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@@ -464,15 +464,16 @@ license.
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\begin{figure*}[p]
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\centering
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\includegraphics[width=145mm]{time-evolution-I-no-NP.pdf}
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- \caption{\label{time-evolution} Temporal EHP (a, c, e) and asymmetry factor
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- $G_{N_e}$ (b, d, f) evolution for different Si nanoparticle radii of
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- (a, b) $R = 75$~nm, (c, d) $R = 100$~nm, and (e, f) $R = 115$~nm. Pulse
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- duration $80$~\textit{fs} (FWHM). \red{\textbf{TODO:} on the plot
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- it looks more than 100 fs for FWHM!!! Anton? }
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- Wavelength $800$~nm in air. (b,
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- d, f) Different stages of EHP evolution shown in Fig.~\ref{plasma-grid}
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- are indicated. The temporal evolution of Gaussian beam intensity is
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- also shown. Peak laser fluence is fixed to be $0.125$~J/cm$^2$.}
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+ \caption{\label{time-evolution} Temporal EHP (a, c, e) and asymmetry
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+ factor $G_{N_e}$ (b, d, f) evolution for different Si nanoparticle
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+ radii of (a, b) $R = 75$~nm, (c, d) $R = 100$~nm, and (e, f)
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+ $R = 115$~nm. Pulse duration $80$~\textit{fs}
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+ (FWHM). \red{\textbf{TODO:} on the plot it looks more than 100 fs
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+ for FWHM!!! Anton? } Wavelength $800$~nm in air. (b, d, f)
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+ Different stages of EHP evolution shown in Fig.~\ref{plasma-grid}
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+ are indicated. The temporal evolution of the incident Gaussian beam
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+ intensity is also shown. Peak laser fluence is fixed to be
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+ $0.125$~J/cm$^2$.}
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\vspace*{\floatsep}
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\centering
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\includegraphics[width=150mm]{plasma-grid.pdf}
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@@ -542,7 +543,7 @@ license.
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permittivity corresponding to each stage is shown in
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Fig.~\ref{plasma-grid}. For better visual representation of time
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scale of the whole incident pulse and its single optical cycle we put a
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- squared electric field profile on all plots at
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+ squared electric field profile on all plots in
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Fig.~\ref{time-evolution} in gray color as a backgroud image (note
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linear time scale on the left column and logarithmic scale on the
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right one).
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@@ -570,36 +571,70 @@ license.
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place on a 10~\textit{fs} scale it results in the excitation of the
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low-\textit{Q} ED resonance, which dominates MD and MQ independently
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on the exact size of NPs. Moreover, during the first optical cycle
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- there is no multiple mode structure inside of NP, which results into
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- a very similar field distribution for all size of NP under
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- consideration as shown in Figs.~\ref{plasma-grid}(a,e,i) . We address
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+ there is no multipole modes structure inside of NP, which results
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+ into a very similar field distribution for all size of NP under
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+ consideration as shown in Fig.~\ref{plasma-grid}(a,e,i) . We address
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to this phenomena as \textit{'Stage~1'}. This stage demonstrates the
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initial penetration of electromagnetic field into the NP during the
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first optical cycle.
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\textit{'Stage~2'} corresponds to further electric field oscillations
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- ($t \approx 2$--$15$) leading to the unstationery EHP evolution
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- with a maximum of the EHP distribution in the front side of the Si NP
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- owing to the starting excitation of MD and MQ resonances that require more
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- time to be excited. At this stage, the density of EHP ($N_e < 10^{20}$~cm$^2$)
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- is still not high enough to significantly affect the optical properties
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- of the NP.
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-
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- A number of optical cycles ($>$10 or $t>$25~\textit{fs}) is necessary
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- to achieve the stationary intensity pattern corresponding to the
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- Mie-based intensity distribution at the \textit{'Stage~3'} (see
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- Fig.~\ref{time-evolution}). The EHP density is still relatively small to affect
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- the EHP evolution or for diffusion, but is already high enough to
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- change the local optical properties. Below the MD
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- resonance $R \approx 100$~nm, the EHP is mostly localized in the
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- front side of the NP as shown in Fig.~\ref{plasma-grid}(c). The highest
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- stationary asymmetry factor $G_{N_e} \approx 0.5$--$0.6$ is achieved
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- in this case. At the MD resonance conditions, the EHP
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- distribution has a toroidal shape and is much closer to the
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- homogeneous distribution. In contrast, above the MD
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- resonant size for $R = 115$~nm, and the $G_{N_e} < 0$ due to the fact
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- that EHP is dominantly localized in the back side of the NP.
