Review Reports - M-Lines Spectroscopy for Thin Films: A New Perspective

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors utilized M-line spectroscopy as a new prospective approach for high-precision measurement of thin films. However, this is not a new method, as the authors themselves noted that it was published by Tien in 1969.

The evaluation of this method for testing samples did not cover many types of thin film systems, especially thinner films in the range of a few nanometers.

The paper shows that incident radiation with TM and TE polarizations was used, with data presented in most tables.

The reviewer completely agrees that the refractive index is dependent on thickness W, and the paper mainly focused on how TE or TM polarization affects the study results. However, one question remains: why do you claim the difference in calculation originates from simulation and is stable for TE mode?

How does this technique demonstrate its precise resolution to provide useful data for comparison with numerical calculations such as those from FemSIM?

The precise angular step is provided by the electric rotary stage, but can you show how the device functions with an angular step of 10⁻³ degrees?

Additionally, the following suggestions should be addressed:

1. Even for calculated results, the data accuracy and estimated error digits in the tables should be unified.
2. The subscript expression for Si₂C₂N₆ samples should be corrected.
3. Section 4 (Discussion) in the manuscript is incomplete.
4. The experimental setup is unclear, especially regarding the optical apparatus. Please provide more details to support the explanation in Fig. 5.
5. It should be noted that the resonant angles correspond to the techniques mentioned.

The paper is not finished. Without clear revisions addressing the above issues, it cannot be recommended for publication.

Comments on the Quality of English Language

English expression can be refined again.

Author Response

Comments and Suggestions for Authors

The evaluation of this method for testing samples did not cover many types of thin film systems, especially thinner films in the range of a few nanometers.

The paper shows that incident radiation with TM and TE polarizations was used, with data presented in most tables.

That is not an issue anymore, since the manuscript has been rewritten and is now reporting comparison results of a sample analyzed through DektakXT profiler and the m-lines spectroscopy method calculation when using two modes of the same polarization and solely the fundamental modes of each polarization.

How does this technique demonstrate its precise resolution to provide useful data for comparison with numerical calculations such as those from FemSIM?

The new version of the manuscript reports comparison results of a sample where the thickness has been obtained by DektakXT profiler and then checked against the results provided by the m-lines spectroscopy method calculation. We removed the comparison between the results obtained with the m-lines method and the ones provided by FemSIM. Nevertheless, we still mention FemSIM results but only as an example to show the limits imposed in calculating the film width when the m-lines method uses 2 modes of the same polarization.

The precise angular step is provided by the electric rotary stage, but can you show how the device functions with an angular step of 10⁻³ degrees?

It is not an issue in the new version of the manuscript.

Additionally, the following suggestions should be addressed:

Even for calculated results, the data accuracy and estimated error digits in the tables should be unified.

In the new manuscript we use 4 decimal places and, since the system is limited by the accuracy of the angular actuator, we use the repeatability accuracy error of the device (0.03º) to determine the measurement error.

The subscript expression for Si₂C₂N₆ samples should be corrected.

It is not an issue in the new version of the manuscript.

Section 4 (Discussion) in the manuscript is incomplete.

The manuscript has been rewritten and is now reporting comparison results obtained through DektakXT profiler and the m-lines spectroscopy method calculation when using two modes of the same polarization and solely the fundamental modes of each polarization. We believe the analysis is now complete.

The experimental setup is unclear, especially regarding the optical apparatus. Please provide more details to support the explanation in Fig. 5.

Figure 5 has been replaced by a diagram of the optical setup and its description, which we believe is more adequate.

It should be noted that the resonant angles correspond to the techniques mentioned.

Addressed in new version of the manuscript.

The paper is not finished. Without clear revisions addressing the above issues, it cannot be recommended for publication. Please, see new version of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

Review of the manuscript in the attached file.

Comments for author File: Comments.pdf

Author Response

What is the condition for mode excitation in a thin-film waveguide? Under what circumstances will waveguide modes appear at certain angles of incidence of radiation on a prism?

