Optimizing Evanescent Efficiency of Chalcogenide Tapered Fiber

Round 1

Reviewer 1 Report

The authors have properly addressed all my previous concerns. I recommend publishing this manuscript in Materials MDPI.

Author Response

Thank you very much for all the useful comments. 

Reviewer 2 Report

correction  done

Author Response

Thanks a lot. We have asked the help with Prof. Zhang to improve the English again. Hope this version can reach the publication's requirement. The cited references have been carefully checked and some new references have been added.

Reviewer 3 Report

The manuscript submitted for review studies evanescent radiation from a tapered fibre. I would like to present the following considerations on its subject:

 

1. The work approaches the tapered portion of an optical fibre as a mathematical object—what it should be like for sensor applications. As a result, however, the desirable waist diameter of the fibre may be very small and/or the tapered stretch relatively long. This must be considered from the practical point of fragility of such sensors and their limitations, for example, in detection of liquids. These aspects must also be factored into determination of the optimal waist parameters. It is necessary to provide appropriate comments in relation to the practical considerations of applications of the tapered fibres in question.
2. The Conclusion to the manuscript should also pay attention to practical limitations of such sensors arising from their fragility, difference in thermal expansion coefficient, &c. 

This manuscript may be published in Materials on condition that the above-listed considerations be addressed in a further revision.

 

Author Response

see the enclosed response letter

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

In the manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber”, the authors have numerically studied the optimization of evanescent field-based sensing tapered fibers. In particular, the authors considered an incident wavelength of 7 um. Although the work seems to be technically correct and scientifically sound, there are some points that the authors need to address before I recommend publication of this manuscript.

 

• The use of “sensing sensitivity” along the text does not sound well, it seems redundant. Since the authors are dealing with a sensing device, I recommend simply using “sensitivity”.

 

• In Figure 1, the authors use “Goos-Haerchen shift”, which should be corrected to “Goos-Hänchen shift”.

 

• In line 71, the authors mention the use of a homemade tapering platform. However, the work is fully numerical. From my point of view this can confuse the readers. I recommend the authors to edit this sentence to give the idea that “in a potential experimental setup, it should be used a homemade tapering platform for…”

 

• In the discussion of Figure 2, the authors should also comment that this is a hypothetical experimental setup to illustrate the system they are simulating.

 

• In the simulation setup, the authors limit the discussion to say that they used COMSOL. However, for reproducibility purposes, more details should be given about.

 

• The use of 7 um as the incident wavelength should be justified. The authors should discuss the advantages and disadvantages of using this wavelength instead of shorter ones.

 

• I noticed that the authors never compared their sensitivities and performance with the case of plasmonic-based fibers. I recommend that the authors make comparisons using some recent works listed below:
  • DOI: 3390/bios10070077
  • DOI: 3390/s21196333
  • DOI: 3390/molecules25204654

 

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

In the manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber”, the authors have numerically studied the optimization of evanescent field-based sensing tapered fibers. In particular, the authors considered an incident wavelength of 7 um. Although the work seems to be technically correct and scientifically sound, there are some points that the authors need to address before I recommend publication of this manuscript

• The use of “sensing sensitivity” along the text does not sound well, it seems redundant. Since the authors are dealing with a sensing device, I recommend simply using “sensitivity”

Response: We have made revision in the revised manuscript.

 

• In Figure 1, the authors use “Goos-Haerchen shift”, which should be corrected to “Goos-Hänchen shift”.

Response: We have made revision in the revised manuscript.

 

• In line 71, the authors mention the use of a homemade tapering platform. However, the work is fully numerical. From my point of view this can confuse the readers. I recommend the authors to edit this sentence to give the idea that “in a potential experimental setup, it should be used a homemade tapering platform for…”

Response: We have made revision in the revised manuscript.

