Full Explicit Numerical Modeling in Time-Domain for Nonlinear Electromagnetics Simulations in Ultrafast Laser Nanostructuring
Round 1
Reviewer 1 Report
The authors developed a fully explicit nonlinear finite-difference time-domain model to study the electromagnetics of nonlinear media with Kerr and Raman effects. They first deduced the algorithm for modeling the electromagnetic fields in nonlinear media. Then, the model was implemented to study the nonlinear propagation of an ultrafast laser pulse through a bulk dielectric medium or through a bulk silica with additional embedded voids or metallic nanoparticles. This paper is well organized and will be interested to researchers working in this field, and therefore I suggest the paper be accepted for publication with the following corrections or clarifications.
- Figure 6 illustrates the history of the power density for a pulsed Bessel beam propagating from air to a bulk silica. However, the boundary between the air and silica is not clear, making the discussion less convincing and hard to understand. They should add some details in Fig. 6 for clearness. In addition, the figure caption illustrated “At the interface between the silicon bulk…” Since silicon and silica are distinct materials, they should check the correctness to avoid confusion. The same problems happen in Figure 7b, 7c, 8, and 9 as well. I cannot observe where those voids or metallic nanospheres are located, which severely limits the understanding for readers about their discussion for the electrodynamic phenomena within these systems.
- The meaning of Figure 3 is hard to understand. What do the exporting probes and domain backup mean? How to judge they save more than forty hours in computation from Fig. 3?
- Since they include 650 regions or voids that range in size from 200 to 650 nanometers in radius. Such huge number of nanoparticles with the diversity in dimensions will require high capacity computational resource and calculation time. Is the mesh fine enough to discretize for smaller particles? Or they use a non-uniform meshing scheme so that the mesh size for the small and large nanoparticles are different? They should provide some detail about this.
- There are some typo that should be corrected.
Line 167: “…permits to switches the algorithm…” switches should change to switch
Line 172: “the stability conditions of all these effect together o separately” should be or?
Author Response
1. Figure 6 illustrates the history of the power density for a pulsed Bessel beam propagating from air to a bulk silica. However, the boundary between the air and silica is not clear, making the discussion less convincing and hard to understand. They should add some details in Fig. 6 for clearness. In addition, the figure caption illustrated “At the interface between the silicon bulk...” Since silicon and silica are distinct materials, they should check the correctness to avoid confusion. The same problems happen in Figure 7b, 7c, 8, and 9 as well. I cannot observe where those voids or metallic nanospheres are located, which severely limits the understanding for readers about their discussion for the electrodynamic phenomena within these systems.
In figure 6 we have added a subsample with dimensions that allows the reader a better understanding of the plotted region. In the case of the nanovoids locations we have enriched figure 7a) with some coordinates and Cartesian references of coordinates that facilitates the nanovoids position in the computational domain depicted in figure 4.
We have also add a text in the manuscript: “Fig.6c) shows the history of the power density at the critical threshold separating medium and high power regimes, along with a few steps of time. In this figure we can identify the interface air-fused silica due to the rings which record the history of a stationary wave formed after the interaction.” Finally, in Fig.6c) we have added a label which identified the interface clearly.
2. The meaning of Figure 3 is hard to understand. What do the exporting probes and domain backup mean? How to judge they save more than forty hours in computation from Fig. 3?
We have added some explanations in the manuscript: “Figure 3 shows the number of simulation status updates on the abscissa axis and the on the ordinates axis the time needed so as to update these simulation states. Each step or update corresponds to executing the 14 algorithms shown by Figure 2. In addition to these algorithms that are necessary to perform a system/computational domain status update, there are two more algorithms. One exports simulation data or results (every 40 updates) and the other exports the complete simulation status (every 500 updates). The latter is done for two reasons, the first is to recover a state of a simulation in case of computer collapse/failure (for example a failure in the computer electric power source). The second reason has to do with the alteration of the computational domain (electromagnetic properties or/and size of the computational domain) without the need to restart the simulation from the first time stepping. Table 3 lists the computational resources employed in the simulations. Under these conditions we reach a performance which can be summarized by the computational burdens and performance details. Those are a computational domain size in RAM of 121.5GBs, a maximum number of Yee’s cell charged and computed of 1.2Giga Cells, a minimum number of Yee’s cell computed of 13Mega Cells, a speed at minimum and maximum load of 6.5Mcells/Second and 38Mcells/Second respectability, a Probe exportation time of 1.47Seconds and a computational domain backup time of 8.76Seconds.
… In a simulation with the same characteristics and static nested loop, we should have a constant duration per time step updating of 32 seconds which is equal to the asymptotic value in Fig.3. The total simulation duration is the accumulated time or area under the plot portrayed in Fig.3. Hence, the triangle in gray color is the time save by means of dynamic nested loops.”
3. Since they include 650 regions or voids that range in size from 200 to 650 nanometers in radius. Such huge number of nanoparticles with the diversity in dimensions will require high capacity computational resource and calculation time. Is the mesh fine enough to discretize for smaller particles? Or they use a non-uniform meshing scheme so that the mesh size for the small and large nanoparticles are different? They should provide some detail about this.
