stage 4

main.tex

@@ -450,7 +450,7 @@ Mie theory~\cite{Bohren1983}. It is only valid in the absence of
 nonlinear optical response, thus we can compare it against
 above-mentioned FDTD-EHP model only for small plasma densities, where
 we can neglect EHP impact to the refractive index. Non-stationary
-nature of a femtosecond pulse increase the complexity of the
+nature of a~\textit{fs} pulse increase the complexity of the
 analysis. A detailed discussion on the relation between Mie theory and
 FDTD-EHP model will be provided in the next section.
 
@@ -524,12 +524,12 @@ license.
  oscillations inside the Si NP. Further on we present transient
  analysis, which reveals much more details.
 
- To achieve a quantative description for evolution of the EHP
+ To achieve a quantitative description for evolution of the EHP
  distribution during the \textit{fs} pulse, we introduced another
  asymmetry factor
  $G_{N_e} = (N_e^{front}-N_e^{back})/(N_e^{front}+N_e^{back})$
  indicating the relationship between the average EHP densities in the
- front and in the back halfs of the NP. This way, $G_{N_e} = 0$
+ front and in the back halves of the NP. This way, $G_{N_e} = 0$
  corresponds to the quasi-homogeneous case and the assumption of the
  NP homogeneous EHP distribution can be made to investigate the
  optical response of the excited Si NP. When $G_{N_e}$ significantly
@@ -542,7 +542,7 @@ license.
  Fig.~\ref{plasma-grid}.  For better visual representation of time
  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
+ 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).
 
@@ -582,13 +582,13 @@ license.
  Fig.~\ref{plasma-grid}(f,j). We would like to stress the
  unstationery nature of field pattern at this stage. The energy
  balance between extinction and pumping is not set, moreover, there is
- a simultaneous growth of the incident pulse apmlitude. This leads to
+ 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
  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 supression inside of NP predicted by Mie theory). At this
+ for field suppression inside of NP predicted by 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.
 
@@ -608,36 +608,36 @@ license.
  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.
 
- Once again, due to presence of continous pumping the Stage~3 is
+ Once again, due to presence of continuous pumping the Stage~3 is
  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.
+ variation steadily decrease as it goes to Stage~3.
 
  The explain this we need to consider time evolution of mean EHP
- densities $N_e$ in the front and back halfs of NP presented in
+ densities $N_e$ in the front and back halves of NP presented in
  Fig.~\ref{time-evolution}(a,c,e). As soon as recombination and
  diffusion processes are negligible at \textit{fs} time scale, both
- $N_e^{front}$ and $N_e^{back}$ curves experience monotonous behaviour
+ $N_e^{front}$ and $N_e^{back}$ curves experience monotonous behavior
  with small pumping steps synced to the incident pulse. Front and back
- halfs are separated in space, wich obviously leads to the presence of
- time delay between puping steps in each curve caused with the same
+ halves are separated in space, which obviously leads to the presence of
+ time delay between pumping steps in each curve caused with the same
  optical cycle of the incident wave. This delay causes a large value
- of the assymetry factor during first stage. However, as soon as mean
+ of the asymmetry 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 synced with the period of
+ resulting asymmetry becomes smaller and the synced with the period of
  incident light variation of $G_{N_e}$ decreases.
 
  Higher excitation conditions are followed with large values of
- electric field amplitude, which lead to apperance of high EHP
+ electric field amplitude, which lead to appearance 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
+ optical properties becomes strong enough 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
@@ -651,7 +651,7 @@ license.
  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,
+ to change optical properties the NP is still out of resonance,
  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,
@@ -660,22 +660,22 @@ license.
 
  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 incresases the absorption, it suppresses the
+ soon as presence of EHP increases 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}
+ can be increased. This was actually observed in
+ Fig.~\ref{time-evolution}(d) with a local maximum near 100~\textit{fs}
  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
  front shifted. They serve to be a starting seed for EHP formation,
- the interplay between them forms a complex behavior of the assymetry
+ the interplay between them forms a complex behavior of the asymmetry
  factor curve. Namely, it changes the sign from negative to positive
  and back during the last stage. This numerical result can hardly be
  explained in a simple qualitative manner, it is too complex to
  account all near-field interaction of incident light with two EHP
- regions inside a single NP. However, it is intersing to note, that in
+ regions inside a single NP. However, it is interesting to note, 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
  EHP. As soon as this EHP region is quite visible on the last snapshot