“As shown in Fig. 2, a potential fiber-puller system consists of an electrical heater, two motorized translation stages, a temperature controller, a CCD and a computer. ”

“Remarkably, the parameters chosen have the potential to be realized by our home-made tapering platform. ”

 

• In the discussion of Figure 2, the authors should also comment that this is a hypothetical experimental setup to illustrate the system they are simulating.

Response: We have made revision in the revised manuscript. As shown in the figure, this taper platform is the equipment we have implemented, and the related work is in progress.

“Remarkably, the parameters chosen have the potential to be realized by our homemade tapering platform.”

 

Figure 1. Experimental setup for the chalcogenide fiber tapering.

 

• In the simulation setup, the authors limit the discussion to say that they used COMSOL. However, for reproducibility purposes, more details should be given about. 

Response: Thanks for your constructive comments. The following paragraph were added in the revised manuscript.

“Specifically, the electromagnetic wave frequency domain (EWFD) module is used for calculation.”

“In order to ensure the correctness of the calculation, it is necessary to ensure the accuracy of the energy at the incident end (P_in) before calculating the evanescent efficiency. According to the theory of wave optics, the energy at the incident end can be obtained by taking the surface integral of Poynting vector. However, since this is a two-dimensional model, it is necessary to determine the height of the two-dimensional model first, as shown in the following formula,

                   (2)

where l is the incident end of the fiber, S_av is the Poynting vector, H refers to the the height of the model. Significantly, the height is also applicable to the calculation of the following formula. In this model, H is calculated to be 1.939.” (Page 4)

• The use of 7 um as the incident wavelength should be justified. The authors should discuss the advantages and disadvantages of using this wavelength instead of shorter ones.

Response: Thanks for your constructive comments. The following paragraph were added in the revised manuscript.

“The main reason that 7 μm is selected is this wavelength corresponds to the position of the characteristic peak of glucose, which absorption coefficient is large, and the loss of this chalcogenide fiber at 7 μm is small. Another reason for this selection is that the cut-off radius corresponding to the same mode are different for different wavelengths. Among them, the shorter the wavelength, the smaller the corresponding mode cut-off radius and the smaller the radius of the optimized structure.”(Page 3)

 

• I noticed that the authors never compared their sensitivities and performance with the case of plasmonic-based fibers. I recommend that the authors make comparisons using some recent works listed below:

Response: We have made revision in the revised manuscript.

“The plasmonic-based fibers have high sensitivity in the visible region by using the SPR effect of coating nanoparticles. The infrared fibers work in the infrared region and have relative low sensitivity. However, the sensitivity can be improved by decreasing the fiber size as proposed in this study.” (Page 2)

“22. Esfahani Monfared, Y. Overview of Recent Advances in the Design of Plasmonic Fiber-Optic Biosensors. Biosensors 2020, 10, doi:10.3390/bios10070077

23. 23. Cennamo, N., Arcadio, F., Zeni, L., et al. The Role of Tapered Light-Diffusing Fibers in Plasmonic Sensor Configurations. Sensors 2021, 21, doi:10.3390/s21196333
24. 24. Carvalho, W. O. F. and Mejía-Salazar, J. R. Surface Plasmon Resonances in Sierpinski-Like Photonic Crystal Fibers: Polarization Filters and Sensing Applications. Molecules 2020, 25, doi:10.3390/molecules25204654”

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Paper is well written, based on an idea to achieve best sensing of a tapered chalgogenide fiber by optimizing its geometry. It is of interest to the readership and fits into the scope of the MDPI journal Materials. However there is some place for improvement in the domain of its scientific soundness.

Overall, I recommend acceptance after minor revision. 

My first remark is that the the abstract, keywords and the main text body should be extended with some more info on optimization methods used for finding the optimized geometry (built in methods of the simulation software, parametric sweep, other methods if any). 

Similarly to explaining the laboratory experiment in detail (instrument settings etc), so the numerical experiment should be explained with details that allow for the reproduction of results by the interested readers. I suggest adding more details on conducting the numerical experiment.

