We sent a paper to a third journal and appear to have had the same reviewer again! The review appears below. Is it the same person?
The manuscript contains a confusing and irrelevant approach to estimate maximal values that second and third order dipolar polarizabilities can attain. The authors also claim that this approach can be exploited to find nonlinear materials with optimal values for these coefficients without specifying structural, chemical or other related material characteristics: the Holy Grail in the quest of nonlinear optical materials.
The approach is an extension of previous ones with vaguely similar ingredients and claims that appeared in a series of publications essentially by the same group and are extensively and exclusively referred in the ms . For a change this time the approach is disguised with “cartoons” representing “quantum graphs” (QG) and “star motifs” that can be stressed and bent to any purpose with adjustable assumptions and parameters to meet the authors wishful claims. These QG bear little, if any, relation to chemical structural characteristics of the material as the usual quantum chemical approaches do and are far more complicated to estimate and guide the search for nonlinear materials .
In a way their approach is a disguised, unphysical and complicated version of a qualitative “assessment” of the nonlinear polarizabilities/susceptibilities based on an expansion of the induced el-dipole/polarization in terms of the parameter (E/Eat) where E is the el-field of the light and Eat is an average atomic(roughly the ionization field) or cohesive el-field of the atom (molecule)/solid. This qualitative approach served to qualitatively justify the use and range of the perturbation approach in powers of E and to also get a rough estimate of the susceptibilities in the form of ?(n+1) = 1/(Eat)n; although the estimates were order of magnitude off some trends were plausibly accounted. A short account of this approach is given in any respectable book on nonlinear optics (see for instance introductory chapter in Y.R. Shen, The Principles of Nonlinear Optics, John Wiley). The present authors in a cavalier manner make no reference to this approach and proceed with their complicated and useless to any purpose approach .
I shall accordingly not comment any longer on the inconsistencies of their approach and the irrelevance of their quantum graphs for conceiving nonlinear materials with optimal values for the second and third order coefficients. In fact the whole discussion in the ms proceeds with ill defined terminology and unsubstantiated vague statements. I do not recommend acceptance of the present ms for publication in JOURNAL XXX.