Update on Overleaf.

main.tex

@@ -460,7 +460,9 @@ license.
   in Fig.~\ref{plasma-grid} are indicated. The temporal evolution of
   Gaussian beam intensity is also shown. Peak laser intensity is fixed to
    be 10$^{12}$~W/cm$^2$. For better visual representation of time scale at a single optical cycle we put a  squared electric field profile in all plots in  Fig.~\ref{time-evolution} in gray color as a background image (note  linear time scale on the left column and logarithmic scale on the  right one). \red{Please, remove italic style of font for 't, fs' on titles of X-axises. Also, all fonts should be the same: please don't mix Times and Arial.}}
-\vspace*{\floatsep}
+    \end{figure*}
+    
+\begin{figure*}   
  \centering
  \includegraphics[width=150mm]{plasma-grid.pdf}
  \caption{\label{plasma-grid} EHP density snapshots inside Si nanoparticle of
@@ -548,56 +550,54 @@ To describe all the stages of non-linear light interaction with Si
  According to these considerations, after few optical cycles taking
  place on a 10~\textit{fs} scale it results in the excitation of the
  low-\textit{Q} ED resonance, which dominates MD and MQ independently
- on the exact size of NPs.  Moreover, during the first optical cycle
+ on the exact size of NPs. Moreover, during the first optical cycle
  there is no multipole modes structure inside NP, which results
- into a very similar field distribution for all sizes of NP under
- consideration as shown in Fig.~\ref{plasma-grid}(a,e,i) . We address
+ in a very similar field distribution for all sizes of NP under
+ consideration as shown in Fig.~\ref{plasma-grid}(a,e,i). We address
  to this phenomena as \textit{'Stage~1'}. This stage demonstrates the
  initial penetration of electromagnetic field into the NP during the
- first optical cycle.
+ first optical cycle. Resulting factors $G_{N_e}$ exhibit sharp increase at this stage (Fig.~\ref{time-evolution}(b,d,f), yielding strong and ultrafast symmetry breaking. 
  
  \textit{'Stage~2'} corresponds to further electric field oscillations
- ($t \approx 5$--$15$) leading to the formation of ED field pattern in
- the center of the NP as it can be seen in
+ ($t \approx 5$--$15$~fs) leading to the formation of ED E-field pattern in
+ the center of the Si NP as shown in
  Fig.~\ref{plasma-grid}(f,j). We stress the
- unstationery nature of field pattern at this stage. The energy
- balance between extinction and pumping is not set, moreover, there is
+ nonstationary nature of E-field pattern at this stage, whereas there is
  a simultaneous growth of the incident pulse amplitude. This leads to
- a superposition of ED field pattern with the one from the Stage 1,
- resulting into the presence for the maximum of the EHP distribution
- in the front side of the Si NP. This effect dominates for the
+ a superposition of ED near-field pattern with that from the Stage 1,
+ resulting in EHP concentration in the front side of the Si NP. This effect dominates for the
  smallest NP with $R=75$~nm in Fig.~\ref{plasma-grid}(b), where ED
  mode is tuned far away from the resonance (see Fig.~\ref{mie-fdtd}(c)
  for field suppression inside NP predicted by the Mie theory). At this
  stage, the density of EHP ($N_e < 10^{20}$~cm$^2$) is still not high
- enough to significantly affect the optical properties of the NP.
+ enough to significantly affect the optical properties of the NP (Figs.~\ref{time-evolution}(a,c,e)).
 
  When the number of optical cycles is large enough ($t>20$~\textit{fs})
  both ED and MD modes can be exited to the level necessary to achieve
  the stationary intensity pattern corresponding to the Mie-based
  intensity distribution at the \textit{'Stage~3'} (see
- Fig.~\ref{plasma-grid}). The EHP density for the most volume of NP is
+ Fig.~\ref{plasma-grid}(c,g,k)). The EHP density for the most volume of NP is
  still relatively small to affect the EHP evolution,
  but is already high enough to change the local optical
- properties. Below the MD resonance ($R = 75$~nm), the EHP is
+ properties, i.e. real part of permittivity. Below the MD resonance ($R = 75$~nm), the EHP is
  mostly localized in the front side of the NP as shown in
  Fig.~\ref{plasma-grid}(c). The highest quasi-stationary asymmetry factor
- $G_{N_e} \approx 0.5$--$0.6$ is achieved in this case. At the MD
- resonance conditions, the EHP distribution has a toroidal shape and
+ $G_{N_e} \approx 0.5$--$0.6$ is achieved in this case (Fig~\ref{time-evolution}(b)). At the MD
+ resonance conditions ($R = 100$~nm), the EHP distribution has a toroidal shape and
  is much closer to the homogeneous distribution. In contrast, above
  the MD resonant size for $R = 115$~nm the $G_{N_e} < 0$ due to
  the fact that EHP is dominantly localized in the back side of the NP.
 
