Merge branch 'master' of https://git.overleaf.com/6933504hfrhtkqjvtmk

main.tex

@@ -125,9 +125,9 @@
 \vspace{3cm}
 \sffamily
 \begin{tabular}{m{4.5cm} p{13.5cm} }
-  \includegraphics{head_foot/DOI} & \noindent\LARGE{\textbf{Self-Induced Plasma-Induced Symmetry Breaking in a Spherical Silicon Nanoparticle}} \\%Article title goes here instead of the text "This is the title"
+  \includegraphics{head_foot/DOI} & \noindent\LARGE{\textbf{Photo-generated Electron-Hole Plasma-Induced Symmetry Breaking in Spherical Silicon Nanoparticles}} \\%Article title goes here instead of the text "This is the title"
   \vspace{0.3cm} & \vspace{0.3cm} \\
-                                  & \noindent\large{Anton Rudenko,$^{\ast}$\textit{$^{a}$} Tatiana E. Itina,\textit{$^{a\ddag}$} Konstantin Ladutenko,\textit{$^{b}$} and Sergey Makarov\textit{$^{b}$}
+                                  & \noindent\large{Anton Rudenko,$^{\ast}$\textit{$^{a}$}  Konstantin Ladutenko,\textit{$^{b}$}  Sergey Makarov\textit{$^{b}$} and Tatiana E. Itina\textit{$^{a}$$^{b}$}
  
                                     \textit{$^{a}$~Laboratoire Hubert Curien, UMR CNRS 5516, University of Lyon/UJM, 42000, Saint-Etienne, France }
                                     \textit{$^{b}$~ITMO University, Kronverksiy pr. 49, St. Petersburg, Russia}
@@ -140,20 +140,16 @@ of nonlinear all-dielectric nanophotonics based on high refractive
 index (e.g., silicon) nanoparticles supporting magnetic optical
 response has recently emerged as a powerful tool for ultrafast
 all-optical modulation at nanoscale. A strong modulation can be
-achieved via photogeneration of dense electron-hole plasma in the
+achieved via photo-generation of dense electron-hole plasma in the
 regime of simultaneous excitation of electric and magnetic optical
 resonances, resulting in an effective transient reconfiguration of
-nanoparticle scattering properties. However, previous works assumed
-only homogenized plasma generation in the photoexcited nanoparticle,
-neglecting all effects related to inhomogeneous plasma
-distribution. Here numerical studying of the plasma photogeneration
-allows us to propose a novel concept of deeply subwavelength
+nanoparticle scattering properties. Because only homogeneous plasma generation was previously considered in the photo-excited nanoparticle, a possibility of symmetry breaking, however, remain unexplored. To examine these effects, numerical modeling is performed. Based on the simulation results, we propose an original concept of a well-controlled deeply subwavelength
 ($\approx$$\lambda$$^3$/100) plasma-induced nanopatterning of
-symmetrical silicon nanoparticle. More importantly, we reveal strong
-symmetry breaking in the initially symmetrical nanoparticle during
-ultrafast photoexcitation near the magnetic dipole resonance. The
-ultrafast manipulation by nanoparticle inherent structure and symmetry 
-paves the way to novel principles for nonlinear optical nanodevices.}
+spherical silicon nanoparticles. In particular, the revealed strong
+symmetry breaking in the initially symmetrical nanoparticle, which is observed during
+ultrafast photoexcitation near the magnetic dipole resonance, enables a considerable increase in the precision of laser-induced nanotreatment. Importantly, the proposed
+ultrafast manipulation of the nanoparticle inherent structure and symmetry 
+paves a way to the novel principles that are also promising for nonlinear optical nanodevices.}
 
 \end{tabular}
 
@@ -233,24 +229,22 @@ distributions in silicon nanoparticle around a magnetic resonance.}
   \label{fgr:concept}
 \end{figure}
 
