The Influence of Ultrashort Laser Pulse Duration on Shock Wave Generation in Water Under Tight Focusing Conditions
Awanish Pratap Singh
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease find my comment attached.
Comments for author File: 
Comments.pdf
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsPhotonics – 3881278
The reviewed manuscript “Nikita Rishkov, Nika Asharchuk, Vladimir Yusupov, and Evgenii Mareev: The influence of ultrashort laser pulse duration on shock wave generation in water under tight focusing condition” is devoted to the experimental and theoretical study of the amplitude of the shock wave induced in water by laser pulses of different duration and fluence. I think this work is in a good shape. I would like to recommend it for publication by Photonics after some minor revisions.
On line 209, page 7: “Figure 4a demonstrates” …delete “a”.
Figure 5: The scale on the right side of Fig. 5b should be moved to the left in Fig. 5a.
On line 236, page 7: “This relationship is logical“ could be edited to „This relationship is obvious”.
Figure 6: It is not surprising that the experimental data are given in arbitrary units. However, it is striking that the calculated dependencies of plasma energy (Eplasma or Ekin?) on pulse duration and fluence is not given in Joules. This reduces the significance of the calculations presented in Fig. 6.
Author Response
We sincerely thank the reviewers for their time, insightful comments, and constructive criticism, which have helped us significantly improve our manuscript. In response to the points raised, we have thoroughly revised the manuscript. The key modifications include:
- Rewriting the Introduction and Conclusion to better frame the study's contributions and contextualize the findings.
- Adding a detailed parameter table for the DRE model and including a sensitivity analysis.
- Expanding the descriptions of the experimental and numerical methods to enhance reproducibility.
All changes have been implemented in the manuscript, and a red-line version highlighting all modifications is provided for the reviewers' convenience. Our point-by-point responses to the specific comments are detailed below.
- On line 209, page 7: “Figure 4a demonstrates” …delete “a”.
Answer: We fixed this typo.
- Figure 5: The scale on the right side of Fig. 5b should be moved to the left in Fig. 5a.
Answer: We added the scale to the left part.
- On line 236, page 7: “This relationship is logical“ could be edited to „This relationship is obvious”.
Answer: We removed this phrase from the manuscript.
- Figure 6: It is not surprising that the experimental data are given in arbitrary units. However, it is striking that the calculated dependencies of plasma energy (Eplasma or Ekin?) on pulse duration and fluence is not given in Joules. This reduces the significance of the calculations presented in Fig. 6.
Answer: We acknowledge that presenting the plasma energy in Joules would be the ideal case for a direct quantitative comparison. However, we must respectfully clarify that the use of arbitrary units (a.u.) in this specific calculation was a deliberate and necessary choice. The primary reason for this is that our model does not definitively classify the plasma as strictly ideal or non-ideal across the entire range of parameters studied. The correct calculation of the total plasma energy from first principles requires different theoretical treatments and, crucially, different pre-factors and coefficients in front of the sum of kinetic energies for ideal versus non-ideal plasmas. Since the state of the plasma is transitional and model-dependent in our simulations, applying a single, specific conversion factor would be unjustified and could potentially be misleading.
Reviewer 3 Report
Comments and Suggestions for AuthorsIn the abstract, the authors are encouraged to elaborate on the research background to provide not only the results, but a more comprehensive context for their study (state of the problem, possible solutions, solution selected, etc.).
The authors should consider condensing the results section of the abstract to no more than two sentences for improved clarity and conciseness.
In the introduction, it is recommended that the authors clearly articulate their main contributions, as well as provide an overview of the manuscript's organization, ideally in separate paragraphs for better clarity.
In the Materials section authors stated that to avoid the influence of preceding pulses, the experiments were performed at a repetition rate of 10 Hz (since the effects of previous pulses become significant at frequencies above 20 Hz). Please state in the text what kind of influence you faced with and why?
It is also suggested that the authors provide additional details regarding the system calibration process to enhance understanding.
The Methods section is rather short. Provide more details on numerical simulations performed. Even if it is already described in [31], the reader should get the basic understanding from the text of the manuscript rather then search for a description in this reference.
Are the results from Fig. 2 experimental or numerical? Please provide a comparison of simulation and experimental results.