- In other words, due to the presence of a quasi-stationary pumping the Stage~3 is
+ In other words, due to a quasi-stationary pumping during the Stage~3 is
  superposed with the Stage~1 field pattern, resulting in an additional
  EHP localized in the front side. This can be seen when comparing
  result from the Mie theory in Fig.~\ref{mie-fdtd}(d) and result of
  full 3D simulation in Fig.~\ref{mie-fdtd}(f). Note that pumping of NP
  significantly changes during a single optical cycle, this leads to a
  large variation of asymmetry factor $G_{N_e}$ at first stage. This
- variation steadily decrease as it goes to Stage~3.
+ variation steadily decrease as it goes to Stage~3, as shown in Fig.~\ref{time-evolution}(b,d,f).
 
- To explain this effect, we consider the time evolution of mean EHP
+ To explain this effect, we consider the time evolution of average EHP
  densities $N_e$ in the front and back halves of NP presented in
  Fig.~\ref{time-evolution}(a,c,e). As soon as the recombination and
  diffusion processes are negligible at \textit{fs} time scale, both
@@ -605,7 +605,7 @@ To describe all the stages of non-linear light interaction with Si
  with small pumping steps synced to the incident pulse. The front and the back
  halves of NP are separated in space, which obviously leads to the presence of
  time delay between pumping steps in each curve caused by the same
- optical cycle of the incident wave. This delay causes a large asymmetry factor during first stage. However, as soon as mean
+ optical cycle of the incident wave. This delay causes a large asymmetry factor during first stage. However, as soon as average
  EHP density increases the relative contribution of this pumping steps to
  the resulting asymmetry becomes smaller. This way variations of asymmetry
  $G_{N_e}$ synced with the period of incident light decreases.
@@ -613,30 +613,28 @@ To describe all the stages of non-linear light interaction with Si
  Higher excitation conditions are followed by larger values of
  electric field amplitude, which lead to the appearance of high EHP
  densities causing a significant change in the optical properties of
- silicon according to the equations (\ref{Index}). From the Mie theory, the initial (at the end of Stage~3) space pattern of
+ silicon according to the equations (\ref{Index}). From the Mie theory, the initial (at the end of Stage~3) spatial pattern of the
  optical properties is non-homogeneous. When non-homogeneity of
- optical properties becomes strong enough it leads to the
- reconfiguration of the electric field inside NP and vice versa. We
+the optical properties becomes strong enough it leads to the
+ reconfiguration of the E-field inside NP, which in turn strongly affects further reconfiguration of the optical properties. We
  refer to these strong nonlinear phenomena as \textit{'Stage~4'}. In
- general the reconfiguration of the electric field is unavoidable as
+ general, the reconfiguration of the electric field is unavoidable as
  far as the result from the Mie theory comes with the assumption of
  homogeneous optical properties in a spherical NP.
 
  Thus, the evolution of EHP density during Stage~4 depends on the
  result of multipole modes superposition at the end of Stage~3 and is
  quite different as we change the size of NP. For $R=75$~nm and
- $R=100$~nm we observe a front side asymmetry before Stage~4, however,
- the origin of it is quite different.  The $R=75$~nm NP is out of
+ $R=100$~nm, we observe a front side asymmetry before Stage~4, however,
+ the origin of it is quite different. The $R=75$~nm NP is out of
  resonance, moreover, Mie field pattern and the one, which comes from
  the Stage~1 are quite similar. As soon as EHP density becomes high enough
  to change optical properties, the NP is still out of resonance,
  however, the presence of EHP increases absorption in agreement with
- (\ref{Index}). This effect effectively leads to a partial screening, and it
- becomes harder for the incident wave to penetrate deeper into EHP. Finally,
- this finishes spilling the NP`s volume with plasma reducing the
- asymmetry, see Fig.~\ref{plasma-grid}(d).
-
- For $R=100$~nm the evolution during the final stage goes in a
+ (\ref{Index}), decreases Q-factor, and destroys optical modes.
+ %This effect effectively leads to a partial screening, and it  becomes harder for the incident wave to penetrate deeper into EHP. Finally,  this finishes spilling the NP`s volume with plasma reducing the asymmetry, see Fig.~\ref{plasma-grid}(d).
+ 
+ For $R=100$~nm, the evolution during the final stage goes in a
  similar way, with a notable exception regarding MD resonance.  As
  soon as presence of EHP increases the absorption, it suppresses the
  MD resonance with symmetric filed pattern, thus, the asymmetry factor
@@ -645,8 +643,8 @@ To describe all the stages of non-linear light interaction with Si
  mark.
  
