Redirecting Incident Light with Mie Resonance-Based Coatings

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript entitled Redirecting incident light with Mie resonance-based coatings demonstrates the enhanced absorption of Ge nanoparticle coated SiO2 substrate due to scattering of Ge nanoparticles. The authors succeeded in providing sufficient background on the study. But I do have several comments on the manuscript:

1. On line 121-122, the author claim that the particles are spherical or hemispherical, while they did not provide SEM images from an oblique angle. The author may want to provide more information on how they determine the shape of the nanoparticle. 

2.  The authors should clarify what objective lens they use to collect data for Fig 3, 4 and 5.

3. Following the question on the objective lens, as the authors claim that the difference of absorption in Fig.6 comes from the nonuniformity of the nanoparticles, the author may consider to acquire data from different regions on the sample and take average to eliminate the effects from nonuniformity. Considering the wavelength of interest and the NA, the focus spot after objective lens might only contain several nanoparticles.

4. I do not quite follow the description in Fig7, where the authors said '33% of the surface area'. Does that mean only 33% of the quartz substrate is coated with 95 nm Ge film? Is this film Intact with no pores in it? Or is it another choice to compare with a 31nm Ge film covering the whole substrate?

5. The author should elaborate on how they calculate the absorption from the lateral radiated energy in figure 8.

Comments on the Quality of English Language

The last sentence in the caption of Fig 1 is a little bit confusing. The author may correct that. Expect for that, I did not detect issue.

Author Response

Dear Reviewer,

Thank you very much for reviewing our manuscript.

 Comments and Suggestions for Authors

The manuscript entitled Redirecting incident light with Mie resonance-based coatings demonstrates the enhanced absorption of Ge nanoparticle coated SiO2 substrate due to scattering of Ge nanoparticles. The authors succeeded in providing sufficient background on the study. But I do have several comments on the manuscript:

1. On line 121-122, the author claim that the particles are spherical or hemispherical, while they did not provide SEM images from an oblique angle. The author may want to provide more information on how they determine the shape of the nanoparticle. 

Previously, the process of Ge particle formation on a silicon substrate covered with a thin SiO₂ film was studied. The obtained there SEM images showed the shape of the Ge particles. The formation of Ge particles on a quartz substrate occurred in a similar way, with the difference that the atomic smoothness of the quartz surface was worse than the SiO₂ film surface, on which the shape of the particles was close to spherical or hemispherical. On a quartz substrate, some Ge particles had some deviation from these shapes. Such explanations were added to the manuscript.

It can be noted that the fused quartz substrate is a good dielectric. At a grazing angle of incidence, we were unable to obtain a sufficient number of high-quality SEM images suitable for publication.

2. The authors should clarify what objective lens they use to collect data for Fig 3, 4 and 5.

Since the dependence on the aperture angle in the studied angle range turned out to be weak, the parameters of the lens at which the spectra were measured in Figs 3, 4 and 5 are given only in the Experimental section: “The spectra presented in the figures were measured using an objective with N.A. = 0.3, except for the figure showing the dependence of the spectra on the aperture angle.”

3. Following the question on the objective lens, as the authors claim that the difference of absorption in Fig.6 comes from the nonuniformity of the nanoparticles, the author may consider to acquire data from different regions on the sample and take average to eliminate the effects from nonuniformity. Considering the wavelength of interest and the NA, the focus spot after objective lens might only contain several nanoparticles.

The scattering in the reflection and transmittance values measured from different surface areas is less than 3%. Taking into account this small difference, we do not present spectra obtained as averaged over different areas, but use the most characteristic ones. We agree that, in the case of high magnification objectives, it is possible to obtain spectra from areas with a small number of particles. In this case the difference in the spectra from different areas could be greater. The purpose of this study was to obtain general, characteristic dependencies. The study of dependences on differences in particle morphology in local areas may be of independent interest.

4. I do not quite follow the description in Fig7, where the authors said '33% of the surface area'. Does that mean only 33% of the quartz substrate is coated with 95 nm Ge film? Is this film Intact with no pores in it? Or is it another choice to compare with a 31nm Ge film covering the whole substrate?

Yes, only 33% of the quartz substrate is covered with a 95 nm thick Ge film. The data for continuous Ge film with a thickness of 95 nm were used. This Ge film thickness corresponds to the average thickness (height) of Ge particles, and the amount of Ge in this 33% of the 95 nm film approximately correspond to the amount of Ge in particles obtained from a 31 nm Ge film.

