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@@ -47,13 +47,13 @@ On behalf of the authors,\\
 
 We are actually not very familiar with Mathematica GLMT Scripts, however, fast review of this code revealed a number of significant differences:
 \begin{itemize}
-\item As it is published at \verb+http://photonicsdesign.jimdo.com/software/+ it does not provide any appropriate license condition, particularly it is not clear, is it valid to distribute this code, to modify it (e.g. to put your own model parameters), to use it for academic or corporate research, etc.
+\item As it is published at \verb+http://photonicsdesign.jimdo.com/software/+ it does not provide any appropriate license condition, particularly it is not clear, is it valid to distribute this code, to modify it (e.g. to put your own model parameters), to use it for academic or corporate research, etc. Our code Scattnlay is distributed under GPL (version 3) --- a well-known permissive license for open source software. 
 \item You need to buy Mathematica license first to use this script.
 \item This script do not provide near-field evaluation inside the particle, at least all provided examples do not have it.
-\item It does not use Mathematica ability to do arbitrary precision for calculation of Mie coefficients for multilayer sphere. Actually it reference our previous paper in CPC, and uses the same evaluation of spherical functions via series with the same error due to $N_{\mathrm{stop}}$ selection. 
+\item It does not use Mathematica ability to do arbitrary precision for calculation of Mie coefficients for multilayer sphere. Actually GLMT Script itself references our previous paper in CPC, and uses the same evaluation of spherical functions via series with the same error due to $N_{\mathrm{stop}}$ selection. Equations needed to do the evaluation of the near-field distribution inside the multilayered spherical particle are provided in our present manuscript.
 \end{itemize}
 
-Finally, we should point out that the authors of Mathematica GLMT started using Scattnlay and, at least the initial versions of their scripts, were heavily based on our code. Indeed, even now most of their varibles use exactly the same names than Scattnlay. Hence, it is safe to say that Mathematica GLMT is a derivative work of our code, even if both projects have diverged over time. To the best of our knowledge the only code available which provide similar posibilities is MSTM by Mackowski and Mishchenko. However, it uses T-matrix approach (which is conisderably less efficient for the case of concentric spheres) to do the evaluation and has no usage license defined. We  had actually verified our code against MSTM results too, however, we do not include them to the manuscript due to abovementioned license restrictions.
+Finally, we should point out that the authors of Mathematica GLMT started using Scattnlay and, at least the initial versions of their scripts, were heavily based on our code. Indeed, even now most of their varibles use exactly the same names than Scattnlay. Hence, it is safe to say that Mathematica GLMT is a derivative work of our code, even if both projects have diverged over time. To the best of our knowledge the only code available which provide similar posibilities is MSTM by Mackowski and Mishchenko. However, it uses T-matrix approach (which is conisderably less efficient for the case of concentric spheres) to do the evaluation and has no usage license defined. We  had actually verified our code against MSTM results too, however, we do not include them to the manuscript due to abovementioned license restrictions of MSTM.
 
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@@ -61,8 +61,7 @@ Finally, we should point out that the authors of Mathematica GLMT started using
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-We do concern the speed of our implementation, however, this is not the main point of the manuscript. To stress the novelty we provide the following changes to the manuscript:
-
+We do concern the speed of our implementation, we have done an optimization of the previous code, which lead to more than a two fold speed-up. However, this is not the main point of the manuscript.  We would like to thank the reviewer for a useful comment, as it seems that our initial version of the manuscript do not stress the novelty enough. To do this we provide a number of changes in the manuscript:
 TODO - stress novelty in the abstract, manuscript, and in the conclusion: 
 1) We provide explicit expressions for Mie coefficients inside the sphere.
 2) We suggest to use Ricatti-Bessel functions for vector spherical harmonics evaluations and prove the correctness of this approach.
@@ -74,9 +73,11 @@ TODO - stress novelty in the abstract, manuscript, and in the conclusion:
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-We would like to thank the reviewer for finding, that just referencing our previous paper can lead to misunderstanding. We add to the manuscript after the corresponding reference ``reported recently [10]'' the following sentence `` using full-wave commercial 3D electromagnetic simulation software CST MWS[TODO add link to cst.com in references ]''
+We would like to thank the reviewer for finding, that just referencing our previous paper can lead to misunderstanding. In our last example we used near-field results obtained with full-wave commercial 3D electromagnetic simulation software CST MWS. Actually the lack of our code to provide near-field data for that project initiated development of the current version of Scattnlay.
+
+We add to the manuscript after the corresponding reference ``reported recently [10]'' the following sentence ``, where we obtained near-field distribution using full-wave commercial 3D electromagnetic simulation software CST MWS[TODO add link to cst.com in references ]'' 
 