What are the limitations of proposed technique? A more structured presentation of these constraints, along with potential strategies for addressing or mitigating them in future research, would enhance clarity and provide valuable insights for readers.
Minor issues
- The manuscript contains several minor linguistic and terminological inaccuracies.
- All numbered equations have to be referenced in the text.
- Please, use inline equation formatting (i.e., for term r right after eq. 2)
- Provide a textual description of axis for Fig. 3.
Author Response
We sincerely thank the reviewers for their time, insightful comments, and constructive criticism, which have helped us significantly improve our manuscript. In response to the points raised, we have thoroughly revised the manuscript. The key modifications include:
- Rewriting the Introduction and Conclusion to better frame the study's contributions and contextualize the findings.
- Adding a detailed parameter table for the DRE model and including a sensitivity analysis.
- Expanding the descriptions of the experimental and numerical methods to enhance reproducibility.
All changes have been implemented in the manuscript, and a red-line version highlighting all modifications is provided for the reviewers' convenience. Our point-by-point responses to the specific comments are detailed below.
- In the abstract, the authors are encouraged to elaborate on the research background to provide not only the results, but a more comprehensive context for their study (state of the problem, possible solutions, solution selected, etc.). The authors should consider condensing the results section of the abstract to no more than two sentences for improved clarity and conciseness.
Answer: We have revised the abstract to address this comment.
The revised abstract now includes: a clear statement of the research background and the specific problem being addressed (the need to understand and control mechanical effects in water), a description of the selected methodology (combined experimental and numerical approach using the DRE model),a results section, limited to two core sentences that highlight the main findings: the governing role of electron kinetic energy and the identified optimal pulse duration with its confidence interval and final sentence stating the practical outcome and application window.
- In the introduction, it is recommended that the authors clearly articulate their main contributions, as well as provide an overview of the manuscript's organization, ideally in separate paragraphs for better clarity.
Answer: We have carefully refined the introduction to more clearly highlight the key findings and novel aspects of our work. We believe the introduction now provides a concise and effective summary of our contributions. Regarding the proposal to add a dedicated paragraph in the Introduction outlining the manuscript's organization, we have given it serious consideration. While we recognize the potential benefit for clarity, we are also mindful of the overall length of the manuscript. After careful revision, we found that integrating the core narrative of our contributions seamlessly into the existing flow of the Introduction allows us to maintain a focused and compact structure without sacrificing clarity. We hope that the current version, which has been further polished, successfully balances a clear presentation of our work with the need for conciseness.
- In the Materials section authors stated that to avoid the influence of preceding pulses, the experiments were performed at a repetition rate of 10 Hz (since the effects of previous pulses become significant at frequencies above 20 Hz). Please state in the text what kind of influence you faced with and why?
Answer: The primary influence of preceding pulses at higher repetition rates (>20 Hz) is the persistence of residual cavitation bubbles and possible long-lived chemical species (e.g., solvated electrons, radicals) from the previous laser-induced breakdown event. When the repetition rate is too high, the subsequent laser pulse does not interact with a pristine liquid. Instead, it interacts with this modified medium. These effects manifest experimentally as a significant increase in the standard deviation of both the transmitted energy and the hydrophone signal amplitude, indicating a loss of reproducibility and control. We have added a sentence to the Materials and Methods section to explicitly state this rationale and also in the Supplementary Materials demonstrate the increase fluctuations.
- It is also suggested that the authors provide additional details regarding the system calibration process to enhance understanding.
Answer: We added the description of the calibration procedure to the text of the manuscript.
- The Methods section is rather short. Provide more details on numerical simulations performed. Even if it is already described in [31], the reader should get the basic understanding from the text of the manuscript rather then search for a description in this reference.
Answer: We provide an additional description, added a Table with simulation parameters, necessary references and sensitivity analysis.
- Are the results from Fig. 2 experimental or numerical? Please provide a comparison of simulation and experimental results.
Answer: It is experimental. The comparison between experimental and numerical results is provided in Fig.4. W also added the description of threshold determination technique to the text of the manuscript.
- What are the limitations of proposed technique? A more structured presentation of these constraints, along with potential strategies for addressing or mitigating them in future research, would enhance clarity and provide valuable insights for readers.
