Effect of Surface Nonlinearity Distribution on Second Harmonic Generation under Tightly Focused Beams
Round 1
Reviewer 1 Report
Authors considered the problem of SHG for tightly focused optical beams (z~optical wavelength). In this case a component of the incident field polarization has a component along z. This makes chi(2)zzz component relevant in overall SHG. Also, SHG driven by lateral tensor components (e.g. chi(2)xzx) have been treated for the case of edge in the beam's foci. Both problems are important with regard to their applications in photonics waveguides, poled glass structures and material interfaces. Authors have treated similar problems in their recent publication (JOSA B 2022). I'm in favor of publishing the manuscript with the following comments/issues that need to be addressed
1) authors claim in the abstract that they considered the SHG problem "for an arbitrary distribution" of chi(2) in the lateral (x-y) direction. In fact, only a straight edge (step function) distribution has been considered.
2) How the edge is defined apart from the illustration of Fig 1? Is there any possible charge accumulations at the boundary of chi(2)=0 and not equal to 0. How that will change the results?.
3) What is the assumed /calculated beam's spot-size for NA=0.9 focusing?
4) At tight focusing conditions one expects the complex diffraction pattern and the foci. Authors assume (?) that the beam still have a Gaussian distribution at foci. What are the limits of validity of this approach?
5) How effects of the beam's diffraction will affect the results?
6) How does the SHG signal (radial components) build up in z- direction?
7) English needs improvements in quite a few areas for better reading and understanding.
8) Some minor improvements and changes are recommended. For example, chi(2) (i.e. with the superscript (2)) should be kept all across the manuscript and the drawings/schematics... as this is a commonly accepted representation for the nonlinearity. The same applies to the nonlinear polarization P(2)xzx, etc (i.e. (2) superscript and xzx is a subscript). Also, positive and negative D values should be clearly identified in the text and/or captions
Fig2,3 , etc legends. What do author mean by "Maximum in xz-plane", etc
Need to be explained in captions and or/text
Author Response
The authors thank the Reviewers for the kind response regarding our manuscript and for valuable comments and suggestions. In the attached file, we answer all the queries in details and outline the changes made in the manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This typoscript provide the account of a purely theoretical study of the effect of tight focussing and surface nonlinearity distribution on the second-order NLO response of the surface.
The main issue with this work is that for this work on nano- or microstructured materials, the electric quadrupolar contribution to the second-order nonlinearity is not considered.
The introduction to this work is not clear. The last sentence of the first paragraph is not clear. The most fundamental requirement of SHG is non-centrosymmetry (not ”central symmetry”, line 23), either from the material itself, or from the combination with a gradient of the electric field over the nanostructured material.
This theoretical work should have better connection with experiments, either directly by showing experimental results on physically realised surface nonlinearity distributions that have been modelled, or the other way around for experimental mappings of surface nonlinearities that have been reported.
A case in point is that the authors mention that the chi(zzz) component is dominant in many structures based on isotropic materials. This should be exemplified to make this work more relevant.
Author Response
The authors thank the Reviewers for the kind response regarding our manuscript and for valuable comments and suggestions. In the attached file, we answer all the queries in details and outline the changes made in the manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Authors have introduced number of changes that satisfactorily address issues and questions raised in my review.
Reviewer 2 Report
All is fine for me now, thank you very much.