Some further remarks are:
line 35: define penetration depth and k in advance
Fig 1,3:  denote materials on pictures

Thank you for contributing to this journal and science with this work.
With kind regards...

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

Paper is well written, based on an idea to achieve best sensing of a tapered chalgogenide fiber by optimizing its geometry. It is of interest to the readership and fits into the scope of the MDPI journal Materials. However there is some place for improvement in the domain of its scientific soundness.

Overall, I recommend acceptance after minor revision. 

• My first remark is that the the abstract, keywords and the main text body should be extended with some more info on optimization methods used for finding the optimized geometry (built in methods of the simulation software, parametric sweep, other methods if any). 
• Similarly to explaining the laboratory experiment in detail (instrument settings etc), so the numerical experiment should be explained with details that allow for the reproduction of results by the interested readers. I suggest adding more details on conducting the numerical experiment.

Response: Thanks for your constructive comments. The following paragraph were added in the revised manuscript.

“Specifically, the electromagnetic wave frequency domain (EWFD) module is used for calculation.”

“In order to ensure the correctness of the calculation, it is necessary to ensure the accuracy of the energy at the incident end (P_in) before calculating the evanescent efficiency. According to the theory of wave optics, the energy at the incident end can be obtained by taking the surface integral of Poynting vector. However, since this is a two-dimensional model, it is necessary to determine the height of the two-dimensional model first, as shown in the following formula:

 

                   (2)

where l is the incident end of the fiber, S_av is the Poynting vector, H refers to the the height of the model. Significantly, the height is also applicable to the calculation of the following formula. In this model, H is calculated to be 1.939.”(Page 4)

 

(3)Some further remarks are:

line 35: define penetration depth and k in advance

Fig 1,3:  denote materials on pictures

Response: We have made revision in the revised manuscript.

“As shown in Fig. 1, the light is propagated through the fiber via successive total inter-nal reflection, among which E=Aexp(-κz)exp[i(k_xx-ωt)] is formula of evanescent wave. Where Aexp(-κz) is the amplitude of evanescent wave. When the amplitude of the ev-anescent wave decays to 1/e of its maximum value, this position is defined as penetra-tion depth, that is, z=1/κ. ” (Page 2)

 

Fig. 3 is a general schematic diagram of bare optical fiber. The optical fiber can be any transparent material.

Author Response File: Author Response.pdf

Reviewer 3 Report

It is necessary to describe the review for each source of literature and show a comparative analysis. "from University of Rennes 1[1-3], Ningbo University[4-9], Zhejiang University[10, 11], and other institutions[12-19] have carried out extensive research on the mid-infrared evanescent wave absorption sensing technology, which proves that this technique can realize the real-time in situ qualitative and quantitative analysis of a variety of organic compounds"

 

You need to add these sources to references

DOI: 10.1016/j.optcom.2022.128091

DOI: 10.1177/0142331220987917
DOI: 10.1016/j.jnoncrysol.2021.120939

Make Figure 4,6 larger. Explain the charts with more detail.

"6. Analysis of micro deformation in waist"
This section needs to be completely redone. Conduct an analysis of mathematical structures or modeling systems, an analysis of the algorithm. Analysis of technology and standards.

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

• It is necessary to describe the review for each source of literature and show a comparative analysis. "from University of Rennes 1[1-3], Ningbo University[4-9], Zhejiang University[10, 11], and other institutions[12-19] have carried out extensive research on the mid-infrared evanescent wave absorption sensing technology, which proves that this technique can realize the real-time in situ qualitative and quantitative analysis of a variety of organic compounds"

Response: We have made revision in the revised manuscript.

“Typically, Dai et al. developed gas sensor based on four hole suspended core As₂S₃ fiber, and its sensitivity is less than 100 ppm for methane, and response time is estimated to be less than 20 s. Romanova et al. prepared the Ge₂₆As₁₇Se₂₅Te₃₂ fiber loop for the detection of antigel additive in diesel fuel. The absorption coefficients of the solution is well approximated by a linear function.”(Page 1)

 

• You need to add these sources to references

Response: We have added the first and third references recommend by the reviewe. However, the second reference reported the mobile robots which is no relationship to our work.