5. The author should elaborate on how they calculate the absorption from the lateral radiated energy in figure 8.

During 3D FDTD modeling, the structure is illuminated by the plane wave which is cropped by the rectangular area that should to include all particles. The simulation area in X and Y coordinates is twice as large to observe the total scattering field. The simulation area in Z diminutions are chosen from the condition that FDTD monitors, that measure transmitting (T) and reflection (R) power, collect the power flow within the scattering angle determined by the numerical aperture N.A.=0.65. Thus, the simulated transmission, reflection and absorption spectra (1-R-T) are corresponded to relative measuring data. Besides, the numerical simulation makes possible to obtain also the fraction of radiation in lateral direction (see Figure 8) that is determined by the absorption spectra minus the internal absorption in Ge particles, which is numerically determined during the simulation. It must be mention that this lateral fraction of radiation is well corresponds to direct numerical measuring of total side scattering by multiple power monitors placed on X and Y boundaries of simulation area.

Comments on the Quality of English Language

The last sentence in the caption of Fig 1 is a little bit confusing. The author may correct that. Expect for that, I did not detect issue.

Corrected.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Report on Manuscript ID: photonics-2664665: Redirecting incident light with Mie resonance-based coatings, by A.A. Shklyaev et. al.

The authors fabricate Ge particles coatings on quartz glass substrates via solid-state dewetting. They determine absorption spectra from these films and show that the substrates coated with Ge particles absorb much stronger than substrates coated with Ge films. They also show that the scattered radiation is predominantly directed at glancing angles to the substrate surface. The find that the lateral propagation of scattered radiation is the result of destructive interference, which suppresses both reflected and transmitted radiation. These coatings increase the scattering of incident EM radiation due to its interference with the magnetic and electric Mie resonance modes excited in the Ge particles, the scattered radiation is broadband distributed due to the wide size distribution of Ge particles.

The manuscript is interesting but requires some elaboration before it may be ready for publication.

My commentaries:

1)      The most important observation that I have, is related to their numerical simulation of the expected absorption produced by a random array of hemispherical droplets-like Ge nanostructures formed in the dewetting process, their result consisting in the absorption curve in Fig 8b, indeed looks similar to that of the experimental results, but only at a first glance. Once closer attention is paid one notices nontrivial differences: i) the absolute values of the absorption coefficient maximum around and above 400 nm are > 0.8 vs 0.66 from the experiment; ii) More importantly: the wavelength region before the absorption curve starts to decay monotonically extends up to 900 nm from the model vs 630 nm from the experiment. This discrepancy is too large and deserves some explanation and one wonders if the simulation might have not been amenable to change some of its input parameter in order to improve the result in comparison with experiment. iii) this last observation reflects something I perceive as a shortcoming of the manuscript: it lacks an adequate description of the input parameters and their possible effect on the results of their simulation, for instance: do they use the actual particle size distribution as presented for the 31 nm Ge film in Fig. 2c? In Fig. 8a I perceive a neat array in ordered files of nanoparticles, this may not be right as the actual distribution of the Ge NP is clearly random in the 4 pictures in Fig. 1, what value of epsilon and mu (the electric and magnetic permittivity’s) they use, etc.

2)      The plots of the base areas, Fig 2a and 2b; require some extra explanation as they don’t look consistent with the results of size distributions. How is it possible to obtain such large number of Ge nanoparticles NP with very small base areas, when the four SEM images in Fig 1 indicate that they are all very flattened structures and hence, one expects that if few particles have smaller diameters also the number of NP with small contact areas should be correspondingly very few of them. How was this base area measured? The 10 degrees image 1d does not reveal or helps to know how this was done.

3)      Some minor details: i) I suggest in Fig 1, the T of preparation of the NP films should be indicated, ii) line 137, I suppose it should be read Fig. 2c,d; iii) Line 153, Figure 3 caption the thickness 115 should be replaced by 95 nm, according to both Figures 3a and 3b.

4)      The Englis is Ok

Author Response

Dear Reviewer,

Thank you very much for reviewing our manuscript.

Начало формы

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper investigated subwavelength-size Ge antireflection coating.

1.  The reviewer has the fundamental doubt if the absorption is
attributed to Mie resonance because there is no direct evidence shown in
the paper.

2.  To show the evidence of Mie resonance, the authors should perfume
the numerical calculation such as FDTD to show the Mie resonance modes.

3.  Please show the reflectance, transmittance, and absorption of the
quartz glass without Ge. It is difficult to evaluate the effect of Ge
without the reference.

4 . Subwavelength coating is well known method, it is not very clear the
novelty of the proposed method. Please clarify the difference from the
previous studies.

