Propagation Property of an Astigmatic sin–Gaussian Beam in a Strongly Nonlocal Nonlinear Media
Round 1
Reviewer 1 Report
I read the manuscript applsci-390706 "Propagation property of an astigmatic sin–Gaussian beam in a strongly nonlocal nonlinear media" by K. Zhu et al. The manuscript deals with vortex beams of the type sine-Gaussian bean. Such topics was already treated by other papers cited by the manuscript. The authors stressed the effect of the astigmatic behaviors of the beams on propagation. Such topics is new in the panorama of the published papers and might deserve publication.
However my doubts are more at the basis, and in particular on the possibility that a sin-Gaussian beam might be solution of the nonlinear problem in strongly nonlocal nonlinear media. Such problem was already treated in ref. 15 which was already published. Thus, I must accept such decision even if I do not feel that this approach is indeed correct.
Author Response
However my doubts are more at the basis, and in particular on the possibility that a sin-Gaussian beam might be solution of the nonlinear problem in strongly nonlocal nonlinear media. Such problem was already treated in ref. 15 which was already published. Thus, I must accept such decision even if I do not feel that this approach is indeed correct.
Response: Firstly, it is well known that the propagation of optical beams through free space or medium is conveniently and accurately analyzed based on the basic law and the standard expression. For example, the propagation of a beam in free space or GRIN medium is determined with the standard generalized Collins formula (with different A, B, C and D parameters). In fact, a great number of studies on the propagation of optical beams in SNNM (seeing most of Refs. [4] – [28] in our manuscript) have used the same formula given by Snyder and Mitchell (Ref. [1]) as done in our paper.
Secondly, it should be pointed out that the work in Ref. [15] cited by our paper only investigated one-dimensional cosh-Gaussian beam propagation in SNNM. In practice, although sin(sinh)-Gaussian beam and cos(cosh)-Gaussian beam belong the same sinusoidal-Gaussian beam (Refs. [29] and [30]), there is clear difference between these two kind beams. For instance, our performed studies (Refs. [35] – [37]) demonstrated that only a sin(sinh)-Gaussian beam can convert into vortex beams with doughnut-shaped pattern under proper conditions but a cos(cosh)-Gaussian beam cannot do.
In summary, as done in most of cited Refs. [4] – [28], we use the standard method to investigate the propagation properties of an astigmatic sin-Gaussian beam in SNNM and find some interesting results, particularly involving that such a sin-Gaussian beam with two-lobe pattern can convert into a vortex beam with perfect doughnut-shaped pattern under proper conditions. Therefore, we almost rewrite the abstract in the revised manuscript. And in the end of the revised manuscript we point out that such transformations of beam patterns can be realized experimentally using a nematic liquid crystal or a lead glass. In addition, we add a reference [40] in the revised manuscript.
Reviewer 2 Report
Authors consider propagation of sine-Gaussian beam in parabolic medium. They claim they discuss the Snyder-Mitchell highly nonlocal solitons which are equivalent (to some extent) propagation of beam in linear system with parabolic refractive index distribution. There have been a number of papers devoted to this subject. As the problem is linear the whole system can be treated using ABCD transfer matrix which for parabolic medium is well known. Authors consider particular type of beam with phase dislocation. The results presented are not surprising since the propagation is periodic. Hence I do not see here enough novelty to warrant publication.
What is really missing here is the comparison with exact nonlinear and nonlocal model. Only then one can make some definite statement about evolution of nonlocal solitons. Otherwise it is just an exercise in ABCD beam evolution.
I cannot support publication of this work.
Author Response
Point 1: The results presented are not surprising since the propagation is periodic. Hence I do not see here enough novelty to warrant publication.
Response 1: Firstly, the topic is interesting and has received a large considerable of attention in recent years because the strongly nonlocal nonlinear media (SNNM) possesses a wide array of potential applications. The theoretical treatment on the medium is first introduced by Snyder and Mitchell in 1997 (Ref.1), where the derived standard propagation formula which is just used in our paper and in most of those references (Refs.4-28) cited by our paper determines the equivalent relation between describing SNNM and GRadient INdex (GRIN) medium. The properties of the material is first experimentally verified with nematic liquid crystals in 2002 (Ref.2) and with lead glass in 2005 (Ref.40), respectively. In particular, in the latter work the stable vortex ring solitons is also first experimentally observed.
Secondly, the propagation properties through various media of optical vortex beams have also received a great amount of attention in the past years. In particular, how to prepare optical vortex beams has always been a challenging task, and various schemes to produce optical vortex beams have been developed, yet. In this paper we investigate the propagation of an astigmatic sin-Gaussian beam in SNNM and reveal such a beam can convert into a vortex beam with perfect doughnut-shaped configuration under appropriate conditions. This is very interesting and proposes another way to generate optical vortices using an astigmatic sin-Gaussian beam with two-lobe pattern.
Thirdly, in this paper it is obtained the parameter conditions to realize the conversion of an astigmatic sin-Gaussian beam with two-lobe pattern into a vortex beam with perfect doughnut-shaped configuration. Since the stable vortex ring soliton propagation in SNNM has been reported to be experimentally realized, the result obtained in this paper can also be achieved using such media, which is pointed out in the end of this revised manuscript.
