Optical Angular Momentum Beam Generation Using Coherent Beam Combination

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review of the manuscript (photonics-3191725)

Optical Angular Momentum Beam Generation using Coherent Beam Combination

Przemyslaw Gontar, Lukasz Gorajek, Waldemar Zendzian and Jan Jabczyński

 

The manuscript considers a semi-analytical model based on the spectral method for solving the paraxial wave equation for forming OAM beams by manipulating the tilts and phases of coherent beams in a hexagonal lattice. The difference in the approach presented by the authors is that the phase is specified as a nonlinear spiral, in which the phase value of each emitter depends on the ordinal numbers (l, n) of the subbeams in the lattice (l is the ordinal number of the corona, n is the ordinal number of the subbeam in the corona). The intensity maps obtained in the calculations are characteristic of the distributions obtained as a result of coherent addition of beams with a spirally distributed phase in a hexagonal lattice and differ from the distributions of classical OAM beams. Verification of the orthogonality of the OAM-CBC amplitude profiles in the far field showed the possibility of using such beams for FSOC optical communication. The results presented in the work do not raise any doubts and correspond to the concepts of vortex beam generation in CBC coherent summation systems. The results presented are of interest to specialists and can be published.

However, questions arise about the correspondence of the obtained results to the declared research objectives.

1. Figure 1 shows the concept of OAM-CBC formation as a result of coherent addition of subaperture array beams with a nonlinear spiral phase distribution. On the other hand, formula (1) is used for calculation, in which the phase of each subbeam depends on the azimuthal angle and, therefore, the phases of all beams located on the same line from the center to the top of the hexagon should be the same and proportional to 2π/6, which does not correspond to the declared concept.

2. The authors indicate that a truncated Gaussian beam was used in the calculations as a "prototype" of the optical field. “We apply a truncated Gaussian beam as a ‘prototype’ optical field” (line 63), however, the presented results correspond to small losses due to beam truncation ε_tr=0.05 (line 100) and it is not clear how truncation will affect the results.

3. It is known that synthesized beams formed as a result of coherent addition of a hexagonal matrix of emitters can have a non-zero topological charge, but carry zero integral orbital angular momentum [See Aksenov, V.P.; Dudorov ,V.V.; Filimonov ,G.A.; Kolosov, V.V.; Venediktov, V.Yu. Vortex beams with zero orbital angular momentum and non-zero topological charge. Opt. Laser Tec. 2018, 104, 159, doi: 10.1016/j.optlastec.2018.02.022]. From this beam, it is possible to extract radiation carrying a non-zero OAM if we use an aperture that transmits only the near-axis region of the beam. In the work under consideration, the OAM value is not defined or used in any way. Therefore, it seems to me that the use of the term OAM in this context is not entirely correct, and it makes sense to use the term "topological charge of a vortex" beam.

 

 

 

Author Response

Comment No1.

Figure 1 shows the concept of OAM-CBC formation as a result of coherent addition of subaperture array beams with a nonlinear spiral phase distribution. On the other hand, formula (1) is used for calculation, in which the phase of each subbeam depends on the azimuthal angle and, therefore, the phases of all beams located on the same line from the center to the top of the hexagon should be the same and proportional to 2π/6, which does not correspond to the declared concept.

Response No1.

Indeed it is true, in each of six spokes of hexagonal matrix the phase difference between following points operation is 0 not m_OAM2p because of used here modulo (m_OAM2p) function;
Note, that a phase as a product of OAM number m_OAM and azimuth angle f_n,l in following  l – corona changes linearly from 0 for to approximately  m_OAMx2π for maximal n = 3*l, phases are linear functions with different slopes  n_OAM *2π/3l  decreasing in the following coronas. Evidently, it does not emulate directly the continuous surface of m_OAM -vortex. The phase jump of m_OAM2π between following coronas does not influence on the results of diffraction in far field
(exp(i m_OAM2p)=1), but indeed in Fig. 1 ( helix in near field) it is depicted continues helix (i.e. between last emitter of l- corona and 1.st emitter of corona (l+1) is not break. Thus I do not agree that our model and calculations do not correspond to declared concept. 

Note, the wavefront of each (n,l) emitter is tilted/skewed (and therefore does not crosses symmetry axis) according to formula (2) and it’s the only one reason of ‘nonlinearity’ of helix in far field in geometrical optics approximation (lower right insert in Fig. 1). In the near field the emitters centres are distributed near ‘uniformly’  according to rule of hexagon symmetry filling with circles.