“  20. Sheng, J., Peng, Q., Sun, W., et al. Influence of extrusion on the properties of chalcogenide glasses and fibers. Opt. Commun. 2022, 513, 128091, DOI: https://doi.org/10.1016/j.optcom.2022.128091

21. 21. Shiryaev, V. S., Sukhanov, M. V., Velmuzhov, A. P., et al. Core-clad terbium doped chalcogenide glass fiber with laser action at 5.38 μm. Journal of Non-Crystalline Solids 2021, 567, 120939, DOI: https://doi.org/10.1016/j.jnoncrysol.2021.120939”

 

• Make Figure 4,6 larger. Explain the charts with more detail.

Response: We have made revision in the revised manuscript.

 

(4)"6. Analysis of micro deformation in waist"

This section needs to be completely redone. Conduct an analysis of mathematical structures or modeling systems, an analysis of the algorithm. Analysis of technology and standards.

Response: Thanks for your constructive comments. The following paragraph were added in the revised manuscript.

“The waist region of fiber with micro taper is a part with changing radius, and the change is quite slow, so it can be approximated as a straight line with small slope. Because the decreasing of fiber diameter will cause the change of mode, the light field in the micro cone is actually a process of coupling from high-order mode to low-order mode.” (Page 8)

“This is because, on the one hand, R_w is fixed, while the mode field distribution in the optical fiber is mainly related to its radius. On the other hand, the taper in the waist area is very small, resulting in the mode conversion efficiency close to 1. Therefore, the mode proportion at R_w is almost unchanged at different R_L. Meanwhile, as the radius changes from R_L to R_w, the equivalent radius of the waist area is greater than R_w. The larger the radius is, the smaller the τ is (as shown in Fig. 4). ”(Page 8)

 

Reviewer 4 Report

Review report

materials-1631221-peer-review-v1

"Optimizing evanescent efficiency of chalcogenide tapered fiber"

 

I found the topic is interesting and falls into the scope of the journal. The results obtained are clearly explained and could be useful. This manuscript reports timely and relevant original results, and certainly deserves publication in the journal.

However, some aspects of the study might be addressed to refine the reported analysis. In particular:

1) The manuscript seems more like a technical report than a scientific paper.

2) The results of the work must be supplemented with equations that form the basis of numerical calculations.

3) It is necessary to clearly indicate all the assumptions and approximations of the model used for numerical calculations.

4) The manuscript must be supplemented with analytical results in simple limiting cases.

5) What computing package did the authors use?

6) What numerical methods were used by the authors? It is necessary to bring the accuracy and error of calculations.

7) There is a weak discussion part in the manuscript. There are no physical causes of the described phenomena related to the molecular structure of the substance that the optical fiber consists of.

 

The manuscript is could to be published after revision.

 

Comments for author File: Comments.pdf

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

I found the topic is interesting and falls into the scope of the journal. The results obtained are clearly explained and could be useful. This manuscript reports timely and relevant original results, and certainly deserves publication in the journal.

However, some aspects of the study might be addressed to refine the reported analysis. In particular:

(1) The manuscript seems more like a technical report than a scientific paper.

(2) The results of the work must be supplemented with equations that form the basis of numerical calculations.

Response: Thanks for your constructive comments. This paper has given the basic calculation formula of fiber evanescent efficiency. Based on COMSOL software, the energy distribution under different conditions can be obtained directly, and the calculation can be realized completely.

Because the mode distribution in the optical fiber is directly related to the size of the optical fiber, the derivation of more equations is very difficult. This work is the first time to put forward the concept of evanescent efficiency, more work are still in progress.

 

• It is necessary to clearly indicate all the assumptions and approximations of the model used for numerical calculations.

Response: Thanks for your constructive comments. The following paragraph were added in the revised manuscript.

