In the past, I have complained about reviewers who have evaluated my papers. However, it is a time-consuming job with almost no rewards, so I do appreciate their efforts. It is a service that we are all expected to provide. Given the time others have spent on my papers, I feel obligated to return the favor.
The most rewarding reviews are those from which I learn. I spent this morning reviewing a paper by some very distinguished scientists in my field. While I admit to the possibility that I may be wrong, I believe that there are serious issues with their paper, which will require attention before it is suitable for publication.
As usual, one activity leads my mind jumping around to other thoughts. This paper is an example of one in a series that is trying to simultaneously correct errors in the literature while introducing new science. This got me thinking again about the curse of information overload.
I am concerned that modern-day science, with the huge number of venues available for disseminating research results, is producing too much information along with lots of junk. The signal to noise levels are dropping while the whole system is bursting at the seems. People are becoming more specialized and less aware of other work. Since researchers are being judged on numbers of publications and citations, they overload existing top journals with so many papers that editors often cut good papers based on arbitrary guidelines. More second-tier journals are popping up to meet the growing demands by authors.
It's getting difficult for me to find useful information in the literature. For example, when searching electronically using very specific keywords, I get too many irrelevant hits that take forever to sort. It is also frustrating to have done what I believe to be great work in the past, only for it to be ignored for 20 years. Even more annoying is seeing the same identical topic of my research appearing many years later in Nature or Physical Review Letters with no citations to my papers. It is even more irksome when the modern work is but a subset of my original research, yet gets lots of recognition.
Sometimes, I send these modern-day authors reprints of my older papers. Some will respond apologetically pleading ignorance of my research, then continue not to cite my work. Others ignore my emails. These are indicators of a system that is not serving its purpose in producing research that serves society.
My review reminded me of the past era of more responsibility in publishing. Perhaps I view the past with unfounded fondness. However, I can atest to the fact that the authors of the manuscript that I have just reviewed are interested in the seeking truth. I therefore feel confident that they will carefully consider my comments and will only move forward with a revised manuscript if they are certain that they can make a real contribution to the field.
Below, I include a copy of my review for all to read. I, of course, will not reveal the identity of the authors, nor the journal to which this paper has been submitted. I take the risk of being exposed as the reviewer, but, I am sure that they will have already guessed my identity based on the flavor of my review; and, I will not deny being the reviewer if asked. Having gotten this off my chest, I need to get back to writing a proposal and grading homework. Perhaps I can then squeeze in a few moments to think about physics, and achieve the bliss that accompanies such thoughts.
And now, finally, the review:
The authors do some combinatorial wizardry to determine the coefficients of the various orders of the nonlinear birefringence. I am not willing to check all of the math, but from what I have checked, I trust that this is done correctly. However, I have a serious concern that may invalidate the approach, as I describe below.
The fundamental property of a material is its nonlinear susceptibility, not the nonlinear birefringence. The nonlinear susceptibility is what governs the physics of light/light interactions while the nonlinear birefringence is the quantity measured. They are related through the constitutive relationship D = epsilon E = E + 4 pi P. In the process of relating the two, one takes a square root of a power series in the field with the susceptibilities as coefficients. The crux of what I believe to be the fallacy of this paper is that n_m is related only to chi^(n+1). In the process of doing the expansion of the square root, one gets cross terms that are products of various lower-orders of the nonlinear susceptibilities that coincidentally may look like expressions that one sees in cascading calculations. The authors have in effect only expanded the square root to the first term. I believe that if the calculations are done properly, then it may be impossible to define unique constants of proportionality. However, under certain approximations, it may be able to define unique constants in the spirit of the authors' original intention.
A second problem along these lines is the neglect of the imaginary parts of the susceptibility. While experiments are off-resonance, there is always a small imaginary part. The cross-terms that I mention above can include products of imaginary parts that give a real response. Since it is possible that effects due to the imaginary part may get large for higher-order susceptibilities, they also need to be considered in the calculation. The fact that in practice, higher-order susceptibilities are by necessity more resonantly enhanced is a problem with applying this theory to real experiments at ultra-high intensities, and should be mentioned.
Nonlinear dichroism can also lead to polarization rotation, a common way of measuring the nonlinear birefringence. This contribution might also be large in practical experiments. While a good experimentalist would take this into account, I am concerned that a blind application of your results could lead to the unintended consequence of more junk in the literature. Thus, if not accounted for specifically, I would suggest adding at least a cautionary note.
I believe that the above issue needs to be carefully addressed before the manuscript is reconsidered for publication.
As a more minor point, In the introduction, the authors mention that the proportionality constant depends on the number of eigenmodes. I usually associate this factor with the number of degenerate frequencies. Is it true that if the frequencies are the same in a pump-probe geometry one gets the factor of 2/3? I thought that if the prorogation directions are different in the non-collinear polarization geometry, the effect shows up in the tensor properties of the susceptibility. That is, if the polarizations are different, then one is probing that particular component of the nonlinear susceptibility tensor. In any case, the meaning of eigenmode needs to be clarified or the sentence needs to be reworded. The use of the expression "eigenmode" in the rest of the paper may also need to be reconsidered.
I find the issue of cross terms to be a major one. If the authors choose to argue that the results hold in some limiting cases, that might diminish the relevance of the paper in loss of generality. If the calculation includes the terms that I believe to be missing, the coefficients will no longer be well defined. In either case, I believe that this paper may need major revision before it is suitable for publication. If I am wrong in my assessment, then the paper may be suitable for publication after minor revisions. In this scenario, it would be useful if the authors provided a more detailed explanation of the relationship between the nonlinear birefringence and the nonlinear susceptibility.