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-
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+ ($t \approx 5$--$15$) leading to the formation of ED field pattern in
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+ the center of the NP as it can be seen in
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+ Fig.~\ref{plasma-grid}(f,j). We would like to stress the
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+ unstationery nature of field pattern at this stage. The energy
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+ balance between extinction and pumping is not set, moreover, there is
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+ a simultaneous growth of the incident pulse apmlitude. This leads to
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+ a superposition of ED field pattern with the one from the Stage 1,
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+ resulting into the presence for the maximum of the EHP distribution
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+ in the front side of the Si NP. This effect dominates for the
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+ smallest NP with $R=75$~nm in Fig.~\ref{plasma-grid}(b), where ED
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+ mode is tuned far away from the resonance (see Fig.~\ref{mie-fdtd}(c)
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+ for field supression inside of NP predicted by Mie theory). At this
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+ stage, the density of EHP ($N_e < 10^{20}$~cm$^2$) is still not high
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+ enough to significantly affect the optical properties of the NP.
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+
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+ When the number of optical cycles is big enough ($t>20$~\textit{fs})
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+ both ED and MD modes can be exited to the level necessary to achieve
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+ the stationary intensity pattern corresponding to the Mie-based
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+ intensity distribution at the \textit{'Stage~3'} (see
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+ Fig.~\ref{plasma-grid}). The EHP density for the most volume of NP is
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+ still relatively small to affect the EHP evolution or for diffusion,
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+ but is already high enough to change the local optical
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+ properties. Below the MD resonance $R \approx 100$~nm, the EHP is
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+ mostly localized in the front side of the NP as shown in
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+ Fig.~\ref{plasma-grid}(c). The highest stationary asymmetry factor
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+ $G_{N_e} \approx 0.5$--$0.6$ is achieved in this case. At the MD
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+ resonance conditions, the EHP distribution has a toroidal shape and
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+ is much closer to the homogeneous distribution. In contrast, above
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+ the MD resonant size for $R = 115$~nm, and the $G_{N_e} < 0$ due to
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+ the fact that EHP is dominantly localized in the back side of the NP.
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+
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+ Once again, due to presence of continous pumping the Stage~3 is
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+ superposed with Stage~1 field pattern, resulting in the EHP localized
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+ in the front side. This can be seen when comparing result from the
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+ Mie theory in Fig.~\ref{mie-fdtd}(d) and result of full 3D simulation
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+ in Fig.~\ref{mie-fdtd}(f). Note that pumping of NP significantly
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+ changes during a single optical cycle, this leads to a large
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+ variation of asymmetry factor $G_{N_e}$ at first stage. This
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+ variation stedialy decrease as it goes to Stage~3.
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+
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+ The explain this we need to consider time evolution of mean EHP
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+ densities $N_e$ in the front and back halfs of NP presented in
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+ Fig.~\ref{time-evolution}(a,c,e). As soon as recombination and
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+ diffusion processes are negligible at \textit{fs} time scale, both
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+ $N_e^{front}$ and $N_e^{back}$ curves experience monotonous behaviour
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+ with small pumping steps synced to the incident pulse. Front and back
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+ halfs are separated in space, wich obviously leads to the presence of
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+ time delay between puping steps in each curve caused with the same
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+ optical cycle of the incident wave. This delay causes a large value
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+ of the assymetry factor during first stage. However, as soon as mean
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+ EHP density increases the contribution of this pumping steps to
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+ resulting assymetry becomes smallar and the variation of $G_{N_e}$
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+ synced with the period of incident light decreases.
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+
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+ %A bookmark by Kostya
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+
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For the higher excitation conditions, the optical properties of
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silicon change significantly according to the equations
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(\ref{Index}). As a result, the non-resonant ED
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