Electromagnetic polarization-controlled perfect switching effect with high-refractive-index dimers and the beam-splitter configuration

Sub-wavelength particles made from high-index dielectrics, either individual or as ensembles, are ideal candidates for multifunctional elements in optical devices. Their directionality effects are traditionally analysed through forward and backward measurements, even if these directions are not convenient for in-plane scattering practical purposes. Here we present unambiguous experimental evidence in the microwave range that for a dimer of HRI spherical particles, a perfect switching effect is observed out of those directions as a consequence of the mutual particle electric/magnetic interaction. The binary state depends on the excitation polarization. Its analysis is performed through the linear polarization degree of scattered radiation at a detection direction perpendicular to the incident direction: the beam-splitter configuration. The scaling property of Maxwell's equations allows the generalization of our results to other frequency ranges and dimension scales, for instance, the visible and the nanometric scale.

In the "Supporting Information" text: 1. Page 17, lines 13 and 14, the statement "In the finite element method" is inaccurate, because the definition given in (67) is common practice in the antenna field to plot the so-called radiation patterns.
End of comments.
Reviewer #3 (Remarks to the Author): The authors expand previously reported work on scattering by a pair of high refractive index (HRI) dielectric structures with sub-wavelength size to directions normal to the input wave propagation. To the best of my knowledge the work is original and properly addresses prior literature.
The paper is well written and the contribution clearly presented. The work is well structured and the results supported by simulation, theoretical analysis and measurements on a fabricated prototype at microwave frequencies.
The application potential in building switching devices is highlighted and experimental results in microwave frequencies are presented, while the results are proposed to be general in application all the way to optical frequencies due to the scaling properties of Maxwell equations. 1) it is recommended to further comment on the challenges in implementing these structures at optical frequencies, a) in terms of fabrication and b) in terms of size and the effect of the presence of multiple pairs of HRI elements as it is unlikely that a single pair only can be fabircated in optical frequencies. how does this generalize into an array of hri elements? 2) some further detail on the measurement setup could be appreciated. how does the gain and directivity and polarization purity of the transmit and receive antennas affect the measurement. this is also related to the sensitivity of the system in terms of various parameters such as the angle of incidence of the incoming wave, and the system dimensions.
3) some quantitative results on the amount of scattered intensity relative to the input signal power should be included and how this can be controlled or optimized, as this has a direct effect on the application potential of the proposed structure as a beam splitter, ie what would be the loss associated with the device. 4) how does the input power affect the performance of the system? it is understood that this is a linear system but as the theoretical model includes only electric and magnetic dipole expressions, how would this be affected when higher order multipoles become significant. 5) although the presented results in figure 4 and 5 already hint on this, it would be interesting to further comment on the sensitivity of the system dimensions in order to observe the desired phenomenon.
1 Responses to Reviewers' comments:

Reviewer #1
The authors reported all-dielectric HRI dimer as new multifunctional elements for building optical switching devices. They used right angle scattering configuration rather than the widely used back and forward directions to realize optical switching. Although the physical mechanisms of magnetodielectric behavior in dimer have been investigated, the experimental characterization and the proposed "beam splitter" are interesting. Thus, I suggested reconsidering in Nature Communications after major revisions noted below.
(1) The title is a little bit confusing. Usually, only one sentence is allowed in title, so I recommend removing "THE BEAM-SPLITTER CONFIGURATION".
As the title should contain the key aspects of this research, we would like to ask for keeping the title as it is because this feature ("beam-splitter") is very important and makes our proposal different to other previous configurations based on either forward or backward conventional directions. Our configuration allows having two separated and controlled beams by using a single incident one. Also, Nature Communications allows for titles of maximum 15 words. Ours is 14. In any case, we are open to further suggestions.
(2) The authors discussed the disadvantage of using forward/backward scattering as "switching" in Introduction. In fact, the forward and backward scattering light can be easily collected using dark-field objective. More reasons should be given on why using this kind of side scattering (90 o ).
For configurations located on flat substrates for building optical devices, the 90º configuration is very attractive as compared to back/forward arrangements. For backward directions and taking into account our application purpose [see point 3) in response to referee's question #4], the necessity of introducing a beam-splitter (basically, this is the concept when dark-field microscopy is used) would complicate too much the device. For the forward direction, this is completely useless for practical purposes unless also, an additional element is added to avoid the incident beam which could mask the wanted signal. In summary, in these two specific directions, the use of additional elements (optical (beam-splitter) or not (mask or equivalent)) is necessary to play with the desired scattered radiation. Also, it is important to mention that the wanted effect is optimum at 90º as it is shown in the figure R1 below. "0" corresponds to forward direction and "180" to backward direction.
The blue line indicates the position of the switching frequency at q ≈ 0.77. A sentence has been added in the main text to clarify this point.

Figure R1: Spectral evolution of the ratio (in dB) between I s and I p with respect to the measurement angle
(3) The authors said "the proposed switching device show more advantages than the devices based on the directional scattering between forward and backward", but they didn't demonstrate the scattering light between any two directions is different. They only showed that the scattered intensity at only one direction can be null or maximum by changing the polarization of a single frequency excitation, which has nothing to do with directional scattering.
It is well known that the light scattered in two different directions will behave differently (see for example Ref 19 for some measurement results for a single HRI sphere as well as Figure R1 above where the intensities are plotted with respect to the detection angle).
The idea here is not to exploit two different detection directions, but instead to work with a single one and take advantage of the intensity variation in polarization. Among

