probe for plasmonic nanofocusing and sensing applications.
We thank the Reviewer for the generous feedback.
Reviewer 3:
R3.1: I was quite surprised by the results in Fig. 9(a), claiming a collection efficiency close to a percent-level. Intuitively, I would have expected that the emission of a radiating dipole in extremely close proximity (here about 1 nm, corresponding to about l/1500) to a metallic object is very strongly quenched by the Ohmic losses of the metal. I would like to ask the authors to comment on the role of Ohmic losses in the mentioned configuration.
This is an excellent question that also allows us to present some of the advantages of the geometry presented here with respect to other plasmonic geometries.
As the Reviewer points out, when a point source is too close to a metallic object, Ohmic losses quench the dipole through energy dissipation into non-radiative modes, leading to a loss of power. To show this for a typical geometry, let us consider a gold cylinder with a diameter of 60 nm, in the proximity of a point dipole oriented along z [λ = 1550 nm, Fig. R3(a)].
In order to characterize the role of Ohmic losses, and its relation to plasmonic field enhancement/quenching in this system, we integrate the Poynting vector magnitude over a circle in the far field [Pff in Fig. R3(a), green dashed line] and over a 1nm circle surrounding the point source [Ps in Fig.R3(a)]. The resulting Pff and Ps obtained are shown in Fig. R3(b). Note that both quantities are the same for large distances, and increase as the point source is brought in contact with the cylinder (comparable to the 1 nm distance mentioned by the Reviewer), however the ratio Pff/Ps decreases dramatically when the point source approaches the cylinder, as a result of the absorption induced by the Ohmic losses of the cylinder, see Fig.R3(c). The electric field intensity is also shown in Fig. R3(d). This is in agreement with what is typically reported in the literature, see for example, P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement”, Opt. Express 15, 14266 (2007). Note that repeating these calculations at λ=650nm, which is closer to the localized plasmonic resonance, yields similar results.
Fig. R3: (a) Schematic of the first example geometry under consideration. A z-oriented point source is (λ = 1550 nm) placed in proximity of a gold cylinder of diameter 60 nm. Ps refers to the Poynting vector magnitude integrated over a 1 nm circle surrounding the point source. Pff refers to the Poynting vector magnitude integrated in the far-field (integration radius 2μm). (b) Ps (blue) and Pff (green) as a function of z. (c) Pff/Ps as a function of z. (d) Field intensity when the point dipole is placed at z = 1 nm.
We are now in the position to analyze the case considered in our submission, namely that of a gold strip which tapers down from a width of 15 nm to 1 nm over a length of 1μm. We repeat the numerical analysis mentioned using this geometry, see the schematic Fig. R4(a).
Fig. R4: (a) Schematic of the geometry under consideration, for comparison with our submission. A z-oriented point dipole (λ = 1550 nm) is placed in proximity of a gold nanotip, which tapers up from 1 nm to 15 nm over a distance of 1 μm. Ps refers to the Poynting vector magnitude integrated over a 1 nm circle surrounding the point source. Pff refers to the Poynting vector magnitude integrated in the far-field (integration radius 2μm). (b) Ps (blue) and Pff (green) as a function of z. (c) Pff/Ps as a function of z. (d) Field intensity when the point dipole is placed at z = 1 nm.
In this case, the behavior is remarkably different from that of the nanocylinder shown earlier, in two ways. Firstly, it is evident that although there is indeed a power enhancement in the near field, this is comparable to the increase in the far field, with this ratio staying approximately constant (Pff/Ps ≈ 0.5) for distances z < 50 nm, all the way down to the 1 nm distance considered in our submission [Fig. R4(b) and R4(c)]. Secondly, from the field intensity profile [Fig. R4(d)] it can be seen that a significant amount of energy is transferred along the tip to the thicker side [Fig. R4(d)] via the SR-SPP, which in turn will couple to the waveguide, as is the case discussed in our submission.
As a result, although Ohmic losses do play a part for the strip geometry considered here, this is less than that appearing for that of nanoparticles [see also, for example, P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007).]
We have added the following sentence to address this issue (page 16, end of Section 3.2)::
Finally, we have observed that quenching of the point dipole as a result of Ohmic losses in proximity to the gold nanotip under consideration is significantly less than that typically observed, e.g., in nanocylinders or nanospheres [47]; this, combined with the efficient excitation of the SR-SPP mode which couples to the dielectric waveguide, yields the comparably large collection efficiencies observed.
We have thus added Reference [47]:
[47] P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007).
R3.2: Throughout the manuscript, I would appreciate a more quantitative approach regarding the presentation of the material. To just name one example, Fig. 7 claims to show a Poynting-vector distribution. I do not see how a vectorial quantity should be displayed in an intensity plot. Furthermore, all colorbars should carry appropriate units, unless they show dimensionless quantities.
We have addressed this issue, by referring to either the (normalized) z-component of the Poynting vector, or the (normalized) Poynting vector magnitude.
We take the opportunity to thank the reviewers once again for their constructive comments and suggestions, which have helped us to substantially improve the quality of our manuscript. Having responded to their queries in detail, we look forward to your response.
Best regards,
Dr. Alessandro Tuniz
Alessandro Tuniz 