“Specifically, the electromagnetic wave frequency domain (ewfd) module is used for calculation.”

“The main reason that 7 μm is selected is this wavelength corresponds to the position of the characteristic peak of glucose, which absorption coefficient is large, and the loss of this chalcogenide fiber at 7 μm is small. Another reason for this selection is that the cut-off radius corresponding to the same mode are different for different wavelengths. Among them, the shorter the wavelength, the smaller the corresponding mode cut-off radius and the smaller the radius of the optimized structure.”(Page 3)

“In order to ensure the correctness of the calculation, it is necessary to ensure the accuracy of the energy at the incident end (P_in) before calculating the evanescent efficiency. According to the theory of wave optics, the energy at the incident end can be obtained by taking the surface integral of Poynting vector. However, since this is a two-dimensional model, it is necessary to determine the height of the two-dimensional model first, as shown in the following formula:

                   (2)

where l is the incident end of the fiber, S_av is the Poynting vector, H refers to the the height of the model. Significantly, the height is also applicable to the calculation of the following formula. In this model, H is calculated to be 1.939.” (Page 4)

 

• The manuscript must be supplemented with analytical results in simple limiting cases.

Response: Thanks for your constructive comments. The following paragraph were added in the revised manuscript.

“The waist region of fiber with micro taper is a part with changing radius, and the change is quite slow, so it can be approximated as a straight line with small slope. Because the decreasing of fiber diameter will cause the change of mode, the light field in the micro cone is actually a process of coupling from high-order mode to low-order mode.” (Page 8)

“This is because, on the one hand, R_w is fixed, while the mode field distribution in the optical fiber is mainly related to its radius. On the other hand, the taper in the waist area is very small, resulting in the mode conversion efficiency close to 1. Therefore, the mode proportion at R_w is almost unchanged at different R_L. Meanwhile, as the radius changes from R_L to R_w, the equivalent radius of the waist area is greater than R_w. The larger the radius is, the smaller the τ is (as shown in Fig. 4). ”(Page 8)

 

• What computing package did the authors use?

Response: We use COMSOL 5.5 for calculation.

“Here, we systematically investigate the evanescent field in different geometries by using the finite-element method based full-vector solver COMSOL. Specifically, the electromagnetic wave frequency domain (EWFD) module is used for calculation.”

 

• What numerical methods were used by the authors? It is necessary to bring the accuracy and error of calculations.

Response: Thanks for your constructive comments. We use the electromagnetic wave frequency domain (EWFD) module of COMSOL wave optics for calculation. The calculation accuracy depends on the meshing. The calculation accuracy depends on the meshing. We control the meshing according to the physical field. This way can ensure the accuracy of the results and get the results we want to explore.

 

• There is a weak discussion part in the manuscript. There are no physical causes of the described phenomena related to the molecular structure of the substance that the optical fiber consists of.

Response: In this simulation work, only refractive index of As₂Se₃ chalcogenide fiber was used to calculate the evanescent efficiency. The molecular structure has no effect on the sensitivity.

Author Response File: Author Response.pdf

Reviewer 5 Report

The reviewed manuscript studies calculation of the optimal configuration of optical fibre ensuring the best interaction of evanescent field with the organic groups of materials. I find the following considerations important in this relation:

1. It is necessary to discuss the general problem of this sensor type. It consists in that the more sensitive the sensor is, the less it is protected from external damage (which may originate from both wild life and ambient conditions, such as rain, ice, wind, &c). Smaller fibre diameters further exacerbate this problem. Hence, the practical aspects of this sensor should be discussed—where and how it may be actually used.
2. The described tapered fibre is only a part of the sensor. This latter also comprises the radiation source and the equipment needed for detection of radiation parameter evolution. The entire sensor is a relatively complicated (and expensive) system. The Authors need to list competing solutions and their drawbacks in comparison with the proposed one.
3. The reviewed work studies theoretically different tapered fibre geometries and finds the optimal profile. It is important to comment on the practical possibility of its fabrication and measurement thereafter. What kind of equipment is necessary, how reproducible the fabrication procedure is, whether or not such profile may be fabricated in laboratory conditions, at least. It is necessary to demonstrate that the desired tapered fibre may be actually produced.