4) It can be shown that the switching effect is for a HRI dielectric dimer and at the 90º
configuration it is "perfect" in the sense that a real "0" for the "off" position is possible.
Apart from these clarifications, we have made explicit reference to the suggested article in the introductory part of the manuscript. We believe that the corresponding comments have enriched the discussion about the differences (advantages/disadvantages) in either the backward or forward configurations with respect to the right-angle one proposed in our research. We want to thank this reviewer for this comment.
(5) The statement that "this switching effect is produced by the spectral evolution of one of the natural resonances of the isolated particle to an asymmetric shape resonance (Fanolike)" needs to be demonstrated. Where is the Fano line shape? Where are the broad mode and the narrow mode to produce Fano dip? All need to be marked in spectra.
We would like to thank this reviewer for these considerations.  Fig. 5, why the data are so fluctuant needs to be explained. Why measurements without any dimer (see Fig. 5c) also exhibit the "on" and "off" states?
To answer this question new measurements were made with attenuators to reduce the oscillations (due to resonances)..As the parabolic antennas are indeed designed to work in the 4-8 GHz range (i.e. 0.8<q<0.15) an attenuator between the antenna and the receiver reduces some of the mismatching drawbacks and thus the oscillations (see Fig 5bis).

3). So the behavior of the measured field at q = 0.8 without dimer is just a coincidence.
To help to have a better understanding of the behavior of our experiments we have plotted ( fig. 5ter) the same measurements than those presented in Figure5 but with horn antennas (as in Figure 2). In Figure 2, the results were presented with post-processing, here there are shown without any post-processing of the measured data as in Figure 5.

to prove that, if the signal is sent with a sufficient directivity (which should not be a real problem in optics), even without any special care (raw field measurements are presented), the switching effect related to the polarization states is of real practical interest with a single dimer
and is indeed directly measurable (7) The "Supplementary Information" referred in the manuscript should have serial number.
We are really sorry but we did not understand this comment.

Minor corrections follow below.
In the main text: 1. In Fig. 1, theta should be oriented taking as reference the positive axis z, not the negative one, as illustrated. This must be coherent with the orientation of theta shown in the polar plots of Fig. 3.

In page 8, lines 3 and 4, "are indicated" appears twice.
Done 3. In page 12, lines 4 and 5, it is 4a and 4b, not 4ac and 4bd. The paper is well written and the contribution clearly presented.
The work is well structured and the results supported by simulation, theoretical analysis and measurements on a fabricated prototype at microwave frequencies.
The application potential in building switching devices is highlighted and experimental results in microwave frequencies are presented, while the results are proposed to be general in application all the way to optical frequencies due to the scaling properties of Maxwell equations.

1) it is recommended to further comment on the challenges in implementing these structures at optical frequencies, a) in terms of fabrication and b) in terms of size and the effect of the presence of multiple pairs of HRI elements as it is unlikely that a single pair only can be fabricated in optical frequencies. How does this generalize into an array of HRI elements?
We thank this reviewer for this constructive comment. Although  2) Some further detail on the measurement setup could be appreciated. How does the gain and directivity and polarization purity of the transmit and receive antennas affect the measurement. This is also related to the sensitivity of the system in terms of various parameters such as the angle of incidence of the incoming wave, and the system dimensions.
Part of the elements to answer this question can be found in the answer given to Rev. 1 point (6). With the parabolas, the gain is high (the antenna provider is just indicating a "3dB aperture" equal to 15° at the switching frequency) and the switching effect can directly be measured ( fig 5, 5 bis). With the horn antennas the gain is rather low (about 12 dB at the switching frequency) and we needed a complex subtraction of the fields with and without the dimer to show the switching effect (Fig. 2, Fig. 5 ter). Concerning the polarization purity, both antennas cross polarization isolation is around 20 dB.
In summary a general answer is rather difficult to give but the less directive the source is, the further from the dimer the detector has to be (to avoid to be "blinded" by direct incoming wave). And last but not least, the further the receiver is from the dimer, the more sensitive it has to be, in order to allow separating the 0 and 1 states. Thus the best use of a dimer as a switching device is probably to be made with a rather directive source, which shouldn't be a real difficulty in optics. The sensitivity to the incidence angle and dimensions is numerically studied in the SI (and a 15λ scaling bar is represented on figures 5 to give an idea of the dimensions of the used experimental setup).
3) some quantitative results on the amount of scattered intensity relative to the input signal power should be included and how this can be controlled or optimized, as this has a direct effect on the application potential of the proposed structure as a beam splitter, ie what would be the loss associated with the device.
All the presented intensities are quantitative ones (apart from Figure 5 Figure 5), all the intensity scales are meaningful and directly show the level of measured signal that one can expect at 23λ from the dimer (at the switching frequency).

4) How does the input power affect the performance of the system? It is understood that
this is a linear system but as the theoretical model includes only electric and magnetic dipole expressions, how would this be affected when higher order multipoles become significant.
As the referee suggests we are only interested in linear phenomena because nonlinearity effects would be out of the scope of our research. At present, we have not enough information to judge how the input power would affect system performance. It would depend on the optical properties of the dimer constituents and of course, the input power.
Concerning the influence multiple higher orders than dipolar, new research challenges appear which are out of the goal of our contribution. We have started to analyze this influence and as a first step, I would recommend our recent publication already cited in ref. 19. figure 4 and 5 already hint on this, it would be interesting to further comment on the sensitivity of the system dimensions in order to observe the desired phenomenon.

5) Although the presented results in
As suggested, a sensitivity analysis has been included in the supplementary materials. We have changed the various geometrical parameters, in particular the angle of incidence (by tilting the spheres) as well as the detection angle and the parameters associated to the dimer itself. This study gives good indication that the desired phenomenon is quite stable with respect to all these parameters.