Comments No 2.

The authors indicate that a truncated Gaussian beam was used in the calculations as a "prototype" of the optical field. “We apply a truncated Gaussian beam as a ‘prototype’ optical field” (line 63), however, the presented results correspond to small losses due to beam truncation ε_tr=0.05 (line 100) and it is not clear how truncation will affect the results.

Response No 2.

I do not want to enter in details of applied method it is explained in details in Ref [30,31]. Indeed we limited scope & volume of paper to only one case of truncation 5%, treating it as a preliminary report/communication, not full length paper. We have calculated several other truncation levels but do not decide to include it in that work mainly because of clarity of argument. For higher truncation levels the impact of higher diffraction orders would obscure the results, moreover because of practical reasons, the truncation /dissipation of 5% of power into case can be better accommodated and heat removed. I hope that in the next paper we will consider impact of all these effects.

Comment  No 3. 

It is known that synthesized beams formed as a result of coherent addition of a hexagonal matrix of emitters can have a non-zero topological charge, but carry zero integral orbital angular momentum [See Aksenov, V.P.; Dudorov ,V.V.; Filimonov ,G.A.; Kolosov, V.V.; Venediktov, V.Yu. Vortex beams with zero orbital angular momentum and non-zero topological charge. Opt. Laser Tec. 2018, 104, 159, doi: 10.1016/j.optlastec.2018.02.022]. From this beam, it is possible to extract radiation carrying a non-zero OAM if we use an aperture that transmits only the near-axis region of the beam. In the work under consideration, the OAM value is not defined or used in any way. Therefore, it seems to me that the use of the term OAM in this context is not entirely correct, and it makes sense to use the term "topological charge of a vortex" beam.

Response No 3.

After reading the above mentioned paper I partly agree with this argument. The authors of that paper found that it exists total Optical Angular Momentum (contrary to PIB >0)  value equal zero or even negative for a non-zero topological charge of vortex. Indeed we do not examined the Optical Angular Momentum of those beams but analysed properties CBC beams with non-zero Vortex Topological Charge defined by parameter m_OAM ≠ 0 calculating only irradiance distribution and PIB.  In our paper we have called the topological charge of vortex in the near field/ as an input parameter in calculation/ by m_OAM – Optical Angular Momentum number to be close to this special issue call, we treated it as a kind of acronym/nick name “OAM”. We are convinced that in our CBC-OAM beam in far field exists areas of non-zero OAM. We do not decide to change this notation, hoping that it does not lead to misunderstandings. But opinion of Reviewer is very interesting and we will try to examine it in the next work. The Reference of that paper doi: 10.1016/j.optlastec.2018.02.022 was included as Ref [28].

 

Reviewer 2 Report

Comments and Suggestions for Authors

All comments are in the Letter to the Authors.

Comments for author File: Comments.pdf

Author Response

Letter /comments 

Your paper is short (this is a positive feature!), includes small volume of data (negative feature), and small number of conclusions. I’m very sorry, but I can only evaluate the paper as of having average scientific value. At the same time I would like to highlight the following advantages of the text: the paper deals with a topic of current interest; as far as I can tell, the quality of English is very good; the text is quite short and easy to read.

I think that the positive characteristics of the paper outweigh its shortcomings and recommend it for publication in Photonics.

Response 

Thank You for your  kind and comprehensive letter and  comments. I have nothing to add and response

 

 

 

Reviewer 3 Report

Comments and Suggestions for Authors

Authors present the results of numerical calculations of the OAM beam generation by two methods. The methods itself are known, but the applicability of them for OAM generation is of some interest.

The quality of the numerical calculations are convincing and complete. The results show a moderate level of applicability of this method for real application, which by no means decreases the quality of work. 

I believe, that experimental results would bring the interest to this work on qualitatively higher level. Even though about numerical experiments only, the propagation of the generated beams and consideration of their application for e.g. communication system would add interest to this work.

Anyway, I believe the paper could be published in the presented form.

Author Response

Authors present the results of numerical calculations of the OAM beam generation by two methods. The methods itself are known, but the applicability of them for OAM generation is of some interest. The quality of the numerical calculations are convincing and complete. The results show a moderate level of applicability of this method for real application, which by no means decreases the quality of work. I believe, that experimental results would bring the interest to this work on qualitatively higher level. Even though about numerical experiments only, the propagation of the generated beams and consideration of their application for e.g. communication system would add interest to this work. Anyway, I believe the paper could be published in the presented form.

Response 

Thank You for positive opinion and acceptation.