Mode’s excitation condition is when the wavenumber reflecting at the base of the prism matches the propagation constant of a given mode of the film. Since we know the incidence angle, we can determine the angle of the reflected wave at the prism’s base (Snell’s law). The modal index (N_m) of each propagating mode is then given by:

N_m = n_p sin(θ_synch)

where θ_synch is the angle at the prism’s base w.r.t. the normal at the reflection point and n_p is the prism’s refractive index.

How can the waveguide depth be reconstructed knowing only the set of modes? It is well known that the normalized dispersion curves (Fig. below) shown in Figure 4 (manuscript) depend on the wavelength of the radiation. What wavelength did you use to determine the curves in Figure 4? How do you obtain this without knowing the wavelength? An explanation is required.

We solve numerically the 2 unknown transcendental equation (a.k.a. phase equation) by establishing a ratio between 2 of these equations. This ratio enables removing the width and propagation constant dependence, remaining the unknown refractive index of the film to be solved. Once the refractive index is known, width can be recovered using the same equation.

We used 655 nm as the operating wavelength in FemSIM to obtain Figure 4 (it has been added to the rewritten manuscript), but please note that this was an example to demonstrate that the first modes (TE1 and TM1) are only excited when the width of the film is wide enough to support them. Being able to use the fundamental modes (TE0 and TM0) extends the measurement range to much thinner films.

In fact, the m-lines spectroscopy method is the basis of the so-called prism coupling method, which is widely used in practice. In practice, it's important to know not only the mode set and thickness, but also the waveguide profile. The introduction says nothing about this.

It is a film deposited over an optical glass substrate, ideally a planar waveguide with a step profile.

Are you defining the effective refractive index or the volumetric refractive index? These are different parameters. What is the modal index then?

In this work we designate as the modal index (also referred to as the effective refractive index in the literature) to establish a clear separation to the designation effective refractive index. We reserve the latter to designate the refractive index sensed by an incoming EM beam onto a heterogeneous structure consisting of subwavelength features, which effective refractive index depends on the filling factor.

Figure 5 doesn't convey any information. It's unclear.

Figure 5 has been replaced by a diagram of the optical setup which we believe is more adequate.

"We used this sample to test, verify, and confirm the validity of our hypothesis: - The limit in the m-line spectroscopy method is the thickness necessary to propagate the fundamental modes of both polarizations, Transverse Electric (TE0) and Transverse Magnetic (TM0)." What is the hypothesis here? It is known that there is a waveguide cutoff wavelength. See normalized dispersion curves by Nishihara (for example).

Manuscript has been rewritten and these phrases have been removed.

The results in Fig. 6 are very strange. Since the experimental setup is missing, it is impossible to understand how the signal was detected. The method involves exciting a mode in the waveguide and, accordingly, amplifying the signal at the photodetector. If dips are observed, does this mean that we were analyzing not the excitation of waveguide modes, but some back reflections from the prism?

In the new version of the manuscript it is now Figure 7 and is the response of the photodetector. These are not back reflections from the prism because when the exerted force on the back of the substrate is small or removed, no dips are observed.

What determines the accuracy of the effective refractive index measurement in your experiment? Why do you use 6 decimal places instead of 7 or 8? The accuracy of your resonance angle measurements does not exceed 2 decimal places, but the refractive index is measured with an accuracy of 6 decimal places. How can this be? Is it possible?

The decimal places result from the calculation in Matlab for an angular accuracy of 0.01º. In the new version of the manuscript we use 4 decimal places and, since the system is limited by the accuracy of the angular actuator, we use the repeatability accuracy error of the device (0.03º) to determine the measurement error.

The conclusion implies that the authors plan to further test this approach experimentally. In my opinion, the text is completely unclear about what new the authors have proposed; the experiment is unclear, and the experimental design is missing. Dispersion curves are presented that are independent of wavelength. The accuracy of the results is questionable. The graphs require improvement. There are numerous tables. The manuscript requires significant revision.

The new version of the manuscript covers experimental conditions. It presents an optical setup developed to either confirm or deny the use of fundamental modes of propagation to provide more accurate measurements of the refractive index and thickness of a given film and to extend those measurements to thinner films.