Answer: We added the additional paragraph to the Discussion section, as it is presented below:
“For processes aiming to maximize mechanical effects, such as histogenesis in laser surgery or nanoparticle synthesis via laser ablation in liquids, we identify an optimal parameter window of 4–6 ps pulse duration and 5–8 J/cm² fluence under our experimental conditions (1030 nm, NA=0.45). Operating within this window ensures efficient energy coupling into a shock wave while maintaining a confined plasma volume. It is crucial to delineate the boundaries of these trends. The observed saturation of shock wave amplitude and its peak versus duration are expected to break down in two key scenarios: 1) very close to the breakdown threshold, where plasma formation could be stochastic and inefficient, and 2) at very high fluences where the plasma becomes elongated into a superfilament or plume, transitioning the shock wave front from a spherical to a cylindrical geometry, which fundamentally alters its propagation and decay.
The finite bandwidth of the hydrophone, while compensated for, sets a limit on the temporal resolution of the measured pressure profile. Furthermore, potential aberration-driven changes in the focal volume, inherent to focusing through a water-glass interface with an objective, could influence the absolute energy density and thus the amplitude plateaus. We have accounted for this in our loss budget, but it remains a source of systematic uncertainty. The direct correlation between shock wave amplitude and total electron kinetic energy is strongly supported by our combined experimental and numerical data. However, we posit as a hypothesis that the peak at ~5 ps is due to a balance between the increasing efficiency of avalanche ionization and the growing influence of recombination. While this is the most plausible explanation given our model, future time-resolved studies of the plasma emission could provide direct validation.
Finally, we specify that our conclusions are valid within the boundary conditions of this study: near-infrared radiation (1030 nm) and tight focusing in water. Generalization to other wavelengths (e.g., in the visible or mid-IR) or different focusing geometries (e.g., loose focusing or water-immersion objectives) would require verification, as the relative roles of photoionization and avalanche ionization are wave-length-dependent, and the focal energy density is strongly NA-dependent”
- The manuscript contains several minor linguistic and terminological inaccuracies.
Answer: We tried to fix all inaccuracies
- All numbered equations have to be referenced in the text.
Answer: We referenced all equations.
- Please, use inline equation formatting (i.e., for term r right after eq. 2)
Answer: We fixed non-inline equations.
- Provide a textual description of axis for Fig. 3.
Answer: We harmonized axis ticks/titles, legend fonts, and panel letters per journal template. The description of axis labels is given in the legend.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease find the attachment.
Comments for author File: Comments.pdf
Author Response
- Unify the numerical aperture (NA). Methods and Abstract use NA = 0.42 (OptoSigma PAL-20), whereas Conclusions still state NA = 0.45 and the response mentions NA ≈ 0.35 once. Please standardize all occurrences to NA = 0.42 across Abstract, Methods (including the in-figure label in Fig. 1), Results/Discussion, and Conclusions.
Answer: we corrected all NA in the manuscript.
- Reconcile the “saturation fluence” number and definition. The Abstract says saturation occurs “above ∼5 ” (defined as >90% of the plateau), while the response cites “>90% above ∼8 .” Please choose one quantitative definition (e.g., 90% of the asymptote) and one consistent value, and use it uniformly in Abstract, main text, and response. If it depends on F or τ ranges, state this explicitly.
Answer: We have reconciled this discrepancy throughout the manuscript. The unified and precise definition is as follows: The saturation fluence is defined as the value at which the shock wave amplitude reaches 90% of its maximum plateau level. For pulse durations around the optimum (4-6 ps), this occurs at a fluence of ~7 J/cm².
- Keep the “operating window” consistent. You now articulate a practical window of 4–6 ps and 5–8 ; please ensure these values (and NA) appear identically in Abstract, body, and Conclusions so readers do not encounter mixed endpoints.
Answer: we harmonized the values in abstract, body and conclusion.
- One-sentence clarification on absolute-pressure extraction. Methods report geometry, bandwidth, sensitivity, and that absolute pressure is anchored to the shadowgraph-derived pressure (uncertainty ∼10%). Please add one clarifying line indicating that you did not perform transfer-function deconvolution and, as a result, the hydrophone bandwidth primarily limits the retrieved peak.