-Recently, highly localized plasma inside the nanoparticles, irradiated by femtosecond laser, has been directly observed using plasma explosion imaging \cite{Hickstein2014}. Additionally, inhomogeneous resonant scattering patterns inside single silicon nanoparticles have been experimentally revealed \cite{Valuckas2017}.  
-
-In this Letter, we show that electron-hole plasma (EHP) generation in
-a spherical dielectric (e.g., silicon) nanoparticle leads to strongly
-nonhomogeneous EHP distribution. To reveal and study this effect, we
-for the first time provide full-wave numerical simulation of intensive
-femtosecond (fs) laser pulse interaction with a dielectric
-nanoparticle supporting Mie resonances and two-photon generation of
-EHP. In particular, we couple finite-difference time-domain (FDTD)
-method of the Maxwell's equations solving with equations describing
-nonlinear EHP generation and its variation of material dielectric
-permittivity. The obtained results propose a novel strategy to create
-complicated nonsymmetrical nanostructures by using only a photoexcited
-spherical silicon nanoparticle. Moreover, we show that dense EHP can
+Recently, femtosecond lasers have been used to ionize nanoparticles locally and to produce electron-hole plasmas (EHP) inside them, which have been directly observed by using plasma explosion imaging\cite{Hickstein2014}. Interestingly, inhomogeneous resonant scattering patterns have been experimentally revealed inside a single silicon nanoparticle\cite{Valuckas2017}.  
+
+In this Letter, we show that ultra-short laser-based EHP photo-excitation in
+a spherical semiconductor (e.g., silicon) nanoparticle leads to a strongly
+inhomogeneous carrier distribution. To reveal and study this effect, we
+ perform a full-wave numerical simulation of the intense
+femtosecond (fs) laser pulse interaction with a silicon
+nanoparticle supporting Mie resonances and two-photon free carrier generation. In particular, we couple finite-difference time-domain (FDTD)
+method used to solve  Maxwell equations with kinetic equations describing
+nonlinear EHP generation.  Three-dimensional transient variation of the material dielectric permittivity is calculated for nanoparticles of several sizes. The obtained results propose a novel strategy to create
+complicated non-symmetrical nanostructures by using  photo-excited
+single spherical silicon nanoparticles. Moreover, we show that dense EHP can
 be generated at deeply subwavelength scale
-($\approx$$\lambda$$^3$/100) supporting formation of small metallized
-parts inside the nanoparticle which transforms all-dielectric
-nanoparticle to a hybrid one that extends functionality of ultrafast
+($\approx$$\lambda$$^3$/100) supporting formation of small metalized
+parts inside the nanoparticle, which transforms all-dielectric
+nanoparticle to a hybrid one that extends functionality of the ultrafast
 optical nanoantennas.
 
 
@@ -276,40 +270,33 @@ optical nanoantennas.
 
 \section{Modeling details}
  
-% TEI for Anton: please describe what you model first (what physical
-% processes). Then, we speak about "pulse", but never "laser". Should
-% we provide more details concerning irradiation source?
 
 We focus out attention on silicon because this material is promising
-for the implementation of nonlinear photonic devices thanks to a broad
-range of optical nonlinearities, strong two-photon absorption and EHP
+for the implementation of numerous nonlinear photonic devices. This advantage is based on a broad
+range of optical nonlinearities, strong two-photon absorption, as well as a possibility of the photo-induced EHP
 excitation~\cite{leuthold2010nonlinear}. Furthermore, silicon
 nanoantennas demonstrate a sufficiently high damage threshold due to
 the large melting temperature ($\approx$1690~K), whereas its nonlinear
 optical properties have been extensively studied during last
-decays~\cite{Van1987, Sokolowski2000, leuthold2010nonlinear}. High melting point for silicon preserves up to EHP densities of order $n_{cr} \approx 5\cdot{10}^{21}$ cm$^{-3}$ \cite{Korfiatis2007}, for which silicon acquires metallic properties ($Re(\epsilon) < 0$) and contributes to the EHP reconfiguration during ultrashort laser irradiation.
+decays~\cite{Van1987, Sokolowski2000, leuthold2010nonlinear}. High silicon melting point typically preserves structures formed from this material up to the EHP densities on the order of the critical value $n_{cr} \approx 5\cdot{10}^{21}$ cm$^{-3}$ \cite{Korfiatis2007}. At the critical density and above, silicon acquires metallic properties ($Re(\epsilon) < 0$) and contributes to the EHP reconfiguration during ultrashort laser irradiation.
 
-Since the 3D modeling of EHP photo-generation in a resonant silicon
-nanoparticle has not been done before in time-domain, we develop a
-model considering incidence of ultrashort light pulse on a silicon
-sphere, where EHP is generated via one- and two-photon absorption
-processes, and then decayed via Auger recombination. Importantly, we
+The process of three-dimensional photo-generation of the EHP in silicon
+nanoparticles has not been modeled before in time-domain. Therefore, herein we propose a model considering ultrashort laser interactions with a resonant silicon
+sphere, where the EHP is generated via one- and two-photon absorption
+processes.  Importantly, we
 also consider nonlinear feedback of the material by taking into
-account intraband light absorption on the generated free carriers. In
-order to simplify our model, we neglect diffusion of EHP, because the
-aim of our work is to study EHP dynamics \textit{during} laser
-interaction with the nanoparticle.
+account the intraband light absorption on the generated free carriers. To simplify our model, we neglect free carrier diffusion at the considered short time scales. In fact, the aim of the present work is to study the EHP dynamics \textit{during} ultra-short laser interaction with the nanoparticle. The created electron-hole plasma then will recombine, however, as its existence modifies both laser-particle interaction and, hence, the following particle evolution.
 