Reviewer 3 Report

Comments and Suggestions for Authors

This study proposes an extension to the traditional m-lines spectroscopy method, which is widely used for determining the refractive index and thickness of thin films on substrates. Historically, this method requires at least two guided modes of the same polarization to solve for the optical parameters, inherently limiting its applicability to multi-mode films only. The authors address this limitation by introducing a strategy that enables the use of the fundamental mode alone, thereby expanding the technique’s application to single-mode and thinner films. Through high-resolution angular measurements of a silicon carbonitride film on glass, they demonstrate that using only the fundamental transverse electric (TE) and transverse magnetic (TM) modes results in smaller discrepancies between calculated values of refractive index and thickness compared to traditional multi-mode methods. Notably, their results show improved agreement between TE and TM calculations as the angular resolution increases, with the smallest differential achieved when only fundamental modes are used. This suggests that the method not only becomes more precise but also more broadly applicable. The authors acknowledge the need for physical validation of these results and propose future work involving atomic force microscopy (AFM) to compare and verify the calculated film thickness.

Can authours provide more details about the experimental setup, especially how the angular resolution of 0.001° was achieved and maintained?
What steps did you take to minimize or account for errors such as alignment, surface roughness, or uncertainties in the substrate properties?
How did you identify and confirm that the detected mode was the fundamental mode in each case?
Is there a theoretical reason why using only the fundamental modes improves the accuracy of refractive index and thickness measurements?
Is there a minimum film thickness or refractive index contrast below which this method may no longer be reliable?
Have you compared your results with other established thin film characterization methods to validate your findings?
What algorithm or numerical method did you use to solve the transcendental equations, and is it accessible to other researchers?
Do you plan to publish your data or analysis tools to support reproducibility of your approach?

Author Response

Comments and Suggestions for Authors

Can authours provide more details about the experimental setup, especially how the angular resolution of 0.001° was achieved and maintained? It is not an issue in the new version of the manuscript.

What steps did you take to minimize or account for errors such as alignment, surface roughness, or uncertainties in the substrate properties? In the new manuscript we use 4 decimal places and, since the system is limited by the accuracy of the angular actuator, we use the repeatability accuracy error of the device (0.03º) to determine the measurement error. Alignment has been accounted for by determining the 45º reference (please see new version of manuscript). Surface roughness: - using a stylus surface profiler, Brucker DektakXT, we performed a 50 µm step scan over the region of interest.

How did you identify and confirm that the detected mode was the fundamental mode in each case? With FemSIM or by hand calculation using the calculated thickness and refractive index.
Is there a theoretical reason why using only the fundamental modes improves the accuracy of refractive index and thickness measurements? Fundamental modes propagate closer to the center of the waveguide than any other higher order mode. This higher confinement is less prone to be affected by the prism’s base proximity.
Is there a minimum film thickness or refractive index contrast below which this method may no longer be reliable? In this case, yes. It depends on the refractive index of the substrate, which determines the minimum width required to propagate the first mode (TE1 or TM1). In the example presented in Figure 4 is ~450 nm, corresponding to the minimal width to propagate TM1.
Have you compared your results with other established thin film characterization methods to validate your findings? Yes, in this version of the article we are comparing it with ellipsometric measurements. In the new version of the article we compare against measurements provided by a stylus surface profiler (Brucker DektakXT).
What algorithm or numerical method did you use to solve the transcendental equations, and is it accessible to other researchers? Matlab live scripts have been made available online.
Do you plan to publish your data or analysis tools to support reproducibility of your approach? Matlab live scripts have been made available online.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper introduces an innovative approach aimed at expanding the application scope of m-lines spectroscopy to accurately measure the refractive index and thickness of thinner films, including single-mode films. The m-lines spectroscopy requires at least two modes of the same polarization state to determine the optical properties of thin films, a requirement that limits the technique's potential application in cases of very thin films. To address this issue, this research has developed a novel strategy that employs only the fundamental modes of each polarization state (TE0 and TM0) to calculate the refractive index and thickness of the thin film, thereby overcoming the thickness limitations inherent in conventional methods. In this study, the authors have thoroughly considered the impact of the prism and air gap on the propagation modes of light waves and have conducted an in-depth analysis of the potential influence of the scanning angle resolution on the measurement results, providing a comprehensive assessment of these critical factors. Despite the detailed data and analysis presented, further refinements are possible.