5. It is not very clary why Ge was chosen. There are many low-const
materials for antireflection coating. Please discuss the motivation.

Comments on the Quality of English Language

The authors should use porfessional English editing service.

Author Response

Dear Reviewer,

Thank you very much for reviewing our manuscript.

Comments and Suggestions for Authors

The paper investigated subwavelength-size Ge antireflection coating.

1. The reviewer has the fundamental doubt if the absorption is attributed to Mie resonance because there is no direct evidence shown in the paper.

The Kerker conditions are known, according to which both reflected and transmitted radiation can be suppressed due to interference between the incident radiation and the fields of magnetic and electrical resonance modes in dielectric particles. There are many studies in which this is confirmed theoretically and experimentally, references to some of them are given in the manuscript.

2. 
   To show the evidence of Mie resonance, the authors should perfume the numerical calculation such as FDTD to show the Mie resonance modes.

Such FDTD calculations were carried out in our previous articles, as well as in articles by other authors. Taking this into account, this paper presents calculation data using the FDTD method only to determine the scattering fraction in the lateral direction. Below are some additional details about our FDTD calculations.

We examine numerically the dipole Mie resonances in single Ge particles on fused quartz substrates. For this case, a single Ge particle was exposed to a plane wave polarized along the Z axis to measure transmission, reflection, and absorption spectra for different particle sizes. Note, that the absorption amplitude is relatively small, since the particle diameters (100-250 nm) are significantly smaller than the lateral size of the exposed area (1260 nm) of the particle location. We consider the peak in the absorption spectra (see Fig. S1) to be the position of the strongest interference with the fields of the dipole Mie resonances. This assumption is proved by measurements of the electric and magnetic field distributions at this peak wavelength. For example, Figure S2 presents the field distribution for d = 200 nm at optical wavelength 800 nm. It can be noted that the structure under study contains an array of Ge particles with randomly varying size and position. Thus, the absorption peaks of resonance excitations of an array of different Ge particles become broad and depend on the particle size.

Figure S1. 3D FDTD simulation results for the total absorption (A = 1-R-T) of a single Ge particle of diameter d, marked with the corresponding spectrum.

Figure S2. Results of 3D-FDTD modeling of the distributions of magnetic (a,c) and electric (b,d) fields for a single Ge particle in various coss-sections (Y=0 and Z=0.0779, i.e. half the height of the particle). A particle with d = 200 nm is illuminated by a plane wave with a wavelength of 800 nm.

3. Please show the reflectance, transmittance, and absorption of the quartz glass without Ge. It is difficult to evaluate the effect of Ge without the reference.

Data on the reflectance and transmittance of fused quartz are known and added to the manuscript. They are in good agreement with the characteristics of our quartz substrates. The absorption of a 0.5 mm thick quartz substrate is about 2% and is equally included in the absorption of samples coated with both Ge particles and Ge films, and therefore does not affect our estimate of the amount of scattered light propagating at small angles to the substrate surface.

4. Subwavelength coating is well known method, it is not very clear the novelty of the proposed method. Please clarify the difference from the previous studies.

Continuous dielectric films of subwavelength thickness practically do not change the propagation direction of incident radiation. Coatings of subwavelength dielectric particles can suppress both reflected and transmitted radiation and, therefore, change the direction of scattered radiation. The spatial distribution of radiation under Mie resonance conditions was previously studied only for individual particles, and for a coating in the form of an array of dielectric particles, such studies, as far as we know, have not been carried out. This work is the first to obtain data on the direction of radiation propagation after scattering on such coatings.

5. 
   It is not very clary why Ge was chosen. There are many low-const materials for antireflection coating. Please discuss the motivation.

It is fundamentally important that the material used has a high refractive index. Among the single-component materials widely used in conventional Si technology, Si and Ge have this property, and Ge has a higher refractive index than Si. A discussion of this aspect has been added to the manuscript.

Comments on the Quality of English Language

The authors should use porfessional English editing service.

The English grammar of the manuscript has been checked by a professional editor.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Thank you very much for reviewing our manuscript.

Comments and Suggestions for Authors

peer-review-32641200.v2.pdf

1) SEM images of fig. 1 show that particles have spheroidal forms for thicknesses below

31 nm and start to be composed of bridges for higher thicknesses. Inverted image b) and d) to preserve the ascending order. Values of thicknesses of this analysis does not

correspond to thus of the optical measurements. Authors must gives some comments

that only the 2 small thicknesses have been studies.