If the Authors address the above-listed concerns in a further revision of their manuscript, it may be published in Materials

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

The reviewed manuscript studies calculation of the optimal configuration of optical fibre ensuring the best interaction of evanescent field with the organic groups of materials. I find the following considerations important in this relation:

• It is necessary to discuss the general problem of this sensor type. It consists in that the more sensitive the sensor is, the less it is protected from external damage (which may originate from both wild life and ambient conditions, such as rain, ice, wind, &c). Smaller fibre diameters further exacerbate this problem. Hence, the practical aspects of this sensor should be discussed—where and how it may be actually used.

Response: Thanks for your constructive comments. Sulfur optical fiber sensing is mainly used in organic liquid detection, and can not be used in outdoor extreme environment. Since the optical fiber is made of stable glass, most organic substances, such as ethanol and glucose, will not damage the optical fiber and can be reused for many times.

 

• The described tapered fibre is only a part of the sensor. This latter also comprises the radiation source and the equipment needed for detection of radiation parameter evolution. The entire sensor is a relatively complicated (and expensive) system. The Authors need to list competing solutions and their drawbacks in comparison with the proposed one.

Response: The entire system in the lab is complicated and expensive. However, the portable FTIR with the sensor fiber can largely decrease the cost. Moreover, only the fiber need to be replced when it was broken. Since this paper focuses more on theoretical research, no detailed description is given in this work. At present, the optical fiber detection platform we have built is shown in the figure below, and the relevant experimental work will be published in the future.

 

Figure 1. Experimental setup for sensing.

 

• The reviewed work studies theoretically different tapered fibre geometries and finds the optimal profile. It is important to comment on the practical possibility of its fabrication and measurement thereafter. What kind of equipment is necessary, how reproducible the fabrication procedure is, whether or not such profile may be fabricated in laboratory conditions, at least. It is necessary to demonstrate that the desired tapered fibre may be actually produced.

Response: We use the high precision fiber-puller platform as illustreted in Figure 2 (original text). We can fabricate the taper fiber with diameter of 4 μm in the lab as shown in the Figure below. 

Figure 2. Waist region control and cone region control in tapered fiber.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have properly addressed all my previous concerns. However, before accepting the publication of this work, I think it is of great importance that the authors improve the quality of Figure 1, which is really poor.

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

The authors have properly addressed all my previous concerns. However, before accepting the publication of this work, I think it is of great importance that the authors improve the quality of Figure 1, which is really poor.

Response: Thanks for your constructive comments. We have made revision in the revised manuscript.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors have made corrections. But the article does not contain enough justification for the scientific component. The idea is interesting, but the authors implemented it poorly.

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

The authors have made corrections. But the article does not contain enough justification for the scientific component. The idea is interesting, but the authors implemented it poorly.

Response: Thanks for your constructive comments. For the deficiency of the theory of the article, we make the following explanation:

Light is a kind of electromagnetic wave with extremely short wavelength which follows Maxwell’s equations. Since chalcogenide fiber is a uniform transparent medium without free charge and current, its differential form is as follows

    (1)

    (2)

   (3)

   (4)

where E and D are the electric field strength and potential shift-vector respectively, H and B are the magnetic field strength and magnetic induction strength respectively, which meet the equations of D = ɛE, B = µH, where ε and µ are the dielectric constant and permeability of chalcogenide glasses respectively. By taking the curl of (1 and 2) and using the vector expression, among which A is E or H, we can obtain the wave equation, as shown in (5 and 6). We can solve the wave equation with the help of different algorithms, such as FDTD, FEM, etc. Fortunately, various numerical calculation software based on these algorithms are developed to solve problems involved with computational optoelectronics.

