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@@ -521,7 +521,7 @@ license.
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(a, c, e) and time (b, d, f) for different Si nanoparticle radii
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(a, b) $R = 75$ nm, (c, d) $R = 100$ nm, (e, f) $R = 115$ nm. Pulse
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duration $50$~\textit{fs} (FWHM). Wavelength $800$ nm in air. (a, c, e)
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- Different stages of EHP evolution shown in \ref{fig2} are
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+ Different stages of EHP evolution shown in Fig.~\ref{fig2} are
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indicated. (b, d, f) The temporal evolution of Gaussian beam
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intensity is also shown. Peak laser fluence is fixed to be $0.125$
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J/cm$^2$.}
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@@ -543,17 +543,17 @@ license.
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two-photon absorption. Fig.~\ref{mie-fdtd}(b) shows $G$ factors
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as a function of the nanoparticle size. For the nanoparticles of
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sizes below the first magnetic dipole resonance, the intensity is
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- enhanced in the front side as in Fig. \ref{mie-fdtd}(c) and
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+ enhanced in the front side as in Fig.~\ref{mie-fdtd}(c) and
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$G_I > 0$. The behavior changes near the size resonance value,
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corresponding to $R \approx 105$ nm. In contrast, for larger sizes,
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the intensity is enhanced in the back side of the nanoparticle as
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- demonstrated in Fig. \ref{mie-fdtd}(d). In fact, the similar EHP
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+ demonstrated in Fig.~\ref{mie-fdtd}(d). In fact, the similar EHP
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distributions can be obtained by applying Maxwell's equations coupled
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with the rate equation for relatively weak excitation
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$N_e \approx 10^{20}$ cm$^{-3}$. The optical properties do not change
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considerably due to excitation according to (\ref{Index}). Therefore,
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the excitation processes follow the intensity distribution. However,
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- such coincidence was achieved in quasi-stationary conditions, when
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+ such coincidence was achieved in quasi-stationary conditions, after the
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electric field made enough oscillations inside the Si NP. To achieve
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a qualitative description of the EHP distribution, we introduced
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another asymmetry factor
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@@ -566,8 +566,8 @@ license.
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differs from $0$, this assumption could not be proposed. In what
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follows, we discuss the results of the numerical modeling revealing
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the EHP evolution stages during pulse duration shown in
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- Fig. \ref{fig2} and the temporal/EHP dependent evolution of the
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- asymmetry factor $G$ in Fig. \ref{fig3}.
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+ Fig.~\ref{fig2} and the temporal/EHP dependent evolution of the
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+ asymmetry factor $G$ in Fig.~\ref{fig3}.
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% Fig. \ref{Mie} demonstrates the temporal evolution of the EHP
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% generated inside the silicon nanoparticle of $R \approx 105$
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@@ -614,7 +614,7 @@ license.
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shown in Figs.~\ref{fig2} and~\ref{fig2}. The first stage at the
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first optical cycle demonstrates the dominant electric dipole
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resonance effect on the intensity/EHP density distribution inside the
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- NPs in Fig.~\ref{fig2}(a,e,j) and \ref{fig3}. The larger the NPs size
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+ NPs in Fig.~\ref{fig2}(a,e,j) and~\ref{fig3}. The larger the NPs size
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is, the higher the NP asymmetry $G_{N_e}$ is achieved.
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\textit{'Stage 2'} corresponds to further electric field oscillations
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@@ -632,7 +632,7 @@ license.
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influence the EHP evolution and strong diffusion rates but already
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enough to change the optical properties locally. Below the magnetic
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dipole resonance $R \approx 100$ nm, the EHP is mostly localized in
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- the front side of the NP as shown in Fig. \ref{fig2}(c). The highest
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+ the front side of the NP as shown in Fig.~\ref{fig2}(c). The highest
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stationary asymmetry factor \red{$G_{N_e} \approx 3-4$ (should be
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changed)} is achieved in this case. At the magnetic dipole
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resonance conditions, the EHP distribution has a toroidal shape and
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@@ -652,7 +652,7 @@ license.
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$Re(\epsilon) \approx 0$ and to the electron plasma resonance, is
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overcome. Further irradiation leads to a decrease in the asymmetry
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parameter down to $G_{N_e} = 0$ for higher EHP densities, as one can
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- observe in Fig. \ref{fig2}(d, h, l).
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+ observe in Fig.~\ref{fig2}(d, h, l).
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As the EHP acquires quasi-metallic properties at stronger excitation
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$N_e > 5\cdot{10}^{21}$ cm$^{-3}$, the EHP distribution evolves
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@@ -666,7 +666,7 @@ license.
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deeply subwavelength EHP regions due to high field localization. The
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smallest EHP localization and the larger asymmetry factor are
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achieved below the magnetic dipole resonant conditions for $R < 100$
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- nm. Thus, the EHP distribution in Fig. \ref{fig2}(c) is optimal for
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+ nm. Thus, the EHP distribution in Fig.~\ref{fig2}(c) is optimal for
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symmetry breaking in Si NP, as it results in the larger asymmetry
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factor $G_{N_e}$ and higher electron densities $n_e$. We stress here
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that such regime could be still safe for NP due to the very small
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