The thicknesses (H_Ge) of the initial Ge films are presented in Fig. 1. When the dewetting phenomenon occurs, Ge forms particles, the projection of which onto the substrate occupy about 33% (depending on H_Ge) of the substrate surface. Accordingly, the average particle height can be estimated as H_Ge /0.33 ≥ 3H_Ge, taking into account that the particles have spheroidal forms. Then the average particle diameter (d) can be estimated to be from 4 to 5 H_Ge. For the initial Ge film with a thickness of H_Ge = 31 nm, we obtain d ≈4.5 × 31 ≈ 140 nm. This value corresponds to the lateral size distribution of particles shown in Fig. 2c.

The thickness of the original films is given in the manuscript, since other characteristics of the Ge particle coatings are estimates.

2) On fig. 2, inset must be add to explain particle base area and lateral particle size. If the particles are spherical, the area see on the MEB or measure with imageJ is not necessary thus on the substrate.

You are right. X axis in the Fig. 2a,b has been renamed: instead of “Particle base area” it is now written “Particle projection area”. We could not measure the size of the particle base, but only measured the size of the particle projection onto the substrate using SEM images obtained at the normal electron beam incidence angle (Fig. 1a,b,c). To obtain the particle size distributions, images of larger surface areas than those shown in Fig. 1 were used. Additional comments on this issue are provided in the revised manuscript.

3) With the reflection and transmission spectra of the Ge thin layer of fig. 3, it is possible

to fit the real and imaginary part of the Ge refractive index versus the wavelength and

compared to the values of bulk material of the literature. In the paper, authors does not

give values of the refractive indexes used for modelling. Legend of the figure is wrong

40, 75 and 95 nm and not 40, 75 and 115 nm.

We studied the reflection and transmission spectra of arrays of Ge particles of the same size in detail experimentally and using simulation in [Shkl SR 2022]. The real and imaginary parts of the Ge refractive index are shown in this article for Ge as graphs, data for which were taken from [E.D. Palik, Handbook of Optical Constants of Solids, Academic Press, 1998, pp. 1–999.]. This comment has been added to the manuscript. Including these data in this manuscript would be a repetition.

 The caption to Fig. 3 has been corrected: 115 nm was replaced by 95 nm.

4) Comparison of theoretical spectrum calculate with effective medium model must be

done on fig. 4 to highlight and prove the role of the scattered part or coupling of the

dipole and quadripole modes in the anti-reflection coating behavior of the different

samples.

Our several previous articles were specifically devoted to comparing the results of simulation and experimental data. For this purpose, in particular, arrays of particles of the same size were used and dependencies on their size were obtained. It was shown at what wavelengths dipole and quadrupole resonances occur. The revised manuscript contains a discussion of these aspects based on the literature and our previous publications. The particle coatings used in this work contain a wide particle size distribution and therefore the dependence on particle size is smoothed. At the same time, as can be seen in Fig. 4, the expected strong dependence on size is observed. We carried out additional calculations of the particle size dependence, which, for example, are given below. We did not include data from such calculations, since they do not provide anything significantly new compared to the data in a large number of previously published articles on this topic.

We examine numerically the dipole Mie resonances in single Ge particles on fused quartz substrates. For this case, a single Ge particle was exposed to a plane wave polarized along the Z axis to measure transmission, reflection, and absorption spectra for different particle sizes. Note, that the absorption amplitude is relatively small, since the particle diameters (100-250 nm) are significantly smaller than the lateral size of the exposed area (1260 nm) of the particle location. We consider the peak in the absorption spectra (see Fig. S1) to be the position of the strongest interference with the fields of the dipole Mie resonances. This assumption is proved by measurements of the electric and magnetic field distributions at this peak wavelength. For example, Figure S2 presents the field distribution for d = 200 nm at optical wavelength 800 nm. It can be noted that the structure under study contains an array of Ge particles with randomly varying size and position. Thus, the absorption peaks of resonance excitations of an array of different Ge particles become broad and depend on the particle size.

Figure S1. 3D FDTD simulation results for the total absorption (A = 1-R-T) of a single Ge particle of diameter d, marked with the corresponding spectrum.