-We had to restrict ourselfs to core-shell case due to lack of analytic software, which allow (including usage statements in the software license) to do the simulation of multilayered sphere. The multilayered case was verified against full-wave simulation done with finite-element method using CST MWS and finite-difference time-domain method using Lumerical FDTD.
+We had to restrict ourselves mostly to compare against core-shell cases due to the lack of analytic software, which allows (including usage statements in the software license) to do the simulation of multilayered sphere. We had to verify the multilayered case against full-wave simulation done with finite-element method using CST MWS and finite-difference time-domain method using Lumerical FDTD. After doing this we are pretty sure that our code provides correct results (at least for the tested range of input parameters). As it was stated in ``Restrictions'' line of ``Program description'' section large complex part of layers refractive index leads to convergence problems.  Note that usage of full-wave 3D simulation required 4-5 orders of magnitude more computational resources (time) to get e.g. total scattering cross-section with a comparable accuracy. 
 
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@@ -84,9 +85,9 @@ We had to restrict ourselfs to core-shell case due to lack of analytic software,
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-TODO we do not compare with published result in Fig.2, we have downloaded and run the referenced software - provide changed to the text.
+We do not compare with published result in Fig.2, we have downloaded and run the referenced software. All the results presented in Fig.2 were obtained by ourself. To compare the result obtained from our code (presented in Fig.2b) we used the BHFIELD code developed by Suzuki and Lee to get the field distribution presented in Fig. 2a. To make it more clear we provide the following change to the manuscript: instead of ``For this, we calculated electric and magnetic fields for the example provided with their computer code'' we write ``For this, we calculated electric and magnetic fields using the example provided with their computer code''  
 
-As for other figures, we do not have a permission to reprint figures from other journals, this way we can only provide referenced to them.
+As for other figures, we do not have a permission to reprint figures from several other journals (see the corresponding references) , this way we can only provide the text description and to reference them.
 
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@@ -94,48 +95,46 @@ As for other figures, we do not have a permission to reprint figures from other
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-We have checked each and every program listed at ``Mie type codes'' section off Scattport here http://www.scattport.org/index.php/light-scattering-software/mie-type-codes before starting the development of our code. While really the list of software is very large, most of listed codes re-implement Mie solution as it was published in classical book of Bohren and Huffman ``Absorption and Scattering of Light by Small Particles'' (usually referenced ad BHMIE) or re-implement MIEV0 code by Wiscombe.  The original approaches that we were able to find were referenced in the manuscript as [11-18,22,23]. Note, that most of this solutions to not provide the ability to evaluate field distribution inside the particle and only cover the case of one (bulk sphere) or two (core-shell) layers in the particle.
-
-We are totally agree with the reviewer, that it is a good idea to provide a GUI. However, adding GUI is a very time consuming task and we do not have any funding for this.  Actually, the code described in our previous publication has no GUI either, still that paper has more than 50 citations. So we should expect that this code and the manuscript are valuable and important even without GUI. In our first comment in this reply we have tried to cover the cases, when Mathematica usage is not beneficial. 
-
+We have checked each and every program listed at ``Mie type codes'' section (\href{http://www.scattport.org/index.php/light-scattering-software/mie-type-codes}{link}\footnote{http://www.scattport.org/index.php/light-scattering-software/mie-type-codes}) of Scattport before starting the development of our code (fall of 2014). While really the software list is very large, most of the listed codes re-implement Mie solution as it was published in classical book of Bohren and Huffman ``Absorption and Scattering of Light by Small Particles'' (usually referenced as BHMIE) or re-implement MIEV0 code by Wiscombe.  Few original approaches that we were able to find were referenced in the manuscript as [11-18,22,23]. Note, that most of this solutions to not provide the ability to evaluate field distribution inside the particle and do only cover the case of one (bulk sphere) or two (core-shell) layers in the particle.
 
