Theoretical Analysis of Vernier-Effect-Induced Sensitivity Enhancement of Dual Fiber Fabry-Pérot Cavities in OFDRs

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents a theoretical and numerical investigation of Vernier-effect-induced sensitivity enhancement in dual fiber Fabry-Perot (FP) cavities within Optical Frequency Domain Reflectometry (OFDR) systems. The study compares cascaded and parallel configurations and reveals that only the parallel structure achieves significant sensitivity enhancement under Vernier conditions, contrary to traditional wavelength interrogation systems. The topic is timely and relevant to the field of distributed fiber optic sensing. The theoretical derivations are thorough, and the simulation results are convincing. However, the manuscript could benefit from clearer explanations in certain sections, improved organization, and a more detailed discussion of limitations and practical implications. Below are specific comments and suggestions.

In Section 2.2.1, you state that the cascaded dual FP cavity does not exhibit sensitivity enhancement in either Mode I or Mode II. Could you elaborate on the fundamental physical reason why the Vernier effect fails to amplify sensitivity in the OFDR demodulation scheme for cascaded structures, especially when it does work in direct wavelength interrogation systems? Is this due to the inherent signal processing in OFDR (e.g., windowing, beat frequency selection), or is it a more fundamental limitation?

The parallel FP structure shows a significant sensitivity enhancement (~12.86×). However, such a structure requires careful balancing of optical path differences and may be susceptible to environmental perturbations (e.g., temperature gradients between cavities). How would you propose to stabilize the reference cavity in a practical distributed sensing system to maintain the Vernier condition over long distances and varying environmental conditions?

In optics, the interaction between light and matter—particularly the singular phenomena observed during optical reflection—is of great significance. This will also find corresponding applications in optical fibers. For instance, at the C-point of an optical singularity, reflection can induce a transformation in the state of polarization [Science China Physics, Mechanics & Astronomy, 2025, 68(4): 244211.]. Incorporating this perspective into the introduction would help emphasize the broader implications of the study.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors present a theoretical work on the analysis of vernier-effect-induced sensitivity enhancement of dual-fiber Fabry-Pérot cavities. Overall, the authors try to explain clearly, but I believe there are important aspects that need to be addressed, such as:

 

• In the first sentence of the second paragraph of the introduction, the authors confirm that FP interferometers have low sensitivity. In literature it is indicated that FP-based sensors have high sensitivities, which contradicts the authors' statement. I recommend rearranging this sentence.

 

• Not all variables in the equations are described. For example, it is not described what t and γ (equation 1). Review all equations.

 

• In the last paragraph on page 3, there is no sequence of ideas between the first sentence and the one that follows. The message is unclear. At the end of 10 THz/s, I suggest adding a reference to indicate that there is equipment that can perform the sweep at that frequency.

 

• In that same paragraph, why were these values ​​for refractive index and cavity length chosen? Also, justify the other values ​​used

Besides, I suggest showing on a table all the values ​​used to obtain the theoretical results shown in all the figures.

 

• What is the physical model of the FP? It is not known what delimits the cavity.

If the analysis considers fiber FP (mentioned in the title), I assume the cavities are filled with air. In this sense, I consider it important to mention the physical model used for simulation and cite articles that have published this type of FP.

• The last paragraph on page 6, authors mentioned that both thermal coefficients change, but not all materials have both coefficients of the same magnitude. How is sensitivity affected if one changes more than the other? How does it affect sensitivity if both PFs are temperature-sensitive?

 

• If the changes depend on values of both coefficients, I think it's important to analyze how sensitivity changes based on changes in these values.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This article analyzes the sensitivity enhancement effect of two types of dual-fiber Fabry-Perot (FP) cavity sensing units based on the Vernier effect in optical frequency domain reflectometry (OFDR). The study includes both theoretical analysis and experimental research. When the conditions for the Vernier effect are met, the sensitivity of the cascaded FP sensor sensing unit is 9.99 pm/°C, while the sensitivity of the parallel FP sensor sensing unit reaches 128.97 pm/°C. These findings hold certain value, but there are still some questions that need to be addressed.

 

Question 1: The specific structural configuration of the F-P sensors used in the experiment is not detailed in the article. Could you provide information about the relevant structure?

 

Question 2: In the sensing system described in Figure 4, which F-P cavity's optical path difference changes with temperature, and how does it change?

 

Question 3: While the paper provides a thorough theoretical analysis, it lacks a comparison and analysis of the experimental results alongside the theoretical analysis. Please supplement this.

 

Question 4: The sensor in Figure 8 has a reference cavity structure, whereas the sensor in Figure 4 does not have such a reference cavity structure. I think the lack of amplification effect in the system depicted in Figure 4 may be due to the non-functioning of a structure that should act similarly to a reference cavity. What is your analysis regarding the reason why the Vernier effect did not produce an amplification effect? Please describe it in detail and provide appropriate improvement suggestions.

 

Question 5: The statement “fiber-optic Fabry-Pérot (FP) sensors play an important role for their high sensitivities and simple structures. They have been employed in the measurement of temperature, strain, pressure, refractive index and so on” could be further strengthened by citing some representative works on their applications in acoustic wave sensing. These references would provide additional support to the authors’ discussion.

 

 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper can be accepted.

Reviewer 2 Report

Comments and Suggestions for Authors

Most of the comments were addressed satisfactorily

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have responded all the concerns.