Transmission Matrix-Inspired Optimization for Mode Control in a 6 × 1 Photonic Lantern-Based Fiber Laser

Round 1

Reviewer 1 Report

In this paper, a novel control strategy is proposed using the prior structural information of the photonic lantern. Compared with the random and equal amplitude control methods, the preset method from the transmission matrix presents a significant improvement in the desired mode content. The analysis proposed seems to be solid and the presented results demonstrate that the proposed algorithm has distinct advantages. Using these photonic lantern-related initial amplitudes, the fiber laser system can achieve almost perfect mode content for all six modes within 1 ms. Additionally, the paper is well written, and related literature is well referenced. However, the contents in Figure 3-Figure 5 are not clear. It is recommended that authors make the picture clearer. In view of the above, I generally recommend acceptance of this paper after minor revision.

Author Response

Thank you very much for your positive and constructive review report. Please refer to our response to your comment.

Comment:

The contents in Figure 3-Figure 5 are not clear. It is recommended that authors make the picture clearer.

Response:

We have make Figure 3-Figure 5 more clearer. Besides, we have marked the final contents of the target mode in the figures to help the readers to compare the control effects more directly.

Reviewer 2 Report

The authors demonstrate a novel control strategy by using the prior structural information of the photonic lantern to achieve mode control in LMA fiber laser system. This study is somewhat interesting and original. This report provides sufficient discussion of the subject and is  understandable. Therefore, I would like to suggest publication of this manuscript providing the following comments are addressed:

1. Some terms and variables in the manuscript are introduced without proper explanations. We shall indicate only the first one when the authors on the second page of the manuscript introduce LP modes without explanation or reference.

2. “D_waist” in Fig. 2 is not clear or misleading. I wonder how the outer diameter is so thin as 25um? Perhaps the authors meant to label it " d_waist "?

3. The authors provide simulation results in initializing the amplitude inputs. I think the preset input amplitudes for different modes or the transmission matrix need to be listed in detail or attach to appendix.

Author Response

Thank you very much for your positive and constructive review report. Please refer to our replies below to all your comments.

 

Comment 1:

Some terms and variables in the manuscript are introduced without proper explanations. We shall indicate only the first one when the authors on the second page of the manuscript introduce LP modes without explanation or reference.

Response:

Thanks for this comment. We are sorry to make such a mistake and cause difficulties for readers. We added the explanation that LP modes means linearly polarized mode. And we have double-checked to make sure the other abbreviations in the article were explained.

 

Comment 2:

“D_waist” in Fig. 2 is not clear or misleading. I wonder how the outer diameter is so thin as 25um? Perhaps the authors meant to label it " d_waist "?

Response:

Thanks for this very constructive comment. We have rewritten D_waist into d_waist. d_waist is the waist region diameter of the tapered SMFs bundle.

 

Comment 3:

The authors provide simulation results in initializing the amplitude inputs. I think the preset input amplitudes for different modes or the transmission matrix need to be listed in detail or attach to appendix.

Response:

Thanks for this very constructive comment. We give the transmission matrix of the 6×1 photonic lantern. Please refer to formula (2) in Chapter 2.

Reviewer 3 Report

Review: manuscript ID photonics-2251702

 

The submitted manuscript titled Transmission matrix-inspired optimization for mode control in a 6×1 photonic lantern-based fiber laser focuses on light control through photonic lantern (PL) using stochastic parallel gradient descent (SPDG) optimization. In contrast to conventional wavefront shaping methods for structured light generation using a spatial light modulator in a free-space configurations, the approach followed in this work makes use of spatial degrees of freedom that are provided by multiple single-mode fibers combined in a jacket and tapered to a multimode waveguide. Thus, the PL comprises of a multi single-mode input and multimode output. To the reviewer’s opinion, this approach has among others the highest efficiency gains in terms of low loss light delivery making this research topic highly relevant. However, the authors could improve discussion of trade-offs of their approach work comparing with classic wavefront shaping, although the authors claim that their application field lies in high-power lasers.

 

By controlling the input modes, i.e. amplitude of the SMF front ends, the output is shaped. The scientific challenge to tackle is determining appropriate starting conditions for the SPGD optimization algorithm. The authors compare three different strategies namely random, equal and transmission matrix inspired conditions to shape the modes at the output. Their research work comprises of simulations only, which could benefit from at least a vague estimation of how it could be realized experimentally. Although no experiments are shown, the results are interesting and to the reviewer’s opinion well suited for the readership of MDPI photonics. However, some details of the work are unclear, somewhat confusing and have to be revised carefully, before acceptance can be recommended.

