Local Energy Velocity of the Air-Core Modes in Hollow-Core Fibers

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

First of all, I would like to thank the Reviewer for valuable comments on the article. Here are the answers to them:

1. Energy Velocity (EV) in Context: While EV is crucial for characterizing electromagnetic waves in the near field, its usefulness is significantly increased when considered alongside core physical parameters such as energy density and the Pointing vector (flux density). For example, an important question concerns the need to investigate EV in a limit of very low-energy. In this domain the EV is not an important physical parameter. To improve comprehension, the manuscript could use fewer repetitive illustrations of EV and instead include some diagrams and explanations that clarify the behaviors of vector P~ and energy density w

In connection with this remark, I would ask the Reviewer not to insist that the distributions of the Poynting vector, etc. were presented in this work. The fact is that we have already done similar work before and these studies have already been published. I have shown them in Section 2 highlighted in red. I also gave the corresponding new references. I would just really like not to overload this work with new data anymore, since it is already quite large. Thanks for understanding.

2. Clarity of Illustrations (Fig. 2): The figure under discussion lacks clarity in distinguishing between the two analyzed fiber types. Enhancing these visuals with including appropriate refractive index values that can aid readers in grasping the disparity between the fiber variants. Additionally, Figures 2, 3, 4 and others could benefit from axis clarification with labels denoted by symbols such as x and y, as introduced in the main text

All wishes of the Reviewer are taken into account in the text. The response to one of the comments is highlighted in red at the beginning of Section 3.

Author Response File: Author Response.docx

Reviewer 2 Report

english is acceptable

Author Response

First of all, I would like to thank the Reviewer for valuable comments on the article. Here are the answers to them:

My main concern is the following. The author does not give the current state of affairs in the field of hollow-core fibers - where they are used, what the requirements are, what losses have been achieved, what are the main limiting factors and what are the development prospects. How do existing model predictions (for example, ARROW one) compare with experimental data? In this context, the motivation for the research in the article is not very clear.

The same goes for conclusions. What characteristics are expected when using hollow – core fibers with a negative curvature of the core boundary? What will it give from a practical point of view? Is this the limit or can the performance be further improved?.

In accordance with the wishes of the Reviewer, the corresponding changes were made to the article in the Introduction and the Discussion section. They are highlighted in yellow.

Minor remarks:
1) ARROW (Anti Resonant Reflective Optical Waveguide) is not deciphered correctly in line 28
2) Please correct typos: introduces->introduced in line 77, ther-> the in line 81, etc.

All wishes of the Reviewer are taken into account in the text.

Author Response File: Author Response.docx

Reviewer 3 Report

The air-core modes have been analyzed and compared for two different hollow core fibers, named negative curvature of the core boundary typed hollow-core fibers and single-capillary fibers. Their local energy velocity and magnitude were concerned. This fundamental research is very important for clearly explain the working mechanism of hollow core fiber-based photonics devices or sensors. Minor revision is recommended for the following comments:

1.       In figure 2, eight capillaries cladding and nested structures have been studied. What about the impact of parameters difference on the performance, such as the numbers of capillaries, the scale difference of the nested structures?

2.       In figure 5 and figure 7, the color bars should be included to illustrate the light intensity; the explanations and units should be added along the axis.

Author Response

First of all, I would like to thank the Reviewer for valuable comments on the article. Here are the answers to them:

.       In figure 2, eight capillaries cladding and nested structures have been studied. What about the impact of parameters difference on the performance, such as the numbers of capillaries, the scale difference of the nested structures?

In accordance with the wishes of the Reviewer, the corresponding changes have been made to the article in Section 3 and are highlighted in green.

In figure 5 and figure 7, the color bars should be included to illustrate the light intensity; the explanations and units should be added along the axis.

All wishes of the Reviewer are taken into account in the text.

Author Response File: Author Response.docx

Reviewer 4 Report

The manuscript presents the behavior of the local energy flow velocity of the funda-mental air – core mode at the core – cladding boundary in two types of hollow – core fibers. Different from the conventional anti-resonance theory, the local energy velocity concept of air-core mode is proposed. The local energy velocity of hollow fiber and nested hollow fiber is calculated, and the reason of local energy velocity difference is analyzed. The paper has good theoretical value, verifies the energy flow relationship between left-handed metamaterials and negative refractive index, and provides a theoretical basis for explaining the low loss mechanism formed by the transmission band center of hollow fiber, that is, the study of the local energy velocity of hollow fiber and nested hollow capillary. There are still some questions to be answered before the article is published, which are listed as follows:

1、 Lin62，section 2. Local energy velocity of the --,（line 69-72）  approximately corresponds to the center of the second transmission band at a wavelength of λ = 1.06 μm. According to the waveguide theory, the electric and magnetic fields of the fundamental air – core mode (HE11 hybrid mode) can be represented in cylindrical coordinates ----，Please supplement the column coordinate diagram and make necessary annotations according to the parameters given by the equation.

2、The article mentions ARROW model many times, such as Line69, but does not give necessary explanation on this model, please make appropriate supplement. The scope of application of the model, the aspects involved in solving the problem, and the applicable conditions. Please make any necessary additions.

3、The author proposed the concept of local energy velocity of the air core mode, I want to konw this research results compared with the anti-resonant periodic spectral response theory of photon band gap, what is the difference? What are the advantages of the method proposed by the author? Please discuss in the appropriate places in the article and make necessary explanations.

Appropriate syntax modifications.

Author Response

First of all, I would like to thank the Reviewer for valuable comments on the article. Here are the answers to them:

.       Lin62，section 2. Local energy velocity of the --,（line 69-72）  approximately corresponds to the center of the second transmission band at a wavelength of λ = 1.06 μm. According to the waveguide theory, the electric and magnetic fields of the fundamental air – core mode (HE11 hybrid mode) can be represented in cylindrical coordinates ----，Please supplement the column coordinate diagram and make necessary annotations according to the parameters given by the equation.

Thanks for the remark, but I would ask the Reviewer not to insist on it, since the article is already so heavily overloaded with information and formulas. I hope that most experts will be able to decide on the cylindrical coordinates for the equations. Thanks for understanding.

The article mentions ARROW model many times, such as Line69, but does not give necessary explanation on this model, please make appropriate supplement. The scope of application of the model, the aspects involved in solving the problem, and the applicable conditions. Please make any necessary additions.

Thanks for the good note. I made an addition to the Introduction. It is marked in purple.

The author proposed the concept of local energy velocity of the air core mode, I want to konw this research results compared with the anti-resonant periodic spectral response theory of photon band gap, what is the difference? What are the advantages of the method proposed by the author? Please discuss in the appropriate places in the article and make necessary explanations.

Thanks for the good note. I also made an addition to the end of the Introduction. It is also marked in purple.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

No suggestions