(5)

(6)

By introducing the simple harmonic function E = E₀exp[i(k·r - ωt)], the time and space components of the wave equation can be separated to obtain the waveguide field equation, as shown in (7).

     (7)

Where ▽_t and χ are the transverse nabla operator and the transverse propagation constant, respectively. Since E_r, E_ϕ and H_r, H_ϕ can are expressed by E_z and H_z which are the components of E and H, Bessel equation can be obtained by bringing E_z and H_z into equation (7), and E_z and H_z are obtained by select different Bessel functions according to the core and cladding, as shown in (8).

     (8)

A₁, A₂, B₁ and B₂ are the constant to be solved by using electromagnetic wave boundary conditions. J_l and K_l are besselj function and besselk function of order l respectively. U and W are the transverse propagation constants of the electromagnetic field in the core and cladding, respectively. R_a = r/a is the normalized radius and a is the radius of the core. By selecting the order of the Bessel function and combining the electromagnetic wave boundary continuity condition, we can obtain the eigenvalue equations of different modes.

For HE_lm and EH_lm：

     (9)

For TE_0m：

     (10)

For TM_0m：

     (11)

According to the order of Bessel function, we can obtain U_lm at the cut-off of different modes, and the linear relationship between longitudinal propagation constant of each mode β and normalized frequency V can be achieved. Moreover, Electromagnetic field equation of different modes can be achieved. By taking the surface integral of Poynting vector (12), the distribution of energy at the section can be obtained, as shown in the following formula:

(12)

          (13)

          (14)

where P_core is the energy inside the core and P_sur is the energy outside the core. The formula corresponds to formula (2) in the article. In order to calculate the evanescent wave ratio, only the energy ratio outside the fiber core needs to be calculated. As shown in the following formula:

   (15)

The formula corresponds to formula (3) in the article. Due to the influence of phase factor, the evanescent proportion of different sections is different. Therefore, axial parameters are introduced for calculation. As shown in the following formula:

   (16)

The formula corresponds to formula (4) in the article. Then the formula of evanescent efficiency can be obtained by introducing light transmittance. COMSOL is a finite element calculation software. According to the finite element algorithm, it can directly solve the wave equation and obtain the electromagnetic field values of each point in the model. Therefore, the calculation accuracy can be guaranteed according to the evanescent efficiency formula based on traditional wave optics.

Moreover, the mode evolution in the core can be directly collected from COMSOL as shown in the Figure S1 and S2.

 

Figure S1 Transmission of light in a diabatic taper

 

Figure S2 The variation of electric field vibration from fundamental mode to higher-order mode to fundamental mode in tapered fiber, 40-470 represents the cross sections at different positions of light incident axis 

 

Author Response File: Author Response.docx

Reviewer 4 Report

I still believe that solutions that are not smooth at the boundaries do not describe the real physical situation and, therefore, are not physical, despite the authors' assertion that their calculations are correct.
If the authors propose a new numerical method, then this physics journal is not suitable for this. At the same time, it is necessary to directly compare the accuracy of their method with existing ones on control examples. It is also necessary to give conditions and proof of convergence.
The authors ignored the comment about the possibility of experimental observation of non-smooth solutions.

Author Response

Dear Editor and Reviewers:

Thanks for your letter and for the reviewer’s comments concerning our manuscript entitled “Optimizing evanescent efficiency of chalcogenide tapered fiber” (manuscript ID:1631221). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. The main corrections in the manuscript and the responds to the reviewer’s comments are as flowing:

Reviewers' comments:

I still believe that solutions that are not smooth at the boundaries do not describe the real physical situation and, therefore, are not physical, despite the authors' assertion that their calculations are correct.

If the authors propose a new numerical method, then this physics journal is not suitable for this. At the same time, it is necessary to directly compare the accuracy of their method with existing ones on control examples. It is also necessary to give conditions and proof of convergence.

The authors ignored the comment about the possibility of experimental observation of non-smooth solutions.

