Modeling Femtosecond Beam Propagation in Dielectric Hollow-Core Waveguides

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, the authors investigated the propagation of femtosecond pulses in a gas-filled hollow-core waveguide. They employed the split-step method to solve Maxwell’s wave equations, and the validity of this approach was confirmed by comparing the results with those obtained from a finite-difference time-dependent (FDTD) calculation. They found that the beam profile at the entrance plane is critical, and they considered a variety of parameters involved in the experiments. Additionally, the scaling of laser beam propagation and high harmonic generation (HHG) was examined. Once more waveguide modes are involved, the scaling no longer holds.

Overall, this is an interesting and timely work, especially given the growing experimental and theoretical efforts to use gas-filled waveguides for HHG, which are expected to significantly improve HHG conversion efficiency. I believe this is a valuable contribution to the attosecond science community. Therefore, I recommend that this manuscript be published in Photonics, pending the resolution of the following points:

(1) When the authors use the split-step method to solve Maxwell’s wave equation, the maximum value of normal modes (Equation 5) is capped at 16. This seems significantly lower compared to recent theoretical work [Optics Express 32, 48972 (2024)], where high intensity and pressure were applied to excite higher waveguide modes. I wonder if the agreement between the two methods in Figure 1 could be improved by significantly increasing the number of normal modes.

(2) In the introduction, it would be helpful to reference several related works that highlight the advantages of gas-filled waveguides. For example, a recent study [Phys. Rev. A 110, 043511 (2024)] demonstrates that a plasma-induced flat-top beam can be formed in a gas-filled waveguide, which effectively mitigates chromatic aberration in HHG. Other relevant references include [Science 336, 1287 (2012); PNAS 106, 10516 (2009); Opt. Express 29, 27416 (2021)].

(3) In the abstract, the authors stated: “Our model is based on a split-step method modified to account for propagation in ionized media and is validated against experimental data and finite-difference time-dependent models.” However, I did not see any experimental data in the manuscript. This statement should be revised.

(4) The authors presented HHG results in Figure 10, but there are no details regarding the calculation methods. Which approach is used to calculate the single-atom response? What equation is used to account for the propagation of high harmonics in the waveguide?

(5) It is very insightful to discuss the scaling of laser propagation and HHG in the gas-filled waveguide. Some points could be presented more clearly. The scaling relations hold when the driving laser couples with only one waveguide mode, as clearly demonstrated in Ref. [19]. However, if the driving laser couples with multiple waveguide modes—either due to the initial beam profile or because additional modes are excited during propagation due to excessive free electrons—the scaling relations are no longer valid. These are important conclusions that should be highlighted more explicitly in the manuscript.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

 

The manuscript details the simulated evolution of an ultrshort laser pulse within a hollow core waveguide (HCW) to use this knowledge to study high harmonic generation (HHG). The focus of the study is on the laser electric field evolution as the function of the length of the HCW, by investigating different spatial profiles, input couplings and waveguide type. Their main claim is on extending the well reknown scaling law of high harmonic generation to HCWs, concluding that the main factor is the mode beating.

 

The proposed study is very interesting and relevant to the new research direction of application of microfluidic devices in HHG. The presented results can be of great interest of experimental researchers helping them both in designing HCWs and understanding the HHG process in these waveguides. I would consider the manuscript for publication after addressing the following minor remakrs, that I think would lead to better understanding of the manuscript:

 

1) Line 77: please give reference citation for the split step method.

2) Equation (7): Please explain why did you omit the diffraction term here and why not in equation (3). It may be trivial, but less experienced researchers would understand it better.

3) The explanation of Figure 5 a and b is not consistent between the text (lines 193-199) and the caption.

4) Lines 315-316: It is not clear what the authors mean under ”fine structure of harmonic field” and how it is related to short coherence length?

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf