General simulation method for spontaneous parametric down- and parametric up-conversion experiments

Dear editors, thank you very much for the insightful response regarding our manuscript with the title “General simulation method for spontaneous parametric down-and parametric up-conversion experiments”, by Felix Riexinger et al., which helped us to improve our manuscript. Please find below our response to the individual remarks, which we briefly summarize: 1) We extended the comparison with our previous work in Ref. [24] and added further discussion on the effects the changes in our model have on the simulations at the end of section 3. This provides the reader with a better understanding of the differences in the approaches as well as their effect on the simulation results. Additionally, we moved the discussion of the fitted values of the nonlinear coefficient from section 2.1 to the end of the results section as well to improve the flow of reading. 2) To better highlight the novel elements in the theory, we added an explicitly momentum-dependent transmission term to Eq (8) and (9). With this we emphasize that while we start with the same fundamental formulation as in our previous work, we not only refined our model for the conversion process in the crystal but also consider many more details of the whole experimental setup. With these changes and additions, we are convinced that our manuscript is now ready for publication in SciPost Physics. Sincerely,

Felix Riexinger (on behalf of all the authors)

Reviewer: the authors should significantly expand the considerations and comparisons with Ref.[24] either in the conclusions, or, better, at the end of Section 3. they should present a one-to-one comparison of the results of Section 3 with the results of Ref. [24]. This would help the reader to understand better the elements of novelty, significance and originality of the present paper.

Answer: To comply with the suggestion of the reviewer we changed the following parts of our manuscript. We removed the following portion of the text at its original location in section 2.1 and added this explanation at a new position in section 3:

Removed text (End of section 2.1):
The fitted χ(2)333 value agrees with a scaled value from the infrared range [25] but is ∼ 1.5 times larger than other scaled values from the terahertz range [26, 27]. The difference can be explained by different factors for the Hamiltonian ( 1/2 and 1/3 ) used in the classical and quantum approaches. Compared to our previous estimation [24] this value is two times larger. There are two reasons for this: First, we did not use Miller’s rule in the previous method, but assumed a constant value. Second, we added the full optical model to the simulation, which changes the shape of the spectrum.

Furthermore, we extended the discussion in section 3 to consider the suggestion of the reviewer, which now reads:

Added text (End of section 3):
Compared to our previous results [24] the simulated images show smoother tails and prominent peaks at emission angles around 0◦. In our previous result there were gaps with vanishing count rates in this region. The better agreement in spectrum shape allows for the estimation of the nonlinear coefficient χ(2)333 from a fit to a large range of the simulation. Previously it was determined separately from a fit to the collinear count rate. The fitted χ(2)333 value agrees with a scaled value from the infrared range [25] but is ∼ 1.5 times larger than other scaled values from the terahertz range [29, 30]. The difference can be explained by different factors for the Hamiltonian ( 1/2 and 1/3 ) used in the classical and quantum approaches. Compared to our previous estimation [24] this value is two times larger. There are two reasons for this: First, we did not use Miller’s rule in the previous method, but assumed a constant value. Second, we added the full optical model to the simulation, which changes the shape of the spectrum.
In the new simulations the ratio of height of the peaks in the up- and downconversion regime match the experiment more accurately (see Fig. 3) due to the inclusion of higher QPM orders as well as the spectral dependence of the nonlinear coefficient. This spectral dependence leads to an increase, the spatial dependence to a decrease of χ(2)eff . The net effect is an increase of counts at larger angles which was not as prominent in the previous work.

Additionally, we modified Eq. (8) & (9) to better highlight all novel aspects of our work compared to [24]:
Added momentum dependency to Eta(k_s)

With these changes, we are convinced to fully comply with the reviewer’s request.