changes

main.tex

@@ -540,8 +540,8 @@ license.
  permittivity corresponding to each stage is shown in
  Fig.~\ref{plasma-grid}.
 
- To describe all the stages of light non-linear interaction with
- Si NP, we present the calculation results obtained by using Maxwell's
+ To describe all the stages of light non-linear interaction with Si
+ NP, we present the calculation results obtained by using Maxwell's
  equations coupled with electron kinetics equations for different
  radii for resonant and non-resonant conditions. In this case, the
  geometry of the EHP distribution can strongly deviate from the
@@ -550,26 +550,28 @@ license.
  nonlinear effects, taking place due to transient optical changes in
  Si. The non-stationary intensity deposition results in different time
  delays for exciting electric and magnetic resonances inside Si NP
- because of different quality factors $Q$ of the resonances. In
- particular, magnetic dipole resonance (\textit{b1}) has $Q \approx
- 8$, whereas electric one (\textit{a1}) has $Q \approx 4$. The larger
- particle supporting magnetic quadrupole resonance (\textit{b2})
- demonstrates \textit{Q} $\approx 40$. As soon as the electromagnetic
- wave period at $\lambda$~=~800~nm is 2.6~\textit{fs}, one needs about
- 10~\textit{fs} to pump the electric dipole, 20~\textit{fs} for the
- magnetic dipole, and about 100~\textit{fs} for the magnetic
- quadrupole. According to these considerations, the first optical
- cycles taking place on few-femtosecond scale result in the excitation
- of the low-\textit{Q} electric dipole resonance independently on the
- exact size of NPs and with the EHP concentration mostly on the front
- side of the NPs. We address to this phenomena as \textit{'Stage 1'},
- as shown in Figs.~\ref{plasma-grid} and~\ref{plasma-grid}. The first stage at the
- first optical cycle demonstrates the dominant electric dipole
- resonance effect on the intensity/EHP density distribution inside the
- NPs in Fig.~\ref{plasma-grid}(a,e,j) and~\ref{time-evolution}. The larger the NPs size
- is, the higher the NP asymmetry $G_{N_e}$ is achieved.
-
- \textit{'Stage 2'} corresponds to further electric field oscillations
+ because of different quality factors $Q$ of the resonances.
+
+ In particular, magnetic dipole resonance (\textit{b1}) has
+ $Q \approx 8$, whereas electric one (\textit{a1}) has $Q \approx
+ 4$. The larger particle supporting magnetic quadrupole resonance
+ (\textit{b2}) demonstrates \textit{Q} $\approx 40$. As soon as the
+ electromagnetic wave period at $\lambda$~=~800~nm is 2.6~\textit{fs},
+ one needs about 10~\textit{fs} to pump the electric dipole,
+ 20~\textit{fs} for the magnetic dipole, and about 100~\textit{fs} for
+ the magnetic quadrupole. 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} electric dipole resonance
+ independently on the exact size of NPs. Moreover, during the first
+ optical cycle there is no multiple mode structure inside of NP, which
+ results into a very similar field distribution for all size of NP
+ under consideration. We address to this phenomena as
+ \textit{'Stage~1'}, as shown in Figs.~\ref{plasma-grid}(a,e,i).
+ and~\ref{plasma-grid}. The first stage at the first optical cycle
+ demonstrates the initial penetration of electromagnetic fild into the
+ NP.
+ 
+ \textit{'Stage~2'} corresponds to further electric field oscillations
  ($t \approx 2\div15$) leading to the unstationery EHP evolution
  with a maximum of the EHP distribution in the front side of the Si NP
  owing to the starting excitation of MD and MQ resonances that require more
@@ -579,7 +581,7 @@ license.
 
  A number of optical cycles ($>$10 or $t>$25~\textit{fs}) is necessary
  to achieve the stationary intensity pattern corresponding to the
- Mie-based intensity distribution at the \textit{'Stage $3$'} (see
+ Mie-based intensity distribution at the \textit{'Stage~3'} (see
  Fig.~\ref{time-evolution}). The EHP density is still relatively small to affect
  the EHP evolution or for diffusion, but is already high enough to
  change the local optical properties. Below the magnetic dipole
@@ -612,7 +614,7 @@ license.
  induced transient optical response and the effect of newly formed
  EHP. This way, the distribution becomes more homogeneous and the
  effect is likely to be enhanced by electron diffusion inside Si
- NPs. We refer to these nonlinear phenomena as \textit{'Stage~$4$'}.
+ NPs. We refer to these nonlinear phenomena as \textit{'Stage~4'}.
      
  It is worth noting that it is possible to achieve a formation of
  deeply subwavelength EHP regions due to high field localization. The