When arguing the superiority of its method, this article has the following two closely related issues:
1. Inherent Logical Flaw: The paper derives a single refractive index value by combining TE₀and TM₀ modes and then calculates the film thickness based on this value, observing that the thickness difference (Δt) becomes smaller. This outcome is an inherent characteristic resulting from the derivation using a single refractive index value, rather than evidence of the method's increased precision. The self-consistency of the results obtained from a preset refractive index does not equate to physical accuracy.
2. Lack of External Validation：The paper mentions future work plans, including the use of high-precision techniques such as atomic force microscopy (AFM) for more accurate physical verification. This is crucial for establishing the accuracy and practicality of the method. Without such experimental benchmarks, all assertions in the paper about being "closer to physical reality" lack support. The accuracy of this method cannot be recognized without providing comparative data with technologies such as AFM. Therefore, it is recommended that the authors provide relevant test data in this paper to enhance the credibility of the research conclusions.

Regarding Figure 5 in the paper, which is a photograph of the experimental setup, it is suggested to replace it with a clearly labeled schematic diagram. A well-crafted schematic diagram would be more effective for understanding the experimental optical path, the spatial relationships between components, and the methodology. The diagram should clearly label key components and illustrate the path of light propagation to facilitate comprehension and replication of the experimental setup by readers.

The paper clearly states that the mechanical force applied to the substrate is crucial for controlling the coupling between the prism and the thin film. However, it does not provide relevant data or analysis and recommendations on how to optimize this parameter to prevent the broadening of coupling resonances and the shifting of resonance peaks.

Moreover, all analyses and conclusions of this study are drawn from aSi₂C₂N₆ film samples. Although this case demonstrates the preliminary feasibility of the method, a single data point is far from sufficient to prove the universality of the proposed new strategy of using only the fundamental modes. Therefore, it is recommended that the authors supplement experimental validation on different types of thin films (such as those with different materials, refractive indices, or thicknesses) to fully demonstrate the applicability and robustness of this method across various systems.

Author Response

Comments and Suggestions for Authors

When arguing the superiority of its method, this article has the following two closely related issues:

Inherent Logical Flaw: The paper derives a single refractive index value by combining TE₀and TM₀ modes and then calculates the film thickness based on this value, observing that the thickness difference (Δt) becomes smaller. This outcome is an inherent characteristic resulting from the derivation using a single refractive index value, rather than evidence of the method's increased precision. The self-consistency of the results obtained from a preset refractive index does not equate to physical accuracy.

It is not an issue in the new version of the manuscript.

Lack of External Validation：The paper mentions future work plans, including the use of high-precision techniques such as atomic force microscopy (AFM) for more accurate physical verification. This is crucial for establishing the accuracy and practicality of the method. Without such experimental benchmarks, all assertions in the paper about being "closer to physical reality" lack support. The accuracy of this method cannot be recognized without providing comparative data with technologies such as AFM. Therefore, it is recommended that the authors provide relevant test data in this paper to enhance the credibility of the research conclusions.

In the new version of the manuscript we use a stylus surface profiler, Brucker DektakXT, to perform a 50 µm step scan over the region of interest. The film thickness measurement of DektakXT is then checked against the results provided by the m-lines spectroscopy method.

Regarding Figure 5 in the paper, which is a photograph of the experimental setup, it is suggested to replace it with a clearly labeled schematic diagram. A well-crafted schematic diagram would be more effective for understanding the experimental optical path, the spatial relationships between components, and the methodology. The diagram should clearly label key components and illustrate the path of light propagation to facilitate comprehension and replication of the experimental setup by readers.

Photograph has been replaced by a diagram and its description.

The paper clearly states that the mechanical force applied to the substrate is crucial for controlling the coupling between the prism and the thin film. However, it does not provide relevant data or analysis and recommendations on how to optimize this parameter to prevent the broadening of coupling resonances and the shifting of resonance peaks.

