changes

main.tex

@@ -464,15 +464,16 @@ license.
 \begin{figure*}[p]
  \centering
  \includegraphics[width=145mm]{time-evolution-I-no-NP.pdf}
- \caption{\label{time-evolution} Temporal EHP (a, c, e) and asymmetry factor
-   $G_{N_e}$ (b, d, f) evolution for different Si nanoparticle radii of
-   (a, b) $R = 75$~nm, (c, d) $R = 100$~nm, and (e, f) $R = 115$~nm. Pulse
-   duration $80$~\textit{fs} (FWHM). \red{\textbf{TODO:} on the plot
-     it looks more than 100 fs for FWHM!!! Anton? }
-   Wavelength $800$~nm in air. (b,
-   d, f) Different stages of EHP evolution shown in Fig.~\ref{plasma-grid}
-   are indicated. The temporal evolution of Gaussian beam intensity is
-   also shown. Peak laser fluence is fixed to be $0.125$~J/cm$^2$.}
+ \caption{\label{time-evolution} Temporal EHP (a, c, e) and asymmetry
+   factor $G_{N_e}$ (b, d, f) evolution for different Si nanoparticle
+   radii of (a, b) $R = 75$~nm, (c, d) $R = 100$~nm, and (e, f)
+   $R = 115$~nm. Pulse duration $80$~\textit{fs}
+   (FWHM). \red{\textbf{TODO:} on the plot it looks more than 100 fs
+     for FWHM!!! Anton? } Wavelength $800$~nm in air. (b, d, f)
+   Different stages of EHP evolution shown in Fig.~\ref{plasma-grid}
+   are indicated. The temporal evolution of the incident Gaussian beam
+   intensity is also shown. Peak laser fluence is fixed to be
+   $0.125$~J/cm$^2$.}
 \vspace*{\floatsep}
  \centering
  \includegraphics[width=150mm]{plasma-grid.pdf}
@@ -542,7 +543,7 @@ license.
  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
- squared electric field profile on all plots at
+ 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
  right one).
@@ -570,36 +571,70 @@ license.
  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
- there is no multiple mode structure inside of NP, which results into
- a very similar field distribution for all size of NP under
- consideration as shown in Figs.~\ref{plasma-grid}(a,e,i) . We address
+ there is no multipole modes structure inside of NP, which results
+ into a very similar field distribution for all size 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.
  
  \textit{'Stage~2'} corresponds to further electric field oscillations
- ($t \approx 2$--$15$) 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
- time to be excited. 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.
-
- 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
- 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 MD
- resonance $R \approx 100$~nm, the EHP is mostly localized in the
- front side of the NP as shown in Fig.~\ref{plasma-grid}(c). The highest
- 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 is much closer to the
- homogeneous distribution. In contrast, above the MD
- resonant size for $R = 115$~nm, and the $G_{N_e} < 0$ due to the fact
- that EHP is dominantly localized in the back side of the NP.
-
+ ($t \approx 5$--$15$) leading to the formation of ED field pattern in
+ the center of the NP as it can be seen in
+ 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 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
+ 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.
+
+ When the number of optical cycles is big 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
+ still relatively small to affect the EHP evolution or for diffusion,
+ but is already high enough to change the local optical
+ properties. Below the MD resonance $R \approx 100$~nm, the EHP is
+ mostly localized in the front side of the NP as shown in
+ Fig.~\ref{plasma-grid}(c). The highest 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
+ is much closer to the homogeneous distribution. In contrast, above
+ the MD resonant size for $R = 115$~nm, and 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
+ 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
+ variation stedialy 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
+ 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
+ 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
+ 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.
+
+ %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 non-resonant ED