Spatio-Temporal Dynamics of Pulses in Multimode Fibers
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors presented experimental measurements of the spatio-temporal dynamics of ultrashort pulses in few-mode fiber. It was demonstrated that the interactions between different modes (LP01, LP11a, and LP11b) are nonlinear. When a single spatial mode was excited, the authors observed symmetry breaking of the spatial overlap integral at specific wavelengths, leading to energy transfer between the modes at these wavelengths. When a combination of spatial modes was excited, the two modes enhance the nonlinear interaction of each mode separately, leading to increased output power at the third mode. So, the authors conclude that it is possible to transfer energy between the modes even when the overlap integral vanishes and the coupling is zero. The work is interesting and results seem to be reliable. I have only the following minor comments.
1. Insets in Fig. 1 show three curves but what each of them corresponds to is not clear.
2. In Fig. 5, all markers are shown in the same color. It would be easier to understand if measurements for different modes were coded by different colors.
3. There are typos in the text, for example:
Lines 81-82 “…the spectral resolution in 0.19 nm”; in ->is;
Fig. 2, y-axis: “Normlized intensity” -> Normalized intensity.
4. Some acronyms are not explained, for example:
Lines 45: “…a propagating mode inside GIMF”.
Author Response
Response letter to reviewer #1
We would like to thank the reviewer for his\her time and effort in reviewing our manuscript. We revised the manuscript according to all the reviewers’ comments.
Here are our responses to each comment:
REVIEWER COMMENTS
- “Insets in Fig. 1 show three curves but what each of them corresponds to is not clear.”
The reviewer is correct, we revised the caption of Fig.1 to include:
“Schematics of the experimental setup. The two insets show representative results acquired by the optical spectrum analyzer (OSA) and oscilloscope (Scope), when we excite . Solid, dashed, and doted curves represent output modes , and , respectively.”
- “in Fig. 5, all markers are shown in the same color. It would be easier to understand if measurements for different modes were coded by different colors."
Per the comment by the reviewer, we coded the measurements of the different modes into different colors as well: blue circle marker - , red star marker - , and green square marker - .
- “There are typos in the text, for example:
Lines 81-82 “…the spectral resolution in 0.19 nm”; in ->is;
Fig. 2, y-axis: “Normlized intensity” -> Normalized intensity.”
We fixed the typos.
- “Some acronyms are not explained, for example:
Lines 45: “…a propagating mode inside GIMF”.”
Per the comment by the reviewer, we explained the suggested acronym, along with some more acronyms:
"... in single-mode fibers (SMFs) "
"...a propagating mode inside garaged-index multimode fiber (GIMF) "
"...of a linearly polarized (??) propagating.. "
"...which occurs in a highly nonlinear fiber (HNLF)."
"...the dispersion-compensating fiber (DCF) "
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper presents experimental measurements of the spatio-temporal dynamics of ultrashort pulses in multimode fibers, investigating the nonlinear interactions between different spatial modes in a few-mode fiber. After a thorough review, I believe that some areas of this manuscript need significant revisions to meet publication standards.
In the introduction section:
The unique contributions of the article should be emphasized to clarify for the reader the originality and contributions of the work.
Four-wave mixing occupies a significant portion of the authors' experimental study. The rationale for designing an experiment on four-wave mixing to study spatio-temporal dynamics needs to be clearly explained.
In the methods section:
The most important parameter affecting mode coupling is the propagating constants of the modes, which was neither discussed nor mentioned in the manuscript.
Modes with similar propagating constants mean that a phase matching condition is achieved. When describing a phase matching scenario, the distance 'z' usually is involved because it requires a certain distance to complement power coupling. However, the parameter 'distance' was not shown in Equation 3 or 4.
In the experimental and discussion sections:
The transmission dynamics of pulses in multimode fibers have been extensively studied, as seen in works like "Wright, L. G., Christodoulides, D. N., & Wise, F. W. (2017). Spatiotemporal mode-locking in multimode fiber lasers. Science, 358(6359), 94-97," "Cao, B., Gao, C., Liu, K., Xiao, X., Yang, C., & Bao, C. (2023). Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers. Light: Science & Applications, 12(1), 260," and "Wright, L. G., Renninger, W. H., Christodoulides, D. N., & Wise, F. W. (2015). Spatiotemporal dynamics of multimode optical solitons. Optics express, 23(3), 3492-3506." Simulation methods are well-developed and even available online. I strongly recommend that the authors include a simulation section in their paper to support their conclusions.
The discussion states, "Specifically, we observe that it is possible to receive energy in the output modes of LP01 and LP11b when we excite LP11a, although the overlap integral of this energy transfer vanishes due to symmetry." However, it is very common for fiber manufacturing processes to cause inhomogeneities in the refractive index. Although this perturbation is small, it can cause coupling of multiple modes over some distances. Therefore, this observation does not support the authors' conclusions.
