Period-Doubling Route to Chaos in Photorefractive Two-Wave Mixing
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper "Period Doubling route to chaos in Photorefractive Two Wave Mixing" contains a numerical study of the dynamical behaviour of a photorefractive two wave mixing process when the material is subjected to an oscillatory external field. The simulations show that the intensity of the dynamically diffracted beam displays chaotic behaviour when the proper conditions are met.
The paper is, in my opinion, interesting and the obtained results are essentially correct. There are however some important points that need to be addressed in order for the treatment to be consistent with literature and not confuse the reader:
Fig. 1: It would be useful to indicate the direction of the externally applied field. Also it is important to mention the crystallographic directions and the polarizations of the two writing beams since the material parameters are strongly dependent on these details.
Eq. 3: The authors choose LiNbO3 (LN) as model system to perform their calculations. However it is well known that LN is a photogalvanic material, i.e. under illumination it spontaneously produces a current J_PG. This corresponds to an equivalent electric field E_PG that in general must be considered in eq. (3). All this is explained in ref. [7] (eq. 3.21, which corresponds to eq. 3 here). Furthermore, the E_PG field is strongly dependent from the experimental configuration (crystal axes orientation and beam polarizations), which is one reason for which it is important to describe those details. Eq. 3 in this form holds for purely diffusive materials (i.e. without a strong photogalvanic effect) such as e.g. BaTiO3. Please correct the equation or change material.
Line 141: the sentence "‘EM’ is the electric field that moves an electron a distance of ‘K/2pi’ during its lifetime" is obviously wrong. It should be: (K/2pi)^-1 or something like that (K has the dimensions of a length ^-1).
In eq. 3 the symbol E_q is used, but in the text below the symbol E_Q is used instead.
Table 1: it would be useful to indicate here also the value of the different "material" fields (E_q, E_M etc. ) so that the reader can get an idea of how strong is the AC field E_0 with respect to them.
Line 204: again the authors speak of a "simple diffusion" case, but as I explained before, this does not apply to LiNbO3, at least in general.
Line 243: the sentence "This bifurcation diagram is unique and is distinct from other bifurcation patterns commonly observed in nonlinear dynamical systems." seems too vague to me and should be better circumstanciated e.g. with a citation or clarifying in which sense the observed patterns are "distinct" from others.
Other minor remarks:
line 230 Fig 5 --> Fig. 6
figure 3: use the same label as in the text to indicate the equations e.g. Eq 2.3 should be Eq. (3).
line 245: Add a reference for non-experts in the field of chaotic systems.
line 269: there is a typo: perturb the a system
line 270: constant sinusoidal applied electric field: I suggest to revise the sentence (either the field is "constant" either it is "sinusoidal" ).
ref. 21 and ref. 22 are identical.
Comments on the Quality of English Language
The level of the English text is good.
Author Response
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Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsComments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsIn this manuscript Saju et al. numerically investigated a method to generate nonlinear dynamic signal by using a photorefractive device and applying an ac electric field across it. The authors numerically solved two coupled equations describing this system, and found unstable output behavior when the ac field strength is large. I can recommend its publication but I found some improvements are needed.
1. Why are new frequency components observed in Fig. 4 and 5? What do those frequencies correspond to?
2. I expect that with chaotic behaviors as the authors reported, the exact way of the numerical simulations, i.e., the size of the time/space steps, would affect the results a lot. How did the authors make sure that their numerical simulations converge, i.e., the same dynamics would be obtained if a smaller time/space step is used?
Author Response
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Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsEven though this is a minor aspect, I encourage the authors to write in the text what is the polarization of the wiriting beams, as I suggested in the previous draft, i.e. in lines (92 - 95) it is not explained whether the beams are polarized perpendicular to the scattering plane (i.e. along y, s-polarization) or within the scatterign plane (i.e. p-polarization). That would provide the reader with a clearer understanding of the experimental arrangement considered.
I also recommend to state somewhere that the two writing beams are considered as plane waves, so that intensity can be considered as uniform and wavefront are planes. Notice that this assumption is often assumed in theoretical modelling but rarely realized in experiments.
Apart from those minor corrections, the quality of the paper has been improved and in my opinion can be considered for publication.
Author Response
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