 \subsection{Light propagation}
 
-The propagation of light inside the silicon nanoparticle is modeled by solving the system of Maxwell's equations, written in the following way
+Ultra-short laser interaction and light propagation inside the silicon nanoparticle are modeled by solving the system of Maxwell's equations written in the following way
 \begin{align} \begin{cases} \label{Maxwell}$$
 	\displaystyle{\frac{\partial{\vec{E}}}{\partial{t}}=\frac{\nabla\times\vec{H}}{\epsilon_0\epsilon}-\frac{1}{\epsilon_0\epsilon}(\vec{J}_p+\vec{J}_{Kerr})} \\ 		
 	\displaystyle{\frac{\partial{\vec{H}}}{\partial{t}}=-\frac{\nabla\times\vec{E}}{\mu_0}},
 	$$ \end{cases} \end{align} 
 where $\vec{E}$ is the electric field, $\vec{H}$ is the magnetizing field, $\epsilon_0$ is the free space permittivity, $\mu_0$ is the permeability of free space, $\epsilon = n^2 = 3.681^2$ is the permittivity of non-excited silicon at $800$ nm wavelength \cite{Green1995}, $\vec{J}_p$ and $\vec{J}_{Kerr}$ are the nonlinear currents, which include the contribution due to Kerr effect $\vec{J}_{Kerr} = \epsilon_0\epsilon_\infty\chi_3\frac{\partial\left(\left|\vec{E}\right|^2\vec{E}\right)}{\partial{t}}$, where $\chi_3 =4\cdot{10}^{-20}$ m$^2$/V$^2$ for laser wavelength $\lambda = 800$nm \cite{Bristow2007}, and heating of the conduction band, described by the differential equation derived from the Drude model
 \begin{equation} \label{Drude} \displaystyle{\frac{\partial{\vec{J_p}}}{\partial{t}} = - \nu_e\vec{J_p} + \frac{e^2n_e(t)}{m_e^*}\vec{E}}, \end{equation} 
-where $e$ is the elementary charge, $m_e^* = 0.18m_e$ is the reduced electron-hole mass \cite{Sokolowski2000}, $n_e(t)$ is the time-dependent free carrier density and $\nu_e = 10^{15}$ s$^{-1}$ is the electron collision frequency \cite{Sokolowski2000}. Silicon nanoparticle is surrounded by vacuum, where the light propagation is calculated by Maxwell's equations with $\vec{J} = 0$ and $\epsilon = 1$. The system of Maxwell's equations coupled with electron density equation is solved by the finite-difference numerical method \cite{Rudenko2016}, based on the finite-difference time-domain (FDTD) \cite{Yee1966} and auxiliary-differential methods for dispersive media \cite{Taflove1995}. At the edges of the grid, we apply absorbing boundary conditions related to convolutional perfectly matched layers (CPML) to avoid nonphysical reflections \cite{Roden2000}. Initial electric field is introduced as a Gaussian focused beam source as follows
+where $e$ is the elementary charge, $m_e^* = 0.18m_e$ is the reduced electron-hole mass \cite{Sokolowski2000}, $n_e(t)$ is the time-dependent free carrier density and $\nu_e = 10^{15}$ s$^{-1}$ is the electron collision frequency \cite{Sokolowski2000}. Silicon nanoparticle is surrounded by vacuum, where the light propagation is calculated by Maxwell's equations with $\vec{J} = 0$ and $\epsilon = 1$. The system of Maxwell's equations coupled with electron density equation is solved by the finite-difference numerical method \cite{Rudenko2016}, based on the finite-difference time-domain (FDTD) \cite{Yee1966} and auxiliary-differential methods for dispersive media \cite{Taflove1995}. At the edges of the grid, we apply the absorbing boundary conditions related to convolutional perfectly matched layers (CPML) to avoid nonphysical reflections \cite{Roden2000}. The initial electric field is introduced as a Gaussian slightly focused beam as follows
 \begin{align}
 \begin{aligned}
 \label{Gaussian}
@@ -317,20 +304,26 @@ where $e$ is the elementary charge, $m_e^* = 0.18m_e$ is the reduced electron-ho
 \times\;{exp}\left(-\frac{(t-t_0)^2}{\theta^2}\right),
 \end{aligned}
 \end{align}
-where $\theta$ is the pulse width at half maximum (FWHM), $t_0$ is a time delay, $w_0 = 3{\mu}m$ is the waist beam, $w(z) = {w_0}\sqrt{1+(\frac{z}{z_R})^2}$ is the Gaussian's beam spot size, $\omega = 2{\pi}c/{\lambda}$ is the angular frequency, $\lambda = 800 nm$ is the laser wavelength in air, $c$ is the speed of light, ${z_R} = \frac{\pi{{w_0}^2}n_0}{\lambda}$ is the Rayleigh length, $r = \sqrt{x^2 + y^2}$ is the radial distance from the beam's waist, $R_z = z\left(1+(\frac{z_R}{z})^2\right)$ is the radius of curvature of the wavelength comprising the beam, and $\varsigma(z) = {\arctan}(\frac{z}{z_R}) $ is the Gouy phase shift. 
+where $\theta$ is the temporal pulse width at the half maximum (FWHM), $t_0$ is a time delay, $w_0 = 3{\mu}m$ is the waist beam, $w(z) = {w_0}\sqrt{1+(\frac{z}{z_R})^2}$ is the Gaussian's beam spot size, $\omega = 2{\pi}c/{\lambda}$ is the angular frequency, $\lambda = 800 nm$ is the laser wavelength in air, $c$ is the speed of light, ${z_R} = \frac{\pi{{w_0}^2}n_0}{\lambda}$ is the Rayleigh length, $r = \sqrt{x^2 + y^2}$ is the radial distance from the beam's waist, $R_z = z\left(1+(\frac{z_R}{z})^2\right)$ is the radius of curvature of the wavelength comprising the beam, and $\varsigma(z) = {\arctan}(\frac{z}{z_R}) $ is the Gouy phase shift. 
 
