stage 4, R=75 and R=100

main.tex

@@ -513,7 +513,7 @@ license.
  size resonance value, corresponding to $R \approx 105$~nm. In
  contrast, for larger sizes, the intensity is enhanced in the back
  side of the NP as demonstrated in Fig.~\ref{mie-fdtd}(d). In fact,
- very similar EHP distributions can be obtained by applying Maxwell's
+ rather similar EHP distributions can be obtained by applying Maxwell's
  equations coupled with the rate equation for relatively weak
  excitation with EHP concentration of $N_e \approx 10^{20}$~cm$^{-3}$,
  see Fig.~\ref{mie-fdtd}(e,f). The optical properties do not change
@@ -540,7 +540,7 @@ license.
  evolution stages during pulse duration. Typical change of the
  permittivity corresponding to each stage is shown in
  Fig.~\ref{plasma-grid}.  For better visual representation of time
- scale of the whole incident pulse and its single optical cycle we put a
+ scale of a single optical cycle we put a
  squared electric field profile on all plots in
  Fig.~\ref{time-evolution} in gray color as a backgroud image (note
  linear time scale on the left column and logarithmic scale on the
@@ -563,14 +563,14 @@ license.
  electric one (\textit{a1}) has $Q \approx 4$. The larger particle
  supporting MQ resonance (\textit{b2}) demonstrates $ Q \approx
  40$. As soon as the electromagnetic wave period at $\lambda = 800$~nm
- is 2.7~\textit{fs}, one needs about 10~\textit{fs} to pump the ED,
+ is $\approx 2.7$~\textit{fs}, one needs about 10~\textit{fs} to pump the ED,
  20~\textit{fs} for the MD, and about 100~\textit{fs} for the MQ.
  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 of NP, which results
- into a very similar field distribution for all size of NP under
+ 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
  to this phenomena as \textit{'Stage~1'}. This stage demonstrates the
  initial penetration of electromagnetic field into the NP during the
@@ -597,9 +597,9 @@ license.
  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
- still relatively small to affect the EHP evolution or for diffusion,
+ still relatively small to affect the EHP evolution,
  but is already high enough to change the local optical
- properties. Below the MD resonance $R \approx 100$~nm, the EHP is
+ properties. 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
@@ -609,12 +609,12 @@ license.
  the fact that EHP is dominantly localized in the back side of the NP.
 
  Once again, due to presence of continous pumping the Stage~3 is
- superposed with Stage~1 field pattern, resulting in the 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
+ superposed with Stage~1 field pattern, resulting in the 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 stedialy decrease as it goes to Stage~3.
 
  The explain this we need to consider time evolution of mean EHP
@@ -628,14 +628,50 @@ license.
  optical cycle of the incident wave. This delay causes a large value
  of the assymetry factor during first stage. However, as soon as mean
  EHP density increases the contribution of this pumping steps to
- resulting assymetry becomes smallar and the variation of $G_{N_e}$
- synced with the period of incident light decreases.
+ resulting assymetry becomes smallar and the synced with the period of
+ incident light variation of $G_{N_e}$ decreases.
 
  %A bookmark by Kostya
  
- For the higher excitation conditions, the optical properties of
- silicon change significantly according to the equations
- (\ref{Index}). As a result, the we observe the forward shifting of
+ Higher excitation conditions are followed with large values of
+ electric field amplitude, which lead to apperance of high EHP
+ densities causing a significant change of optical properties of
+ silicon according to the equations (\ref{Index}). As it follows from
+ Mie theory the initial (at the end of Stage~3) space pattern of
+ optical properties is non-homogeneous. When non-homogeneity of
+ optical properties becomes strong enougth it leads to the
+ reconfiguration of the electric field inside of NP and vice versa. We
+ refer to these strong nonlinear phenomena as \textit{'Stage~4'}. In
+ general the reconfiguration of the electric field is obligatory as
+ far as the result from the Mie theory comes with the assumption of
+ homogeneous optical properties in a spherical NP.
+
+ This way evolution of EHP density during Stage~4 depends on the
+ result of multipole modes superposition in 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
+ resonance, moreover, Mie field pattern and the one which comes from
+ Stage~1 are quite similar. As soon as EHP density becomes high enough
+ to change optical properties the NP is still out of resonanse,
+ however, presence of EHP increases absorption in accordance with
+ (\ref{Index}). This effectively leads to a kind of screening, it
+ becomes harder for incident wave to penetrate deep 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 to during the final stage goes in a
+ similar way, with a notable exception regarding MD resonance.  As
+ soon as presence of EHP incresases the absorption, it suppresses the
+ MD resonance with symmetric filed pattern, thus, the asymmetry factor
+ can be increased. This was actualy observed in
+ Fig.~\ref{time-evolution}(d) with a local maxima near 100~\textit{fs}
+ mark.
+ 
+ The last NP with $R=115$~nm shows the most complex behavior during
+ the Stage~4. 
+
+ as a result, the we observe the forward shifting of
  EHP density maximum. Therefore, EHP is localized in the front part of
  the NP, influencing the asymmetry factor $G_{N_e}$ in
  Fig.~\ref{time-evolution}. Approximately at the pulse peak, the
@@ -652,7 +688,7 @@ 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. 
      
  It is worth noting that it is possible to achieve a formation of
  deeply subwavelength EHP regions due to high field localization. The