Fundamental modes are much less prone to peaks broadening and shifting than higher order modes, except for extreme forces, due to their higher confinement to the core. One more reason for their use…

Moreover, all analyses and conclusions of this study are drawn from aSi₂C₂N₆ film samples. Although this case demonstrates the preliminary feasibility of the method, a single data point is far from sufficient to prove the universality of the proposed new strategy of using only the fundamental modes. Therefore, it is recommended that the authors supplement experimental validation on different types of thin films (such as those with different materials, refractive indices, or thicknesses) to fully demonstrate the applicability and robustness of this method across various systems.

We were able to get one sample with an access region to the bare glass, hence the new version of the manuscript. In future, we will get more samples with these characteristics and different film materials and thicknesses will be tested.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The primary contribution of this manuscript is the determination of refractive index and film thickness using angular resonances obtained through m-line spectroscopy. The authors aim to achieve high-accuracy optical parameters using this non-destructive method. The use of MATLAB scripts for calculations and comparison with DektakXT profiler measurements is commendable. The deconvolution of results from two polarizations combined with numerical methods to determine the final optical parameters presents an interesting approach.

However, significant discrepancies exist between versions 1 and 2 of the manuscript and after Chapter 2, indicating substantial revisions. Additionally, Table 1 is referenced but not inserted into the text.

Several concerns have been raised:

- Why were numerous tables removed from this revised version?
- The new material SiN₂ appears in Chapter 2 ("Materials and Methods") after revision, while the original material Si₂C₂N₆ has disappeared without explanation.
- All experimental parameters, including angular step size and laser wavelength, have been changed. What is the justification for these modifications?
- Beyond standard TM and TE polarization measurements, what new perspective does this work offer for m-line spectroscopy?
- After line 246, table numbering is missing. This critical section comparing measurements and calculations appears incomplete.

Specifically, the thickness values in Table 1 (904.05–992.89 nm) are inconsistent with the final conclusion (approximately 706.37 nm). Can you clarify this discrepancy?

Furthermore, the reported thickness uncertainty (single-digit precision after the decimal point) may be insufficient for most readers seeking high-accuracy measurements.

Given these concerns, I am uncertain whether the manuscript can be accepted in the current form.

Comments on the Quality of English Language

English expression has been refined. But the whole text is under revised.

Author Response

Thank you for taking the time to review this document. Follows the answers to the issues raised:

"However, significant discrepancies exist between versions 1 and 2 of the manuscript and after Chapter 2, indicating substantial revisions. Additionally, Table 1 is referenced but not inserted into the text."

That is true. Chapter 2 has been completely re-done in version 2 of the manuscript. The sample analyzed in version 1 was not adequate to demonstrate our reasoning, for it had no way of confirming the actual thickness of the film deposited over the glass substrate. Hence, we had to prepare another film sample (SiN₂deposited over glass substrate) which provided access to the bare glass substrate and allowed thickness confirmation through profilometry.

"- Why were numerous tables removed from this revised version?
- The new material SiN₂ appears in Chapter 2 ("Materials and Methods") after revision, while the original material Si₂C₂N₆ has disappeared without explanation."

We believe that this has been explained in previous answer.

"- All experimental parameters, including angular step size and laser wavelength, have been changed. What is the justification for these modifications?"

Thank you for noticing it. Previous 656 nm laser diode stopped working and we had to find a new one. Relating to angular steps, we found out there was no need for finer steps, 0.05º step was enough to demonstrate our reasoning as can be confirmed in the manuscript.

"- Beyond standard TM and TE polarization measurements, what new perspective does this work offer for m-line spectroscopy?"

Thank you for pointing out the essence of the work: - Using the fundamental modes of both polarizations instead of any other pair of modes’ combination of the same polarization to calculate the thickness of a given film (which has been the method historically reported in literature), extends the range of thicknesses which we are able to calculate. Moreover, yet to be confirmed with further experiments, our calculations indicated greater agreement with Dektak thickness measurement when calculating this parameter with the fundamental modes, when compared with the traditional calculation method (please see the results in Table 1 and the final results calculated with the fundamental modes, and compare with the measurement from Dektak).

"- After line 246, table numbering is missing. This critical section comparing measurements and calculations appears incomplete."

Maybe we are not addressing the issue, but those are the results obtained when using the m_Lines_SiN2_singleMode.mlx live script with the fundamental modes TM0 and TE0. Table 1 refers to the results obtained when using the m_Lines_SiN2.mlx live script for 3 different pairs of modes of the same polarization. Both scripts were run with the same angular data, given the specificity of each script, and you are welcome to test and check it.