Figure S2. Results of 3D-FDTD modeling of the distributions of magnetic (a,c) and electric (b,d) fields for a single Ge particle in various coss-sections (Y=0 and Z=0.0779, i.e. half the height of the particle). A particle with d = 200 nm is illuminated by a plane wave with a wavelength of 800 nm.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

The manuscript titled by “Redirecting incident light with Mie resonance-based coatings” reports an optical study of subwavelength Ge particles on fused silica 68 substrates by exploiting the solid-state dewetting phenomenon. The authors have measured the reflection (R) and transmission (T) spectra, the absorption spectra (A = 1-R-T) of Ge particles on quartz glass substrates. The substrates coated at RT with Ge films of various thicknesses were prepared. The solid-state dewetting process was then carried out, by annealing in the vacuum chamber to a temperature of about 500°C for 1 hour by the radiation from a heater located from the rear side of the substrate.  The sample surface morphology was studied with a scanning electron microscope (SEM). The reflection (R) and transmission (T) spectra at a normal light incidence were measured with the microscope-spectrophotometer. The results show that these coatings increase the scattering of incident EM radiation due to its interference with the magnetic and electric Mie resonance modes excited in the particles.

The experiments are well planned and carried out. The results are interesting. However, the presentation of the results is poor. The conclusion is qualitative. The data is not analyzed quantitively. Instead, the numerical simulation seems to be informative. But there is no analysis on the thickness or size dependent.

The authors should revise the manuscript to improve the presentation.

1. The distributions of Ge particles (in Fig. 2) as a function of thickness should be given for all the specimen studied. Also, the aspect ratio should be provided. 

2. Absorption spectra of coatings consisting of Ge particles are given by two equations, A=1-R-T and A=(1-R-T)/(1-R). Which one is the better?

3. To confirm the data in Fig. 5, the numerical simulation should be carried out to the particles with different diameter.

4. What is the surface morphology of the Ge films with thickness of 40, 75 and 115 nm? The 115nm should be 95 nm in Fig. 3 caption? What is the meanings of 33% in Fig. 7 legend?

Comments on the Quality of English Language

Some sentences should be revised. For example,

1. in Fig. 1 caption, "The SEM images in (a) - (c) were taken at the e-beam incident angle of 90 and about 10 degrees to the substrate surfaces in (a)-(c) and (d), respectively."

2. In abstract, "which show that the substrates coated 12 with Ge particles absorb much stronger than the substrates with Ge films."

There are more. Extensive editing of English language required

Author Response

Dear Reviewer,

Thank you very much for reviewing our manuscript.

Comments and Suggestions for Authors

The manuscript titled by “Redirecting incident light with Mie resonance-based coatings” reports an optical study of subwavelength Ge particles on fused silica 68 substrates by exploiting the solid-state dewetting phenomenon. The authors have measured the reflection (R) and transmission (T) spectra, the absorption spectra (A = 1-R-T) of Ge particles on quartz glass substrates. The substrates coated at RT with Ge films of various thicknesses were prepared. The solid-state dewetting process was then carried out, by annealing in the vacuum chamber to a temperature of about 500°C for 1 hour by the radiation from a heater located from the rear side of the substrate.  The sample surface morphology was studied with a scanning electron microscope (SEM). The reflection (R) and transmission (T) spectra at a normal light incidence were measured with the microscope-spectrophotometer. The results show that these coatings increase the scattering of incident EM radiation due to its interference with the magnetic and electric Mie resonance modes excited in the particles.

The experiments are well planned and carried out. The results are interesting. However, the presentation of the results is poor. The conclusion is qualitative. The data is not analyzed quantitively. Instead, the numerical simulation seems to be informative. But there is no analysis on the thickness or size dependent.

The authors should revise the manuscript to improve the presentation.

1. The distributions of Ge particles (in Fig. 2) as a function of thickness should be given for all the specimen studied. Also, the aspect ratio should be provided. 

Detailed data on the Ge particle distributions formed as a result of the solid-state dewetting phenomenon on SiO₂ layers on Si substrates are presented in [42]. Similar data are observed on a fused quartz (SiO₂) substrate. We do not present these distributions to avoid repetition, since they differ only slightly from previously published data. A discussion of similarities and differences with previously published data has been added to the revised manuscript. This also applies to the aspect ratio, the values of which were obtained in the previous articles [36,42]. For Ge particles on quartz substrates, we were unable to obtain a sufficient number of high-quality SEM images due to the fact that fused quartz is a good dielectric.

2. Absorption spectra of coatings consisting of Ge particles are given by two equations, A=1-R-T and A=(1-R-T)/(1-R). Which one is the better?

Absorption is usually defined formally as A = 1-R-T. In this case, absorption also includes that part of the radiation that was reflected from the sample surface. To exclude this part of the radiation that was reflected, one must use A = (1-R-T)/(1-R) = 1-T/(1-R). In this case, all the incident radiation reaches the substrate, so the value A determined in this way characterizes only absorption by the substrate. In our case, the definition of absorption as A=(1-R-T)/(1-R) more correctly shows the absorption caused precisely by the Ge particle coatings.