Due to the Nyquist-Shannon Theorem, which places an upper limit on the meshing size and the stability condition that links the size of the temporal step Dt with the spatial ones (Dx,Dy,Dz), and given that in the manuscript we provide both data, that is, Courant number and the size of the temporal step Dt (see figure 5), it is deductible that the smallest spatial element of the mesh is 200nm. However, and despite the fact that FDTD-DPW method allows a non-uniform meshing as we explain in the manuscript1, in this particular work we have used a regular and uniform mesh of 200nm size (Dx=Dy=Dz=200nm). Therefore, the small voids of 200nm in size are more a cube than a sphere. This answer can be completed with the answer seven given to the second referee.
4. There are some typo that should be corrected.
Line 167: “...permits to switches the algorithm...” switches should change to switch
Line 172: “the stability conditions of all these effect together o separately” should be or?
We would like to thanks the referee corrections.
1 This is valid for any angle of propagation, for any grid cell aspect ratio and even for nonuniform grids [https://doi.org/10.1080/02726343.2019.1695089].
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper is well written and the topic is of interest.
Some specific comments which may improve the quality of the paper:
1) There is something wrong at the end of he introduction with the numbering of sections: Section A? appendix 6?
2) Below equation 3, epsilon_inf should be defined
3) "allows + to" is wrongly used. It shuld be replaced with "allow + sbj. + to" or "allow for -ing"
4) Table 1 is unclear. It should be replaced with an algorithm or a block diagram
5) Figure should be placed at the top or at the bottom
6) In the conclusions the authors state "... for a wide range of applications in which optical/electromagnetic nonlinear effects have to be taken into consideration." Can you list some of those applications?
7) Computational perfomances (number of elements, computation time, and memory) should be added in the results sections.
Author Response
1. There is something wrong at the end of he introduction with the numbering of sections: Section A? Appendix 6?
We have corrected the references at last sentence in the introduction section.
2. Below equation 3, epsilon_inf should be defined
In order to clarify this issue, in the manuscript text body, we have added an explanation about this magnitude: “The magnitude epsilon_infinity is the non-unity high-frequency relative permittivity of the media”.
For very high frequencies above electronic absorption the value of the permittivity is one. Going down in frequency, every absorption leads to an increase of the permittivity. Below the frequency range of the electronic absorptions all these contributions due to these absorptions can be summed up in a constant which is the high-frequency permittivity limit often called epsilon_infinity. This is a convention present in many books1.
3. "allows + to" is wrongly used. It shuld be replaced with "allow + sbj. + to" or "allow for -ing"
We would like to thanks the referee correction.
4. Table 1 is unclear. It should be replaced with an algorithm or a block diagram
We have modified table 1 with the aim to clarify the connection with the global flow chart depicted in Fig.2. Table 1 contains the list of the explicit algorithms that are different from the traditional FDTD ones.
5. Figure should be placed at the top or at the bottom
We have tried to arrange all figures at the top. However, if this work is accepted, at the edition state we will explain that all figures should be at the top/bottom of the pages.
6. In the conclusions the authors state "... for a wide range of applications in which optical /electromagnetic nonlinear effects have to be taken into consideration." Can you list some of those applications?
We have added the following applications into the manuscript: Ultrafast laser processing has been extensively applied to fabricate 3D photonic devices based on embedded optical waveguides inscribed in glass materials by inducing permanent refractive index changes in the focal volumes2. Optical couplers and splitters3, volume Bragg gratings4, or even diffractive lenses5 have been efficiently inscribed by refractive-index changes during light propagation.
7. Computational perfomances (number of elements, computation time, and memory) should be added in the results sections.
Obviously, the performance depends on the computational resources. In section 3, where we discuss the algorithm performance it is necessary some additional information. Therefore, we have added a table that summarizes the computational resources as well as the burdens/details for the simulations carried out.
|
Computational resources: CPU: Intel® Core™ i9-10980XE, MB: GIGABYTE X299X, RAM: Crucial CT32G4RF D4293 DDR4-2933, ROM: 2x Crucial P5 2TB PCIe M.2 2280SS SSD, GPU: GeForce GTX 1080 Ti |
In addition, we have explained better Fig.3 in the manuscript. We complete this answer with the answer 2 which we have provided to the first referee.
1 https://ieeexplore.ieee.org/abstract/document/9100982 , https://ieeexplore.ieee.org/servlet/opac?bknumber=5263542 , https://books.google.ru/books?id=mGdH\_W0YBdQC , https://onlinelibrary.wiley.com/doi/book/10.1002/9781118716410
2 https://doi.org/10.1515/nanoph-2016-0004
3 https://doi.org/10.1364/OL.28.002491
4 https://doi.org/10.1109/JLT.2003.808678
5 https://doi.org/10.1364/OL.27.002200
Author Response File: Author Response.pdf