Suggested text (adapt as needed): “Absolute pressure was obtained by anchoring hydrophone voltage to the shadowgraph-derived pressure (method uncertainty ∼10%); no transfer-function deconvolution was applied, so the hydrophone bandwidth primarily limits the retrieved peak.” C. Optics & threshold methodology
Answer: We added the following text fragment to the text of the manuscript:
«Absolute pressure was obtained by anchoring the hydrophone voltage to the shadowgraph‑derived pressure (method uncertainty ∼10%); since no transfer‑function deconvolution was applied, the hydrophone bandwidth primarily limits the retrieved peak.»
- Move beam-quality and spot size from the response into Methods. The response states M2 = 1.2 and a spot diameter of 3.2 ±5 . Please include these values (and how measured/estimated) in the Methods subsection describing focusing and tap-off calibration. This enables readers to reproduce F, I, and peak-intensity estimates.
Answer: we added the following sentence: “The laser beam had an M² value of 1.2 and a focal spot diameter of 3.2 ± 0.5 μm, as estimated from by re-imaging the focal plane onto a CCD array within a confocal microscope setup”
- Segmented-fit threshold recipe (keep as is, but cite it in the caption). The segmented regression with bootstrap 95% CI (n=1000) is exactly what was requested. Please ensure the relevant figure/caption explicitly references the method so readers can cross-walk easily.
Answer: we fixed the caption of the Figure.
- Fix equation rendering and a few typos. In the PDF, Eqs. (1)–(2) are partially garbled. Please retypeset so all symbols are visible and define each symbol once (with units where appropriate). Also correct minor typos (e.g., “shadowgramms” → “shadowgrams”, duplicated phrase “heat map map”, etc.).
Answer: we retypeset all symbols, and corrected these typos.
- Figure 2: unit correction for Eout. In Fig. 2, the transmitted energy Eout axis is labeled in J, whereas the measured values are in the µJ range. Please relabel the axis to µJ and verify unit consistency for Ein and all other parameter across the manuscript (figures, captions, and main text). A final proofread focused on units and labels would help avoid misleading notation at submission.
Answer: we fixed the typo in Fig.2, and check labels in all figures.
- Figure typography, size, and readability (minor but required). Harmonize all figure text (axis titles, tick labels, legends, panel labels, insets, annotations) with the journal template. At the final inserted size in the manuscript, all text must be readable at 100% zoom, and no figure text should exceed the manuscript body font size. Use one font family and keep a simple hierarchy—e.g., axis titles ≈11–12 pt; tick labels/legend ≈9–10 pt; panel tags (a), (b). . . ≈10 pt (one step below axis titles). Determine sizes based on appearance in the manuscript layout (single- vs. multi-panel figures scale differently). Avoid large size variation across panels. Do not over- or under-label axes—target 5–9 major ticks per axis with concise, consistent units. Leave a clear gap between heat maps and their colorbars (do not let them touch). Where sensible, aim for ∼1:1 aspect ratio in multi-panel grids and ∼1:2 or ∼1:3 in single-panel figures. Keep line weights uniform so lines do not appear overly thick or too thin across figures. Use “a.u.” for arbitrary units (avoid “arb. un.”). If any panel uses a dark/black background, render labels/overlays in white with a small light rectangle/halo for contrast.
Outcome-oriented figure captions (authors may fine-tune) Note: captions emphasize what each figure demonstrates, not a step-by-step narration. Please ensure NA/units are consistent and adjust numbers to your final values. For Fig. 1, consider using distinct colors for the dichroic mirror vs. quartz plate, which currently look similar.
Figure 1 — Experimental setup. Outcome: Integrates pump–probe shadowgraphy, energy metrology, and hydrophone diagnostics around a high-NA focus in water to simultaneously measure transmission, shock kinematics, and pressure waveforms under controlled delay. 2 Suggested Caption: Experimental setup and diagnostics. A 1030 nm femtosecond pump (brown) is polarization-attenuated (/2 + Glan prism) and tightly focused into a water cuvette by a high-NA objective (OptoSigma PAL-20, NA = 0.42 (or 0.45?)). A 527 nm nanosecond probe (green) is combined/separated with a dichroic mirror and imaged with an f = 10 cm lens onto a CCD camera for shadowgraphy of the cavitation bubble and shock wave. An FPGA delay generator sets the pump–probe timing; a quartz plate provides fine path-length/dispersion compensation. Photodetectors record incident and transmitted energies Ein and Eout. A needle hydrophone is positioned orthogonally near the focus to capture the pressure waveform. (Update any in-figure label to NA = 0.42; use distinct colors for the dichroic vs. quartz plate.)