+We are totally agree with the reviewer, that it is a good idea to provide a GUI. However, adding a GUI is a very time consuming task and we do not have any funding for this.  Actually, the code described in our previous publication has no GUI either, still that paper has more than 50 citations at the moment as it is listed in Scopus database. So we should expect that this code and the manuscript are valuable and important even without GUI. In our first comment in this reply we have tried to cover the cases, when Mathematica usage is not beneficial. As an intermediate solution we provide bindings to Python language, which are the part of the released code. It can provide good enough plotting (see figures 2,3, and 4 in the manuscript) via MatPlotLib module, Python syntax is about the same complexity as used by Mathematica or Matlab. However, Python can be used free of charge.
 
 \newpage
 \section{Reviewer \#2}
 
+First of all we would like to thank this reviewer for his work. We were really impressed with his detailed review and would like to add to the ``Acknowledgements'' section the following text ``All authors would like to thank two anonymous reviewers for their valuable comments.''
+
+
 \vspace{0.5em}
 \begin{tabular}[!H]{l|p{0.9\textwidth}}
 \quad & 
-1
-Introduction
-This reviewer approaches the manuscript and contributed code by Ladutenko
-et al (herinafter “the paper”, “the code” and “the authors” respectively)
-with background experience in electromagnetic theory and radar cross-sect-
-ion computation.
-\end{tabular}
+The paper does not make any claim to originality as far as the algorithm is
+concerned.
+\end{tabular} 
 \vspace{0.5em}
 
+COPY-PASTE from reviewer 1 answer: We would like to thank the reviewer for a useful comment, as it seems that our initial version of the manuscript do not stress the novelty enough. To do this we provide a number of changes in the manuscript:
+TODO - stress novelty in the abstract, manuscript, and in the conclusion: 
+1) We provide explicit expressions for Mie coefficients inside the sphere.
+2) We suggest to use Ricatti-Bessel functions for vector spherical harmonics evaluations and prove the correctness of this approach.
+3) We verify the provided approach comparing to other codes and full-wave 3D simulation.
+
 \vspace{0.5em}
 \begin{tabular}[!H]{l|p{0.9\textwidth}}
-\quad & 
-2
-General Comments
-The paper does not make any claim to originality as far as the algorithm is
-concerned. The authors claim is that the code is the first publicly-available
-implementation of a scattering code for a multi-layered sphere that includes
-near-field calculation. This reviewer has no knowledge that would contradict
-that claim. They also claim that use of Yang’s [1] algorithm yields a robust
-code that can handle “extreme” cases.
-The authors’ contribution is relevant to two long-established application
-areas in different wavelength ranges, radar cross-section prediction at mi-
-crowave frequencies and aerosol and grain scattering at optical and infra-red
-frequencies, as well as the new area of nanoparticles. The authors’ citation
-list does acknowledge some of this earlier work.
+\quad & The authors’ citation list does acknowledge some of this earlier work.
 The first recursive algorithm for the multi-layered sphere known to this
 reviewer was published by Wait [2] in 1963, although this work does not
 address the numerical issues tackled by the approach of Yang. The algorithm
 is described in a 1970 textbook [3].
-It is the personal experience of this reviewer that the long history of
+\end{tabular}
+\vspace{0.5em}
+
+We already provided Ref. 13 in the manuscript to the Wait paper. However, we found a small small typo (both in our list and in the reviewer comment). According to journal`s web-site Wait published his paper in 1962 \href{http://link.springer.com/article/10.1007/BF02923455}{http://link.springer.com/article/10.1007/BF02923455} )  
+TODO fix reference 12 Wait, J.R. Appl. sci. Res. (1962) 10: 441. doi:10.1007/BF02923455 
+
+\vspace{0.5em}
+\begin{tabular}[!H]{l|p{0.9\textwidth}}
+\quad &  	It is the personal experience of this reviewer that the long history of
 published work on sphere scattering has led to many layers of derivative
 1publications that have introduced and propagated mathematical and typo-
 graphical errors in sloppy work that has not been properly checked by its