  The last NP with $R=115$~nm shows the most complex behavior during
- the Stage~4. The superposition of Mie field pattern with the one from
- Stage~1 results into the presence of two EHP spatial maxima, back and
+ the Stage~4. The superposition of Mie-like E-field pattern with that from
+ Stage~1 results in the presence of two EHP spatial maxima, back and
  front shifted. They serve as starting seeds for the EHP formation,
  and an interplay between them forms a complex behavior of the asymmetry
  factor curve. Namely, the sign is changed from negative to positive
@@ -655,7 +653,7 @@ To describe all the stages of non-linear light interaction with Si
  account all near-field interaction of incident light with two EHP
  regions inside a single NP. It is interesting to note, however, that in
  a similar way as it was for $R=100$~nm the increased absorption
- should ruin ED and MD resonances, responsible for the back-shifted
+ should destroy ED and MD resonances, which are responsible for the back-shifted
  EHP. As soon as this EHP region is quite visible on the last snapshot
  in Fig.~\ref{plasma-grid}(l), this means that EHP seeds are
  self-supporting.
@@ -786,41 +784,11 @@ To describe all the stages of non-linear light interaction with Si
 % and size} It is important to optimize asymmetry by varying pulse
 % duration, intensity and size.
 
-\section{Conclusions} We have considered ultra-short and sufficiently
-intense light interactions with a single semiconductor nanoparticle
-under different irradiation conditions and for various particle
-sizes. As a result of the presented self-consistent calculations, we
-have obtained spatio-temporal EHP evolution inside the
-NPs and investigated the asymmetry of EHP distributions. % for different laser intensities. % and temporal pulse widths.
-%It has been demonstrated that the EHP generation strongly affects
-%NP scattering and, in particular, changes the preferable
-%scattering direction. 
-Different pathways of EHP evolution from the front side to the back
-side have been revealed, depending on the NP sizes, and different behaviors have been explained by the
-non-stationarity of the energy deposition and different quality
-resonant factors for exciting the electric and magnetic dipole
-resonances, intensity distribution by Mie theory and newly
-plasma-induced nonlinear effects. The effect of the EHP strong 
-asymmetric distribution during
-first optical cycles has been revealed for different size
-parameters. The higher EHP asymmetry is established for NPs
-of smaller sizes below the first magnetic dipole
-resonance. Essentially different EHP evolution and lower asymmetry has been achieved for larger NPs due to the stationary intensity
-enhancement in the back side of the NP. The EHP densities
-above the critical value have been shown to lead to the EHP distribution
-homogenization.
-% In particular, the scattering efficiency factor is used to define
-% the optimum NP size for preferential forward or backward
-% scattering. Furthermore, a parameter has been introduced to describe
-% the scattering asymmetry as a ratio of the EHP density in the front
-% side to that in the back side of the NP. This parameter
-% can be then used for two-dimensional scattering mapping, which is
-% particularly important in numerous photonics applications.
-The EHP asymmetry opens a wide range of applications in NP
-nanomashining/manipulation at nanoscale, in catalysis as well as numerous
-nano-bio-applications.  The observed plasma-induced breaking symmetry
-can be also useful for beam steering, or for the enhanced second
-harmonics generation.
+\section{Conclusions} We have rigorously modeled and studied ultra-fast and intense light interaction with a single silicon nanoparticle of various sizes for the first time to our best knowledge. As a result of the presented self-consistent nonlinear calculations, we have obtained spatio-temporal EHP evolution inside the
+NPs and investigated the asymmetry of the EHP distributions. 
+We have revealed EHP strong asymmetric distribution during first optical cycles for different sizes. The highest average EHP asymmetry has been observed for NPs of smaller sizes below the first magnetic dipole resonance, when EHP is concentrated in the front side mostly during the laser pulse absorption. Essentially different EHP evolution and lower asymmetry has been achieved for larger NPs due to the  intensity enhancement in the back side of the NP. The EHP densities
+above the critical value have been shown to lead to homogenization of the EHP distribution.
+The observed plasma-induced breaking symmetry can be useful for creation of nonsymmetrical nanophotonic designes, e.g. for beam steering or enhanced second harmonics generation. Also, the asymmetric EHP opens a wide range of applications in NP nanomashining at deeply subwavelength scale. 
 
 \section{Acknowledgments}
 A. R. and T. E. I. gratefully acknowledge the CINES of CNRS for