3. To confirm the data in Fig. 5, the numerical simulation should be carried out to the particles with different diameter.

Previously, we studied in detail experimentally and using simulation the dependence on particle size and the distance between them [26]. For the current study, we performed preliminary calculations for coatings of Ge particles of different sizes. An example of the result of these calculations is presented in Fig. S3b, which shows good agreement with the experimental data (Fig. S3a and Fig. 5 in the manuscript). However, we did not include the data from these and other similar calculations in the manuscript, since they did not contain anything significantly new in comparison with the known literature and our previous publications. We carried out more careful calculations for the case presented in Fig. 8. Calculations of coatings of particles with different sizes do not provide anything essentially new compared to what presented in the manuscript. A discussion of the simulation results and their agreement with experimental data regarding particle size has been added in the revised manuscript.

Figure S3. Absorption spectra of quartz glass substrates coated with Ge particles. (a) Experimental data for Ge particles obtained from initial Ge films with thicknesses 15, 21, 31, 40 and 50 nm marked in the figure for each spectrum; (b) numerical simulation by 3D FDTD method for the similar structures with randomly distributed Ge particles of different diameter d.

4. What is the surface morphology of the Ge films with thickness of 40, 75 and 115 nm? The 115nm should be 95 nm in Fig. 3 caption? What is the meanings of 33% in Fig. 7 legend?

Yes, there is a mistake in the caption to the Fig. 3: instead of 115 nm it should be 95 nm, as indicated in the Fig. 3. The Ge films with thicknesses of 40, 75 and 95 nm were grown on quartz substrates at room temperature and are continuous atomically smooth.

This means that only 33% of the quartz substrate is covered by a 95 nm thick Ge film. The rest of the quartz surface remains bare. This amount of 95 nm thick continuous Ge film was used because it corresponds to the Ge amount in the Ge particle coating obtained from a 31 nm thick Ge film. It is assumed that Ge material in these two coatings should absorb approximately an equal parts of the incident radiation.

Comments on the Quality of English Language

Some sentences should be revised. For example,

1. in Fig. 1 caption, "The SEM images in (a) - (c) were taken at the e-beam incident angle of 90 and about 10 degrees to the substrate surfaces in (a)-(c) and (d), respectively."

Corrected.

2. In abstract, "which show that the substrates coated 12 with Ge particles absorb much stronger than the substrates with Ge films."

Corrected.

There are more. Extensive editing of English language required

The English grammar of the manuscript has been checked by a professional editor.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors addressed my questions properly, but I do have a further question, and I will recommend a minor revision:

on the 4th line on page 5, the author said: "However, they are more reflective than coatings of Ge particles on SiO2 films [42]." But isn't this paragraph and the previous sentence talking about the Ge particle coated substrate? The authors may want to address this. 

Also, there are several paragraphs with extra spaces at the beginning. The authors may want to double check their format. 

Author Response

Thank you very much for reviewing our manuscript.

Comments and Suggestions for Authors

The authors addressed my questions properly, but I do have a further question, and I will recommend a minor revision:

on the 4th line on page 5, the author said: "However, they are more reflective than coatings of Ge particles on SiO2 films [42]." But isn't this paragraph and the previous sentence talking about the Ge particle coated substrate? The authors may want to address this.

Here we made a comparison with previously obtained data. We have clarified this sentence: “ … than Ge particle coatings obtained on the oxidized Si substrates [42]”.

Also, there are several paragraphs with extra spaces at the beginning. The authors may want to double check their format. 

Corrected

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. I cannot find Figures. S1, S2, or "Data on the reflectance and transmittance of fused quartz". Therefore, I cannot judge this revised manuscirpt.

2. The authors seem to condier anti-reflecting coating among Mie resonance. However, there are many anti-reflecting coating using easier fabrivation such as nano porous materials, subwavelength gratings and so on. In this point of view, Ge leads high cost. The authos should consider thier studied compared to other methods.

Author Response

Thank you very much for reviewing our manuscript.

Comments and Suggestions for Authors

1. I cannot find Figures. S1, S2, or "Data on the reflectance and transmittance of fused quartz". Therefore, I cannot judge this revised manuscirpt.

Figures S1 and S2 are inserted.

Data on the reflectance and transmittance of fused quartz have been added in the manuscript: “Despite the lower reflection of Ge particle coatings than that of Ge films, it remains higher compared to the reflection of the bare quartz surface, which was about 4% and corresponded to [43].” and “…the reduction in the transmission due to the absorption by the quartz substrate itself is insignificant, since after excluding the contribution of reflection from the quartz surface for our samples it is about 2% and is consistent with [44].”.