 

After reading the manuscript it is seriously evident that the authors use a quasi-transmission matrix (TM) method that is neither introduced nor explained in detail. The just claim that the TM of a PL can be used to determine a suitable preset of amplitude coefficients for SPGD optimization. In particular, there are essential points that must be considered in a revision:

·         How do the authors determine the TM of the PL in the simulation? Do they assume random occupation of the TM entries, i.e. matrix A (equation (1))?

·         In coherent optics, the TM is always a complex quantity. Are complex quantities also used here, of which only the amplitude is used after inverting the TM? Since only simulation results are shown in the paper, a deeper mathematical description of the TM is required, especially with reference to seminal papers on optical TM:

o   Popoff, Sébastien M., et al. "Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media." Physical review letters 104.10 (2010): 100601.

Papers on TM in multimode fiber that should be cited:

o   Li, Shuhui, et al. "Memory effect assisted imaging through multimode optical fibres." Nature Communications 12.1 (2021): 3751.

o   Rothe, Stefan, et al. "Securing Data in Multimode Fibres by Exploiting Mode-Dependent Light Propagation Effects." Research (2023).

o   Mounaix, Mickael, and Joel Carpenter. "Control of the temporal and polarization response of a multimode fiber." Nature communications 10.1 (2019): 5085.

o   Turtaev, Sergey, et al. "High-fidelity multimode fibre-based endoscopy for deep brain in vivo imaging." Light: Science & Applications 7.1 (2018): 92.

o   Tzang, Omer, et al. "Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres." Nature Photonics 12.6 (2018): 368-374.

 

·         How is the TM of the PL measured? In an experimental realization a phase retrieval would have to be used. Which one is suitable for the PL for this purpose? Even if the Authors show only simulations, an experimental realization should be discussed.

 

 

(l. 33) In the introduction, the authors claim that PLs can be employed as spatial multiplexer with mode-selective ability. The expert does not want to fundamentally contradict this claim, but would like to emphasize that PLs are much more difficult to fabricate with mode selectivity, and if so, then only with a significantly reduced number of modes than mode multiplexers with programmable optics such as an SLM. Since mode selectivity is generally not present in PLSs, the authors work on transmitter-side presetting in order to achieve selectivity. For this reason, it should be included in the introduction that selectivity is a criterion very difficult to achieve with a high number of modes in PLs. In turn, many more papers could be cited that work with adaptive optical elements in free-space configurations, which can achieve the highest mode selectivity. For example, via standard computer-generated holograms:

 

·         Arrizón, Victor, et al. "Pixelated phase computer holograms for the accurate encoding of scalar complex fields." JOSA A 24.11 (2007): 3500-3507.

·         Goorden, Sebastianus A., Jacopo Bertolotti, and Allard P. Mosk. "Superpixel-based spatial amplitude and phase modulation using a digital micromirror device." Optics express 22.15 (2014): 17999-18009.

·         Forbes, Andrew, Angela Dudley, and Melanie McLaren. "Creation and detection of optical modes with spatial light modulators." Advances in Optics and Photonics 8.2 (2016): 200-227.

·         Rothe, Stefan, et al. "Benchmarking analysis of computer generated holograms for complex wavefront shaping using pixelated phase modulators." Optics Express 29.23 (2021): 37602-37616.

 

or Multiplane Light conversion

·         Labroille, Guillaume, et al. "Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion." Optics express 22.13 (2014): 15599-15607.

·         Fontaine, Nicolas K., et al. "Design of high order mode-multiplexers using multiplane light conversion." 2017 European Conference on Optical Communication (ECOC). IEEE, 2017.

·         Fontaine, Nicolas K., et al. "Laguerre-Gaussian mode sorter." Nature communications 10.1 (2019): 1865.

 

(ll.39-42) The authors describe that LMA fibers are used to reduce transverse instabilities. Do the authors refer to the effect of transverse mode instability (TMI)? If this is the case, they should name it and cite corresponding papers, such as:

·         Gaida, Christian, et al. "Transverse mode instability and thermal effects in thulium-doped fiber amplifiers under high thermal loads." Optics Express 29.10 (2021): 14963-14973.