"Specifically, the thickness values in Table 1 (904.05–992.89 nm) are inconsistent with the final conclusion (approximately 706.37 nm). Can you clarify this discrepancy?"

Thank you for pointing that out. Table 1 addresses results from calculations with 3 different pairs of modes of the same polarization (TE0 with TE1, TE0 with TE2, TE1 with TE2 and TM0 with TM1, TM0 with TM2, TM1 with TM2), which were obtained using the m_Lines_SiN2.mlx live script. The conclusion reports the results obtained with the m_Lines_SiN2_singleMode.mlx live script, when using the fundamental modes TM0 and TE0.

"Furthermore, the reported thickness uncertainty (single-digit precision after the decimal point) may be insufficient for most readers seeking high-accuracy measurements."

We corrected the number of digits after the decimal point in this new version of the manuscript. It is now double-digit precision after the decimal point. We believe this is enough since we are referring to nanometers with double-digit precision after the decimal point.

With our best regards,

The authors

Reviewer 2 Report

Comments and Suggestions for Authors

Thanks to the authors for their comments and clarifications.
My fundamental questions regarding the revised manuscript remain:

1. Abstract: "In this work, we developed a strategy that not only extends the thickness range of the method's calculation down to single-mode operation, but also the results' analysis led us to conclude that by solely using the fundamental modes in the calculation, the method's precision increases and the determined parameters are closer to the physical reality of the film."

What is this strategy? What is the novelty of this work? There's nothing in the text, or I didn't see it.

The accuracy of the method is determined by the accuracy of angle measurements by using a goniometer. The authors draw incorrect conclusions because the goniometer most likely doesn't have this accuracy. We use a similar approach with a measurement accuracy of 0.0002, which is even higher than in the submitted work. However, this is not novel.

2. The authors analyze the optical power at the prism output. Where's the guarantee that the "dips" (Fig. 7) they see are related to modes and not to scattering losses or something else? It's correct to analyze the power output from the film, not the prism, to guarantee the presence of a waveguide mode. The experiment isn't entirely correct.

3. Some calculations have determined a film thickness of 400 nm, and this is claimed to be some sort of acceptable limit at a wavelength of 655 nm. This conclusion is unfounded. Furthermore, it's always possible to calculate the single-mode waveguide parameters and verify this using the prism coupling method at a wavelength of 1.55 µm (for example).

4. The strategy for determining the waveguide width solely from the fundamental mode is unclear from the paper. It's already known that for an asymmetric waveguide, there is a cutoff wavelength, which is essentially determined by the wavelength and the waveguide thickness.

5. I didn't understand either the scientific problem or the novelty of the paper. Therefore, I think that the publication of this work is not justified at this time.

6. Some graphs (Fig. 4, 6 and 7) require design improvement.

Author Response

Thank you for taking the time to review this document. Here are the answers to the issues raised:

"1. Abstract: "In this work, we developed a strategy that not only extends the thickness range of the method's calculation down to single-mode operation, but also the results' analysis led us to conclude that by solely using the fundamental modes in the calculation, the method's precision increases and the determined parameters are closer to the physical reality of the film."

What is this strategy? What is the novelty of this work? There's nothing in the text, or I didn't see it."

Well pointed out. The novelty resides in using the fundamental modes of both polarizations to extend the range of thicknesses we can calculate with the m-lines spectroscopy method. Instead of using any other pair of modes combination of the same polarization to calculate the thickness of a given film (which has been the method historically reported in literature), our strategy uses the fundamental modes and that enables us to estimate the thickness of much thinner films. Moreover, yet to be confirmed with further experiments, our calculations indicated greater agreement with Dektak thickness measurement when calculating this parameter with the fundamental modes, when compared with the traditional calculation method.

"The accuracy of the method is determined by the accuracy of angle measurements by using a goniometer. The authors draw incorrect conclusions because the goniometer most likely doesn't have this accuracy. We use a similar approach with a measurement accuracy of 0.0002, which is even higher than in the submitted work. However, this is not novel."