Figure 2 — Transmission threshold and shock visualization. Outcome: Demonstrates an objective, CI-bearing breakdown threshold and confirms shock formation/expansion at above-threshold fluence. Suggested Caption: Transmission threshold and shock visualization. (a) Eout versus Ein at τ = 2 ps. Breakdown fluence Fth is determined by segmented linear regression with 95% CI (bootstrap). (b) Shadowgraph sequence at F = 10 J cm−2 , τ = 2 ps showing the expanding shock front; radii R(t) yield velocity and pressure via the EOS-based conversion in Methods.
Figure 3 — Shock-wave amplitude vs. pulse duration and fluence. Outcome: Identifies a robust optimum near ∼5 ps and shows saturation at higher fluence; chirp sign has secondary influence. Suggested Caption: Shock-wave amplitude as a function of pulse duration and fluence. (a) 2D heat map of shock amplitude Asw versus pulse duration τ and fluence F. The inset marks the τ where Asw reaches 90% of its plateau (definition of “saturation”). Negative τ denotes negative chirp. (b) Sections of (a) at fixed F highlight the ∼5 ps maximum and its evolution with F; shaded bands show confidence intervals where applicable. The sign of τ encodes chirp (“+”, positive; “–”, negative).
Figure 4 — Breakdown threshold vs. pulse duration. Outcome: Shows Fth(τ ) with uncertainties and the DRE model capturing the trend from sub-ps to few-ps durations. Suggested Caption: Optical breakdown threshold versus pulse duration. Breakdown fluence Fth versus τ . Points are experimental estimates with 95% CI from the segmented-fit procedure; the solid line is the DRE prediction. The sign of τ encodes chirp (“+”, positive; “–”, negative).
Figure 5 — Electron-plasma dynamics (DRE). Outcome: Separates photoionization vs. avalanche contributions and shows how recombination suppresses post-peak density, explaining why few-ps pulses can maximize shock amplitude. Suggested Caption: Electron-plasma dynamics from the DRE model. Temporal evolution of electron density in water at F = 5 J cm−2 for (a) 200 fs and (b) 5 ps. Dashed: photoionization; dotted: avalanche ionization; solid: total (with recombination). For longer pulses, avalanche dominates; beyond ∼1 ps, recombination reduces the total electron density after the pulse peak.
Figure 6 — Linking shock amplitude to electronic kinetic energy. Outcome: Establishes Ekin as a predictive proxy for shock strength, with strong correlation across (F, τ ). Suggested Caption: Relation between shock amplitude and electronic kinetic energy. (a) Shock amplitude Asw (points) and modeled total electronic kinetic energy Ekin (line) versus F at selected τ (legend). Correlation analysis yields R2 = 0.837 with 95% CI 0.634–0.983. (b) 2D heat map of Ekin(F, τ ) showing a maximum near ∼5 ps and saturation at higher F, mirroring Asw.
Closing note. Figure captions should explain the scientific outcome (what the data demonstrate and why it matters) rather than narrate every panel element. The proposed captions above follow that principle; please adjust numbers/labels to your final values and formatting. 3
Answer: we have thoroughly revised all figure captions to ensure they are clear, consistent, and explicitly reference the methodologies used, as requested. Furthermore, we have standardized the formatting across all figures to enhance their clarity and professional appearance. Specifically, we have adopted a uniform style using the Arial font family, with a size of 28 pt for axis ticks and 48 pt for axis labels. We still positioned the color bars to align with the abscissa, which we believe provides a cleaner and more aesthetically pleasing layout.
Reviewer 3 Report
Comments and Suggestions for AuthorsAuthors have addressed all issues
Author Response
Thank you for your attention for our manuscript.