Although the paper describes experimental results, it lacks an in-depth analysis of these results and does not discuss the underlying physical mechanisms.
The experiments both involve the process of four-wave mixing and the coupling between different modes. Discussing these two aspects separately would help readers better understand the authors' intentions, provided that such an experimental design is justified.
Author Response
Response letter to reviewer #2
We would like to thank the reviewer for his\her time and effort in reviewing our manuscript. We revised the manuscript according to all the reviewers’ comments.
Since we added figures and equations, please refer to the PDF file for the detailed changes and corrections done to the manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsReview of “Spatio-temporal dynamics of pulses in multimode fibers,” by Tamir et al.
This paper reports a direct way to monitor nonlinear wave propagation in multimode fiber with high temporal resolution: mode multiplexors are used to launch and detect the propagating modes, and time resolution is obtained by a time lens based on 4-wave mixing. Multimode nonlinear pulse propagation is generally complex and tools that allow researchers to monitor it are welcome. Although the approach is straightforward, I am not aware of its use previously. Simple examples of 3 modes interacting in a graded-index fiber are presented. The technique is illustrated by measuring spectra of the different modes, although it is also capable of measuring the time evolution with ~6-ps resolution (but reduced signal sensitivity). The examples are interesting but really serve to illustrate the technique more than to study new nonlinear wave physics.
For the most part, the work is set in context correctly and motivated well. I think the paper deserves to be published in Photonics.
The technique is conceptually the same as the mode-resolved excitation and detection techniques based on spatial light modulators developed by Joel Carpenter, so that work should be referenced in the introduction.
The paper would benefit from some discussion of the limits of the technique. How many modes can be monitored, with existing technology and ultimately?
Details
What are DCF, CDF, and SMF as subscripts of L? I can guess but they should be defined.
Mux should be defined on first use, even if it is obvious.
Why does the caption to Fig. 2 say “Spatial structures?”
What is CDWM?
Intensity is not measured in mW.
Comments on the Quality of English LanguageThe manuscript has minor language and punctuation errors that should be fixed.
Author Response
Response letter to reviewer #3
We would like to thank the reviewer for his\her time and effort in reviewing our manuscript. We revised the manuscript according to all the reviewers’ comments.
Here are our responses to each comment:
REVIEWER COMMENTS
- “The technique is conceptually the same as the mode-resolved excitation and detection techniques based on spatial light modulators developed by Joel Carpenter, so that work should be referenced in the introduction.”
We added this to the second paragraph of the introduction:
Different theoretical models and advanced numerical tools were developed for analyzing these phenomena, including, the effective potential model [18] the multi-component approach [19], the 3D+1 nonlinear Schrodinger equation [20], the Gross-Pitaevskii equations [21], and the Laguerre-Gaussian mode sorter [22].”
We also cite the paper as reference number [22].
- “The paper would benefit from some discussion of the limits of the technique. How many modes can be monitored, with existing technology and ultimately?"
Per the comment by the reviewer, we added the following paragraph at the end of the results section:
"While our system offers the advantage of high temporal resolution, it has several limitations. The number of spatial modes we can measure and monitor depends on our ability to separate them, namely, the distinguishability of our LP MUX, which degrades as we increase the number of modes. Another limitation is the sensitivity of the fiber to changes, such as temperature variations, physical bending, and mechanical stresses. This sensitivity can cause modal dispersion and redundant coupling between the modes, thereby limiting our ability to identify the nonlinear modal dynamics. We mitigate these limitations by handling the fiber carefully and focusing only on dynamics that have a quadratic power dependence. "
- What are DCF, CDF, and SMF as subscripts of L? I can guess but they should be defined.”
Per the comment by the reviewer, we explained the following:
" ...based on single-mode fibers (SMFs)."
" ...and is the length of the dispersion-compensating fiber (DCF) or SMF."
- “Mux should be defined on first use, even if it is obvious.”
Per the comment by the reviewer, we added the following:
"We excite with the signal pulse different modes in a few-mode fiber (FM GI-4, YOFC) with an LP multiplexer (MUX) (LPMUX3-1550, Modular Photonics)"
- "Why does the caption to Fig. 2 say “Spatial structures?”
Per the comment by the reviewer, we revised the caption of Fig.2:
"Spectral structures of the measured (a) idler and (b) signal at output mode when exciting mode."
- "What is CWDM?"
Per the comment by the reviewer, we explain the acronym:
"We combine the pump and signal waves with a Coarse Wavelength Division Multiplexer (CWDM) before sending them into the HNLF."
- "Intensity is not measured in mW."
Per the comment by the reviewer, we replaced 'intensity' to 'power'.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsMy concerns have been addressed. This manuscript is recommended to be accepted in its present form.