Thank you for pointing that out. In the new version of the manuscript, we use 0.01º as the angular step of the goniometer. We found this precision enough to reveal the discrepancy between the results obtained by the reported in literature m-lines spectroscopy method and ours, the latter being much closer to the measurement provided by Dektak. We made available online both calculation methods as Matlab live scripts (m_Lines_SiN2.mlx, m_Lines_SiN2_singleMode.mlx), which you are more than welcome to test, check and draw your own conclusions.

"2. The authors analyze the optical power at the prism output. Where's the guarantee that the "dips" (Fig. 7) they see are related to modes and not to scattering losses or something else? It's correct to analyze the power output from the film, not the prism, to guarantee the presence of a waveguide mode. The experiment isn't entirely correct."

Very well noted. In this work, we replicated the procedures of the method reported in literature. Moreover, we believe that scattering is not sensitive to polarization and Figure 7 depicts the photodetector response of unpolarized light in a), and in b) TM and TE polarizations, which shows different responses for each polarization and corresponding ones to the unpolarized response.

"3. Some calculations have determined a film thickness of 400 nm, and this is claimed to be some sort of acceptable limit at a wavelength of 655 nm. This conclusion is unfounded."

It was not our intent to claim anything; the statement results from the observation of Figure 4 where the modal indexes of TE1 and TM1 are greater than 1.528 (substrate line) for waveguides thicker than ~450 nm, thus propagating in the film waveguide for thicknesses greater than this value.

"Furthermore, it's always possible to calculate the single-mode waveguide parameters and verify this using the prism coupling method at a wavelength of 1.55 µm (for example)."

Thank you for commenting, but we are not sure how to address this issue.

"4. The strategy for determining the waveguide width solely from the fundamental mode is unclear from the paper. It's already known that for an asymmetric waveguide, there is a cutoff wavelength, which is essentially determined by the wavelength and the waveguide thickness."

Thank you again for commenting. We are afraid we are unable to see why it is unclear.

Best regards,

The authors

Reviewer 4 Report

Comments and Suggestions for Authors

The revised edition reaches the standards.

Author Response

We thank you for taking the time to review our manuscript and recommend it for publication.

With our best regards,

The authors

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

I can not completely agree the reported thickness uncertainty may be insufficient (single-digit precision after the decimal point in deviation).
Unless the authors understand and modify the point, the manuscript will not be accepted for further publication.

Comments on the Quality of English Language

English expression has been refined. But the whole text is under revised.

Author Response

Comments 1: I can not completely agree the reported thickness uncertainty may be insufficient (single-digit precision after the decimal point in deviation).
Unless the authors understand and modify the point, the manuscript will not be accepted for further publication.

Response 1: Thank you for noticing this issue. We have increased to double-digit precision the deviation in Table 1 and in the text (marked red in the bullet point “Thickness” of page 10).

Comment 2: English expression has been refined. But the whole text is under revised.

Response 2: Your concern is most welcomed and we have revised the whole text to improve phrasing and reading clarity (marked red throughout the text). Also, the Abstract and Discussion sections have been changed and improved for clarity (marked red in the Abstract and at the beginning of the Discussion section). Figures 4, 6 and 7 have been changed to enhance readability and understanding (marked red).

Reviewer 2 Report

Comments and Suggestions for Authors

See the comments in the attached file, please.

Comments for author File: Comments.pdf

Author Response

Comment 1: The strategy in your work has become clear to me. It's not at all obvious from the discussion section. The discussion section should compare this approach with other destructive and non-destructive methods for thin-film thickness determination and provide relevant references. It is also necessary to demonstrate the advantages of this approach over other methods and its feasibility.

Response 1: We very much welcome your comments and thank you for pointing that out to us. The Abstract and Discussion sections have been changed to improve understanding and clarity (marked red in the Abstract). In the Discussion section we included how this method compares to previous indirect methods (marked red at the beginning of Discussion section); references [16 – 19] have been added to support this addition. We also added text at the start of the Materials and Methods section with supporting references [12 and 13] (marked red) to place the optical setup within context. The text has been revised for English phrasing and readability (marked red throughout the text). Figures 4, 6 and 7 have been altered to improve readability and understanding (marked red).