Comments and Suggestions for Authors, first round:

The paper investigated subwavelength-size Ge antireflection coating.

1. The reviewer has the fundamental doubt if the absorption is attributed to Mie resonance because there is no direct evidence shown in the paper.

The Kerker conditions are known, according to which both reflected and transmitted radiation can be suppressed due to interference between the incident radiation and the fields of magnetic and electrical resonance modes in dielectric particles. There are many studies in which this is confirmed theoretically and experimentally, references to some of them are given in the manuscript.

2. 
   To show the evidence of Mie resonance, the authors should perfume the numerical calculation such as FDTD to show the Mie resonance modes.

Such FDTD calculations were carried out in our previous articles, as well as in articles by other authors. Taking this into account, this paper presents calculation data using the FDTD method only to determine the scattering fraction in the lateral direction. Below are some additional details about our FDTD calculations.

We examine numerically the dipole Mie resonances in single Ge particles on fused quartz substrates. For this case, a single Ge particle was exposed to a plane wave polarized along the Z axis to measure transmission, reflection, and absorption spectra for different particle sizes. Note, that the absorption amplitude is relatively small, since the particle diameters (100-250 nm) are significantly smaller than the lateral size of the exposed area (1260 nm) of the particle location. We consider the peak in the absorption spectra (see Fig. S1) to be the position of the strongest interference with the fields of the dipole Mie resonances. This assumption is proved by measurements of the electric and magnetic field distributions at this peak wavelength. For example, Figure S2 presents the field distribution for d = 200 nm at optical wavelength 800 nm. It can be noted that the structure under study contains an array of Ge particles with randomly varying size and position. Thus, the absorption peaks of resonance excitations of an array of different Ge particles become broad and depend on the particle size.

Figure S1. 3D FDTD simulation results for the total absorption (A = 1-R-T) of a single Ge particle of diameter d, marked with the corresponding spectrum.

Figure S2. Results of 3D-FDTD modeling of the distributions of magnetic (a,c) and electric (b,d) fields for a single Ge particle in various coss-sections (Y=0 and Z=0.0779, i.e. half the height of the particle). A particle with d = 200 nm is illuminated by a plane wave with a wavelength of 800 nm.

3. Please show the reflectance, transmittance, and absorption of the quartz glass without Ge. It is difficult to evaluate the effect of Ge without the reference.

Data on the reflectance and transmittance of fused quartz are known and added to the manuscript. They are in good agreement with the characteristics of our quartz substrates. The absorption of a 0.5 mm thick quartz substrate is about 2% and is equally included in the absorption of samples coated with both Ge particles and Ge films, and therefore does not affect our estimate of the amount of scattered light propagating at small angles to the substrate surface.

4. Subwavelength coating is well known method, it is not very clear the novelty of the proposed method. Please clarify the difference from the previous studies.

Continuous dielectric films of subwavelength thickness practically do not change the propagation direction of incident radiation. Coatings of subwavelength dielectric particles can suppress both reflected and transmitted radiation and, therefore, change the direction of scattered radiation. The spatial distribution of radiation under Mie resonance conditions was previously studied only for individual particles, and for a coating in the form of an array of dielectric particles, such studies, as far as we know, have not been carried out. This work is the first to obtain data on the direction of radiation propagation after scattering on such coatings.

5. It is not very clary why Ge was chosen. There are many low-const materials for antireflection coating. Please discuss the motivation.

It is fundamentally important that the material used has a high refractive index. Among the single-component materials widely used in conventional Si technology, Si and Ge have this property, and Ge has a higher refractive index than Si. A discussion of this aspect has been added to the manuscript.

Comments on the Quality of English Language

The authors should use porfessional English editing service.

The English grammar of the manuscript has been checked by a professional editor.

 From second round:

2. The authors seem to condier anti-reflecting coating among Mie resonance. However, there are many anti-reflecting coating using easier fabrivation such as nano porous materials, subwavelength gratings and so on. In this point of view, Ge leads high cost. The authos should consider thier studied compared to other methods.

Yes, of course, many different coatings are known that have better antireflection properties compared to coatings based on Mie resonances in dielectric particles. However, these coatings either practically do not change the propagation direction of transmitted radiation, or (textured surfaces with irregularities larger than the wavelength) direct it at different angles to the substrate surface. To significantly change the direction of transmitted radiation, its interference with the fields of resonance modes excited in dielectric particle coatings is required. A detailed discussion of relevant aspects is provided in the Introduction and Discussion sections of the manuscript. At the same time, no data have been published in the literature on estimating the fraction of scattered radiation propagating along the substrate surface layers. This is the first time such an estimate has been carried out in our work.

