Three-Photon Ionization with One-Photon Resonance between Excited Levels

Round 1

Reviewer 1 Report

The paper is well written and describes sufficiently the work which the authors have undertaken.  The conclusions follow from the results of the work.

I think it would be helpful if the authors could say a little more about the significance of their conclusions, given that the experimental work elated to their work is several years old, with apparently no further developments.

Author Response

Dear reviewer,

Thank you for the comment.

Comment: I think it would be helpful if the authors could say a little more about the significance of their conclusions, given that the experimental work elated to their work is several years old, with apparently no further developments.

Response: We have added a paragraph at the end of the conclusions section (page 11, section “Conclusions”, the last paragraph) and one more in-text citation with a corresponding reference ([24]).

We have also changed the position of figures 1–5 and table 3 in the manuscript.

Reviewer 2 Report

The paper is a theoretical investigation on three-photon ionization with one-photon resonance between two excited levels with the lower one being initially unpopulated. The calculations results are thorough and clearly presented. This work could help us to acquire a deeper understanding on the fundamental properties of multiphoton ionization. Overall, it is suitable for publication after considering the following suggestions:

1. The introduction section could be further improved by giving a more comprehensive and detailed review on the previous works (both experimental and theoretical) on the effects of multiphoton ionization in the presence of resonances, so that the readers who are not very familiar with this particular problem could understand the motivation and significance of this study. 
2. The height-to-width ratio of Fig. 5 could be reduced. 
3. Please specify the value of laser pulse width in the calculations.
4.  In the conclusions section, please highlight how the presented theoretical results help us understand some previous relevant experimental results. 

 

Author Response

Dear reviewer,

Thank you for the comments.

Comment 1: The introduction section could be further improved by giving a more comprehensive and detailed review on the previous works (both experimental and theoretical) on the effects of multiphoton ionization in the presence of resonances, so that the readers who are not very familiar with this particular problem could understand the motivation and significance of this study.

Response 1: We have added two new paragraphs to the introduction section (Introduction: page 1, paragraph 1 and page 2, paragraph 2) and new in-text citations with corresponding references (2–12).

Comment 2: The height-to-width ratio of Fig. 5 could be reduced.

Response 2: We have reduced the height-to-width ratio of Fig. 5.

Comment 3: Please specify the value of laser pulse width in the calculations.

Response 3: Sorry, this is our omission. We have specified the value of the laser pulse width which was equal to 20 ns (page 4, paragraph 3, the last sentence).

Comment 4: In the conclusions section, please highlight how the presented theoretical results help us understand some previous relevant experimental results.

Response 4: We have added a paragraph at the end of the conclusions section (page 11, section “Conclusions”, the last paragraph) and one more in-text citation with a corresponding reference ([24]).

We have also changed the position of figures 1–5 and table 3 in the manuscript.

Reviewer 3 Report

Dear Editor,

I have now read the manuscript submitted by the authors and I feel that it represents a well-written theoretical work about the resonant multiphoton ionization (3-photon) of relatively heavy atoms such as Ba, Sr, Ca. The method followed is well established and the authors have followed all the steps required to ensure accurate results. The latter have been presented and discussed in detail by the authors thus providing extra confidence on the validity of their calculations, within their chosen model. Nevertheless I have 2-3 remarks to make which could help the authors to improve their manuscript. 

1. Energies are presented in inverse wavelength, thus making the paper less readable. I believe that it would be a lot better if the energies were expressed in eVs instead (or at least placing somewhere in the text the corresponding conversion factor). In addition it would be useful to give the corresponding intensity in W/cm^2 rather than just the electric field strength in V/cm. This way any reader could have an immediate feeling of the range of the laser parameters used.
2. There is no mention for the pulse's duration. How long the pulse was chosen to be? Not much information is given about how the spontaneous widths of the various states are known.
3. If the laser width is not used eventually why this is introduced after all? Does it play any role in the present investigation?

 

Nevertheless I have very few comments that could

Author Response

Dear reviewer,

Thank you for the comments.

Comment 1: Energies are presented in inverse wavelength, thus making the paper less readable. I believe that it would be a lot better if the energies were expressed in eVs instead (or at least placing somewhere in the text the corresponding conversion factor). In addition it would be useful to give the corresponding intensity in W/cm^2 rather than just the electric field strength in V/cm. This way any reader could have an immediate feeling of the range of the laser parameters used.

Response 1: We have placed the conversion factor from eV to cm^–1 in the text (page 2, paragraph 4, last two sentences). However, we would like to note that it is a common practice in the spectroscopic studies using the laser as a photon source to operate with the wavenumbers expressed in cm^–1.

We also give in the text the corresponding intensity in W/cm² in addition to the electric field strength in V/cm (page 2, paragraph 5, line 3 and page 5, paragraph 2, line 2). Note that we use the electric field strength since it is included in the differential equation system (4) via the V₁₂, V₁₃, and V₂₃ variables as well as g_i2 and g_i3 variables.

Comment 2: There is no mention for the pulse's duration. How long the pulse was chosen to be? Not much information is given about how the spontaneous widths of the various states are known.

Response 2: Sorry, this is our omission. We have specified the value of the laser pulse width which was equal to 20 ns (page 4, paragraph 2, the last sentence).

As for the spontaneous widths, it is said in the text that the spontaneous widths of the excited levels were chosen equal to 10^–4 cm^–1 on the basis of the known lifetime t » 10^–8 s of the 6s6p ¹P₁ level (page 6, paragraph 3). It is also noted that variation in the natural widths values within a range of 10^–3–10^–5 cm^–1 did not noticeably affect the result of the calculation.

Comment 3: If the laser width is not used eventually why this is introduced after all? Does it play any role in the present investigation?

Response 3: But the laser width is included in the differential equation system (4) via g₂ and g₃ variables (see equations 4–6 as well as page 4, the first paragraph, line 7). As a matter of fact, the laser width determines the minimum width of the maximum if there are no other mechanisms of the maximum broadening as well as it affects on the resonance condition along with the detuning and Stark shifts.

We have also changed the position of figures 1–5 and table 3 in the manuscript.