Point 2: What is really missing here is the comparison with exact nonlinear and nonlocal model. Only then one can make some definite statement about evolution of nonlocal solitons. Otherwise it is just an exercise in ABCD beam evolution.
Response 2: In nonlinear optics, nonlocality means that the refractive index of a material at a particular point is not determined solely by the wave intensity at that point (as in local media), but also depends on the wave intensity in its neighborhood. The nonlocal nonlinearity exists in many systems, such as photorefractive crystals, nematic liquid crystals, lead glasses, atomic vapors, Bose–Einstein condensates, etc. If the characteristic width of the material response function is much larger than the beam width, these media are called the strongly nonlocal nonlinear media (SNNM). So far some properties of strongly nonlocal solitons have been observed in SNNM such as nematic liquid crystals (Ref. [2] in our paper) and lead glasses (Ref. [40] in our paper).
In nonlinear optics the dynamics of optical solitons are governed by the well-known nonlinear Schrödinger equation which has been studied extensively in the past several decades. Before 1997, researchers almost focus on the optical solitons in local nonlinear media whose refractive index at a particular point is only related to the beam intensity at that point. By reason of the complexity of the shape-variant beams i.e. solitons or breathers, there are relatively few investigations on such beams in nonlocal media.
In 1997, Snyder and Mitchell (Ref. [1] in our paper) developed the well-known Snyder–Mitchell model today in which the nonlinear Schrödinger equation is linearized in SNNM and greatly simplified the investigation on the soliton evolution and beam propagation in such media. Since then, the propagation of optical beam in SNNM have attracted much attention, because of the discovery of many new novel nonlocal solitons.
To be specific, in the Snyder–Mitchell model the nonlinear Schrödinger equation describing the beam propagation in SNNM is simplified to the equation describing optical beam propagation through a GRIN medium. Then, the description of the beam propagation in SNNM can be also transformed into the generalized Collins integral formula with the ABCD matrix, which is a standard method just done in our manuscript and most of Ref. [4] – [28] cited in our paper.
Therefore, in the SNNM the simplified description used in our paper and in the cited paper (Refs. [4] – [28]) of our paper is equivalent to those in true non-locality nonlinear propagation model. And it is possible to realize the predicted conversion of a sin-Gaussian beam with two-lobe pattern into a vortex beam with perfect doughnut-shaped pattern under proper conditions using nematic liquid crystals and lead glasses.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The paper entitled "Propagation property of an astigmatic sin-Gaussian beam in a strongly nonlocal nonlinear media" by Kaicheng Zhu, Jie Zhu, Qin Su, and Huiqin Tang investigates the propagation of astigmatic sin-Gaussian beams in strongly nonlocal nonlinear media (SNNM). The method they propose is an intriguing means of realizing a doughnut-shaped beam with vortex, which could be of interest for optical trapping applications. The paper is generally well-written and is acceptable for publication to Applied Sciences.
Author Response
Point: The paper entitled "Propagation property of an astigmatic sin-Gaussian beam in a strongly nonlocal nonlinear media" by Kaicheng Zhu, Jie Zhu, Qin Su, and Huiqin Tang investigates the propagation of astigmatic sin-Gaussian beams in strongly nonlocal nonlinear media (SNNM). The method they propose is an intriguing means of realizing a doughnut-shaped beam with vortex, which could be of interest for optical trapping applications. The paper is generally well-written and is acceptable for publication to Applied Sciences.
Response: Thank you very much for the affirmation to our work. As done in most of cited Refs. [4] – [28], we use the standard method to investigate the propagation properties of an astigmatic sin-Gaussian beam in SNNM and find some interesting results particularly involving that such a beam with two-lobe pattern can convert into a vortex beam with perfect doughnut-shaped pattern under proper conditions. Therefore, we almost rewrite the abstract in the revised manuscript. And in the end of the revised manuscript we point out that such transformations of beam patterns can be realized experimentally using a nematic liquid crystal or a lead glass. In addition, we add a reference [40] in the revised manuscript.
Round 2
Reviewer 2 Report
In their response authors avoided answering my criticism. The fact that the linear version of nonlinear equation has been widely used does not mean its results can be accepted at the phase value. In fact, since the Snyder's theory is approximation it definitely breaks down at certain point. That's why I asked authors to contrast their results with numerical solutions of the full nonlocal model.
Authors chose not to address this point.
I cannot support publication of this paper.
Author Response
Because the nonlocal nolnlinear Schrodinger equation governing the evolution dynamics of optical beam propagating in nonlocal nonlinear medium remains mathematically complicated and directly to solve it is difficult, to obtain the exact solution of such an equation the numerical simulations is used. In SNNM the evolution of optical beam can be described by Snyder and Mitchell model and the analytical solution of the evolution equation can be obtained. It has been found [seeing Refs.12, 16 and 18 of our original manuscript] that the analytical solutions obtained from Snyder and Mitchell model and the numerical simulations based on the nonlocal nonlinear Schrodinger equation are in good agreement in the case of strong nonlocality. More importantly, the relation between optical beams propagating in SNNM, in free space, in quadratic- index media and through optical fractional Fourier transform systems has also been determined [seeing Refs. 40, 41 added in the revised manuscript].