The Ge particles coatings are not optimal. As written in the manuscript, it can be improved: “ … has been observed [32]. In this case, a larger part of the incident radiation than here propagated at small angles to the substrate surface due to denser Ge particle arrays in the lattices. This part of scattered radiation can also be increased by using an additional protective antireflection coating, such as a Si₃N₄ film [1], which further reduces the reflection, as well as by utilizing a particle material that absorbs less than Ge and has a higher refractive index.”

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

All of the comments have been adressed in this version of the paper.

Author Response

Thank you very much for reviewing our manuscript.

Reviewer 5 Report

Comments and Suggestions for Authors

I am satisfied the authors' response. However, the English is still poor. The paper can only be published after the authors have their manuscript edited by a native-English speaking language editor who is also a scientific expert.

Comments on the Quality of English Language

The English is still poor. The authors should have their manuscript edited by a native-English speaking language editor who is also a scientific expert.

For example, the sentence "... show that substrates coated with Ge particles absorb much stronger than substrates coated with continuous Ge films" in abstract, should be "... show that substrates coated with Ge particles absorb much more strongly than those coated with continuous Ge films."

There are more issues in whole paper, the authors should look for professional English editing services.

Author Response

Thank you very much for reviewing our manuscript.

Comments and Suggestions for Authors

I am satisfied the authors' response. However, the English is still poor. The paper can only be published after the authors have their manuscript edited by a native-English speaking language editor who is also a scientific expert.

Comments on the Quality of English Language

The English is still poor. The authors should have their manuscript edited by a native-English speaking language editor who is also a scientific expert.

For example, the sentence "... show that substrates coated with Ge particles absorb much stronger than substrates coated with continuous Ge films" in abstract, should be "... show that substrates coated with Ge particles absorb much more strongly than those coated with continuous Ge films.

There are more issues in whole paper, the authors should look for professional English editing services.

In addition to having your manuscript checked for English grammar by a professional editor, we tried to improve the English ourselves and with the help of our colleagues. Corrections made in the manuscript are marked in yellow.

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

1. Please add the Figures S1 and S2 in the manuscript not in the
supplementary because there are no evidence to support your results.

2. In the FDTD calculation, the calculation model was symmetric shape,
but actual shape is strongly asymmetric. Therefore, the calculated
results are not direct evidence.

Author Response

Thank you for your recommendations.

1. Please add the Figures S1 and S2 in the manuscript not in the
   supplementary because there are no evidence to support your results.
   
   2. In the FDTD calculation, the calculation model was symmetric shape,
   but actual shape is strongly asymmetric. Therefore, the calculated
   results are not direct evidence.

When the particles are not distributed randomly over the surface, but in the centers of the lattice, this is not a factor that significantly affects the propagation direction of the scattered light. In the previous articles [24,26] we carried out calculations for the coatings with ordered and disordered particles. There, good agreement between calculations and experiment was demonstrated and the conditions for observing surface lattice resonance were determined for the case of particle lattices [32].

The novelty of this work lies in the study of the direction of radiation propagation after its interaction with particles in coatings. The coatings contained particles of different shapes and sizes. In this case, surface lattice resonance was not observed either in experiment or in calculations. The main goal of this work is to experimentally and computationally show (Fig. 8) that a significant part of the scattered radiation propagates at small angles to the substrate surface.

The manuscript describes in detail the similarities and differences between the real and model structures of the germanium particle coating. The model cannot take into account all the features in the shape and arrangement of particles, since they are formed in a self-organized manner under conditions of a not ideally smooth and uniform surface. In the model, particles are located at lattice sites. We also used other models of particle arrangement on a substrate, in which particles of different sizes were randomly located on the substrate. When forming such a coating, we were unable to get rid of the fact that in the coating formed in this way, some of the particles were located one another or touched neighboring ones. This structure, in our opinion, differed significantly from the experimentally studied one and was less adequate compared to the arrangement of particles at lattice sites.

The addition of Figure S1 to the manuscript is redundant, since its data is partially contained in Figure 8, and the fact that the spectra depend on particle size is an obvious result that we have shown in our previous publications, and is also known from dozens of other papers in the literature.

As for Figure S2, it only shows the field distribution that is typically observed during the excitation of Mie resonances. It doesn't contain anything new. Figures S1 and S2 are presented only to facilitate the work of the reviewer, so as not to review articles from the reference list.