Response: Thanks for your constructive comments. The main reason for the non-smooth solution is that the transmission of light in the optical fiber changes with the phase, and the electromagnetic field distribution is also different. When we conduct volume integration on the energy, we cannot ensure that the phase distribution in the fixed selected volume remains unchanged, because the optical mode will change with the change of the optical fiber structure, which is unavoidable, but does not affect the accuracy of our calculation conclusion. For the deficiency of the theory of the article, we make the following explanation:

Light is a kind of electromagnetic wave with extremely short wavelength which follows Maxwell’s equations. Since chalcogenide fiber is a uniform transparent medium without free charge and current, its differential form is as follows

    (1)

    (2)

   (3)

   (4)

where E and D are the electric field strength and potential shift-vector respectively, H and B are the magnetic field strength and magnetic induction strength respectively, which meet the equations of D = ɛE, B = µH, where ε and µ are the dielectric constant and permeability of chalcogenide glasses respectively. By taking the curl of (1 and 2) and using the vector expression, among which A is E or H, we can obtain the wave equation, as shown in (5 and 6). We can solve the wave equation with the help of different algorithms, such as FDTD, FEM, etc. Fortunately, various numerical calculation software based on these algorithms are developed to solve problems involved with computational optoelectronics.

(5)

(6)

By introducing the simple harmonic function E = E₀exp[i(k·r - ωt)], the time and space components of the wave equation can be separated to obtain the waveguide field equation, as shown in (7).

     (7)

Where ▽_t and χ are the transverse nabla operator and the transverse propagation constant, respectively. Since E_r, E_ϕ and H_r, H_ϕ can are expressed by E_z and H_z which are the components of E and H, Bessel equation can be obtained by bringing E_z and H_z into equation (7), and E_z and H_z are obtained by select different Bessel functions according to the core and cladding, as shown in (8).

     (8)

A₁, A₂, B₁ and B₂ are the constant to be solved by using electromagnetic wave boundary conditions. J_l and K_l are besselj function and besselk function of order l respectively. U and W are the transverse propagation constants of the electromagnetic field in the core and cladding, respectively. R_a = r/a is the normalized radius and a is the radius of the core. By selecting the order of the Bessel function and combining the electromagnetic wave boundary continuity condition, we can obtain the eigenvalue equations of different modes.

For HE_lm and EH_lm：

     (9)

For TE_0m：

     (10)

For TM_0m：

     (11)

According to the order of Bessel function, we can obtain U_lm at the cut-off of different modes, and the linear relationship between longitudinal propagation constant of each mode β and normalized frequency V can be achieved. Moreover, Electromagnetic field equation of different modes can be achieved. By taking the surface integral of Poynting vector (12), the distribution of energy at the section can be obtained, as shown in the following formula:

(12)

          (13)

          (14)

where P_core is the energy inside the core and P_sur is the energy outside the core. The formula corresponds to formula (2) in the article. In order to calculate the evanescent wave ratio, only the energy ratio outside the fiber core needs to be calculated. As shown in the following formula:

   (15)

The formula corresponds to formula (3) in the article. Due to the influence of phase factor, the evanescent proportion of different sections is different. Therefore, axial parameters are introduced for calculation. As shown in the following formula:

   (16)

The formula corresponds to formula (4) in the article. Then the formula of evanescent efficiency can be obtained by introducing light transmittance. COMSOL is a finite element calculation software. According to the finite element algorithm, it can directly solve the wave equation and obtain the electromagnetic field values of each point in the model. Therefore, the calculation accuracy can be guaranteed according to the evanescent efficiency formula based on traditional wave optics.

Moreover, the mode evolution in the core can be directly collected from COMSOL as shown in the Figure S1 and S2.

 

Figure S1 Transmission of light in a diabatic taper

 

Figure S2 The variation of electric field vibration from fundamental mode to higher-order mode to fundamental mode in tapered fiber, 40-470 represents the cross sections at different positions of light incident axis 

 

Author Response File: Author Response.pdf