 

(ll. 43-50) The authors state that coiling is a commonly used measure to reduce instabilities. However, HOMs are lost in the process. Therefore, active methods are explored but not described in detail. These should definitely be mentioned, as the method proposed by the authors should be compared to the state of the art! The authors claim that in the other methods, which are not described, only the intensity is modulated, but not the phase. The reviewer finds that the authors also only set amplitude coefficients with the SPGD algorithm (see line 154 "Next, we have simulated three amplitude control methods"). The reviewer asks for a thorough clarification.

 

(l. 52) The authors claim that linear correlation between input and output can be optimized. The reviewer asks to explain this more clearly. In the following sentences, the authors refer to experiments at MIT, which is extremely misleading.

 

(l. 72) Please consistently use only the abbreviation PL when introduced.

 

At the beginning of section 2.1, the fabrication of PL is discussed in more detail. The manufacturing process is also described again at the beginning of section 3.1. First, the reading flow is disturbed by these redundancies and should be revised. Second, it is not clear why this manufacturing process is important for the work shown if only simulation is used anyway. Simulation results on effective index versus taper ratio would be more important (see Huang, Bin, et al. "All-fiber mode-group-selective photonic lantern using graded-index multimode fibers." Optics express 23.1 (2015): 224-234.)

 

(l. 93) V_LP01 is introduced, but remains without use. In the opinion of the reviewer, the description of this matrix formalism is generally unnecessary and rather looks like a student's work.

 

The introduction and description of the SPGD in section 2.2 is extremely unclear and confusing. Some fragments appear that disturb the reading flow. After reading several times, it is not clear to the reviewer what exactly is being carried out with the SPGD. Which voltages are used in the optimization process and how would this be applied to an experiment? Intuitively, one would assume that initial input amplitude values are adapted and the complex portion of the respective mode is optimized. The algorithm should be described on the basis of these parameters.

 

Figure 2 contains some illustration errors.

 

In chapter 3, the authors show optimization on the modal percentage. It is not clear to the reviewer how the percentage is calculated. A mathematical description such as fidelity is missing. What the reviewer finds confusing is the fact that the modal content refers to complex field quantities. The relative percentage is a real quantity. In the work shown, however, the phase information is missing, which is in contradiction to the claim in the introduction.

 

The authors claim that the method works in real-time. A time scale is given in the plots, but without any comment on real-time capability. Whether a system is real-time or not always varies with the realization environment. What is being measured here?

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

please see the attached file.

Comments for author File: Comments.pdf

Author Response

Thank you very much for your positive and constructive review report. Please refer to our replies below to all your comments.

 

Comment 1:

The reference formats are too chaotic, they should be consistent.

Response:

Thanks for this comment. We are sorry to make such a mistake and cause difficulties for readers. We have cited the references according to the consistent format in our revision.

 

Comment 2:

Most references were published before 2017. I don’t think authors know the literature.

Response:

Thanks for this very constructive comment. Through a broader review of the literatures, we cited seven more papers published after 2017.

Round 2

Reviewer 3 Report

All my concerns have been adressed. The reading of the manuscript has improved clearly.

It is not required to explicitly show entries of the transmission matrix in equation (2). It is sufficient to qualitatively mention that a simulated TM was created by beam propagation method (BPM). A reference should still be given for the BPM!

There are linguistic deficiencies which should be thoroughly checked again by the editorial team.

Author Response

Dear Reviewer,

Thank you very much for your positive and constructive review report. Please refer to our replies to your comments.

Comment 1:
It is not required to explicitly show entries of the transmission matrix in equation (2). It is sufficient to qualitatively mention that a simulated TM was created by beam propagation method (BPM). A reference should still be given for the BPM!

Response:
Thanks for this constructive comment. We have cited references about BPM in the revision. However, please forgive us for keeping equation (2) in the manuscript. As requested by another reviewer in the first round of review, it is necessary to provide the transmission matrix of the 6×1 photonic lantern to present the detailed prefabricated input amplitude conditions for later simulations.

Comment 2:
There are linguistic deficiencies which should be thoroughly checked again.

Response:
Thanks for this comment. We were sorry to make spelling mistakes and grammatical errors. We asked a native speaker to help us. Now we have corrected these mistakes.

Thank you again.

Yours sincerely, 
Yao Lu