Phase Dislocations in Hollow Core Waveguides

Round 1

Reviewer 1 Report

This manuscript that is titled with “Phase Dislocations in Hollow Core Waveguide” presents the theory of the phase feature of hollow-core waveguide modes at 3.39 mm wavelength. It is hard to understand in the detail because all the equations, symbols and drawing are not defined. 

I suggest some points to the author for the first improvement:

• What does the color mean on the graphs? It should be indicated on the graph, not on one sentence in the contents.
• What does a streamline mean at the detail? Is it a vector? Where is the direction? Does it involve the magnitude? Is the distribution density meaningful? Does “projection” mean “direction”?
• What does the coordinate axis, X, Y, Z, mean for the waveguide? Definition for all the parameters is required.
• Page 4, line 126: Why is the spatial factor Z a complex number?
• Page 4, line 121 and Page 5, line 142: Should they be consistent? I found they are different.
• Where is the contents to describe Fig. 2(a)?
• For the 2^nd section, the title is “Role of losses in vortex formation in hollow core waveguides”, but the contents do not discuss the “loss” value or parameter. Does the transverse Poynting vector mean the “loss”?
• Page 3, line 111: Why does the equation mean that?
• Page 3, line 112: Why does the equation mean that?
• Page line 113: Why does the equation mean that?
• Fig. 7: Characters of “μm” are not complete.

Author Response

1. In accordance with the wishes of the reviewer, color scales of the values of all quantities are shown on all figures.
2. The transverse component of the Poynting vector or  of the HE₁₁ mode is tangent to the streamlines shown in the figures. Since the energy of the core mode flows out, the mode energy moves from the waveguide axis outward along the spirals that are the streamlines of the transverse component of the Poynting vector.
3. For clarification, we have introduced a new Figure 1.
4. To denote the argument of the Bessel function, another letter q is introduced.
5. These are two different complex propagation constants β of the fundamental air core mode of a hollow core for a circular hole in an infinite dielectric and a hollow hexagon in an infinite dielectric.
6. Now, it is a figure 3a but the phrase referring to it remained the same as in the previous variant of the paper: “This means that the real and imaginary parts of the axial components of electric and magnetic fields simultaneously tend to zero and at  forming a vortex (Fig.3a).”
7. The imaginary part of the propagation constant of the hollow core mode is a parameter describing the losses of the waveguide according to the formula: Loss (dB/km) = (4e10*π*log₁₀(e)/λ)*β^Im. In our case, λ is constant.
8. All the equations on lines 111, 112, 113 are derived by decomposing the argument of the Bessel function describing the fields in the waveguide core into a Taylor series. A small parameter in this case is β^Im as stated in the text.

Author Response File: Author Response.docx

Reviewer 2 Report

The author performed theoretical research on interesting topic concerning hollow core waveguides. In specific, he was investigating the propagation of optical vortices in such fibers with either cylindrical or hexagonal symmetry.

The reviewer finds this article well prepared and written, with some typos and unclear figures.

The author uses acronimes without first explaining what they stand for, which might be confusing for a reader. An example can be found in the first paragraph of the introduction, where the author writes about ARROW mechanism. On the second page, the author writes about PCFs without explaining what they are.

The reviewer found few typos, with the most common being misspelling the "Poynting". This is frustrating, as the phrase Poynting vector is repeated many times in this manuscript. In the first paragraph, the author writes about Fabry-Pierrot resonators instead of Fabry-Perrot.

These are very minor mistakes and they do not disturb the reader too much.

The reviewer believes it would be strongly beneficial to the reader if the author draw a scheme presenting the coordinate system and display the radial and axial components of electric field, which he then refers to on page 3. Additionally, he writes a set of equations on page 3 and after that he states that r and phi refer to axes in cylindrical system. The reviewer believes it would improve the readability of the manuscript if the coordinate system was drawn on a scheme and described before the set of equations.

It is not clear why the specific wavelength of 3.39 um was chosen for the calculations?

How imaginary part of the propagation constant was determined?

The white and red lines in figures 5, 6 and 7 are not visible for the reader. Please enlarge it, or indicate where they are.

Even though, there are some points of the manuscript which may be improved, the reviewer finds this work very interesting and meaningful for other researchers. The calculations were clearly presented and properly performed. Finally, the results support the conclusions. I recommend the Editor to accept this manuscript after minor revisions.

Author Response

Author’s notes to Reviewer 2

1. All typos were corrected according to the reviewer's wishes.
2. According to the reviewer's request, Figure 1 was introduced to clarify the equations into the article.
3. The wavelength of 3.39 microns was introduced to reduce the counting time by the finite element method (COMSOL), here is a phrase from the article: “The numerical calculations were carried out with a COMSOL commercial package at a wavelength of λ = 3.39 µm to reduce the number of finite elements in the calculations.”. Since at the same time it was possible to observe the necessary calculation accuracy based on the size of the final element and the wavelength. In addition, we experimented in the mid-IR spectral range with a laser at a given wavelength.
4. The thicknesses of all the lines in the figures were increased according to the wishes of the reviewer.
5. For numerical calculation of the imaginary part of the propagation constant of the core mode β^Im, an additional absorbing layer outside the waveguide is introduced in COMSOL. This is a reliable technique, it gives a good match with the experiment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The issues were checked.