 \subsection{Material ionization}
 
-To account for material ionization, we couple Maxwell's equations with the kinetic equation for EHP generation and relaxation inside silicon nanoparticle.
+To account for the material ionization that is induced by a sufficiently intense laser field inside the particle, we couple Maxwell's equations with the kinetic equation for the electron-hole plasma as follows
 \begin{figure*}[ht!]
 \centering
 \includegraphics[width=120mm]{fig2.png}
 \caption{\label{fig2} Free carrier density snapshots of electron plasma evolution inside Si nanoparticle taken a) $30$ fs b) $10$ fs before the pulse peak, c) at the pulse peak, d) $10$ fs e) $30$ fs after the pulse peak. Pulse duration $50$ fs (FWHM). Wavelength $800$ nm in air. Radius of the nanoparticle $R \approx 105$ nm, corresponding to the resonance condition. Graph shows the dependence of the asymmetric parameter of electron plasma density on the average electron density in the front half of the nanoparticle. $n_{cr} = 5\cdot{10}^{21}$ cm$^{-3}$ is the critical plasma resonance electron density for silicon.}
 \end{figure*}
 
-The time-dependent conduction-band carrier density evolution is described with a rate equation, firstly proposed by van Driel \cite{Van1987}, taking into account photoionization, avalanche ionization and Auger recombination as 
+The time-dependent conduction-band carrier density evolution is described by a rate equation that was proposed by van Driel \cite{Van1987}. This equation takes into account such processes as photoionization, avalanche ionization and Auger recombination, and is written as
 \begin{equation} \label{Dens} \displaystyle{\frac{\partial{n_e}}{\partial t} = \frac{n_a-n_e}{n_a}\left(\frac{\sigma_1I}{\hbar\omega} + \frac{\sigma_2I^2}{2\hbar\omega}\right) + \alpha{I}n_e - \frac{C\cdot{n_e}^3}{C\tau_{rec}n_e^2+1},} \end{equation} 
-where $I=\frac{n}{2}\sqrt{\frac{\epsilon_0}{\mu_0}}\left|\vec{E}\right|^2$ is the intensity, $\sigma_1 = 1.021\cdot{10}^3 cm^{-1}$ and $\sigma_2 = 0.1\cdot{10}^{-7}$ cm/W are the one-photon and two-photon interband cross-sections \cite{Choi2002, Bristow2007, Derrien2013}, $n_a = 5\cdot{10}^{22} cm^{-3}$ is the saturation particle density \cite{Derrien2013}, $C = 3.8\cdot{10}^{-31}$ cm$^6$/s is the Auger recombination rate \cite{Van1987}, $\tau_{rec} = 6\cdot{10}^{-12}$s is the minimum Auger recombination time \cite{Yoffa1980}, and $\alpha = 21.2$ cm$^2$/J is the avalanche ionization coefficient \cite{Pronko1998} at the wavelength $800$ nm in air. Free carrier diffusion can be neglected during and shortly after the excitation \cite{Van1987, Sokolowski2000}.
+where $I=\frac{n}{2}\sqrt{\frac{\epsilon_0}{\mu_0}}\left|\vec{E}\right|^2$ is the intensity, $\sigma_1 = 1.021\cdot{10}^3 cm^{-1}$ and $\sigma_2 = 0.1\cdot{10}^{-7}$ cm/W are the one-photon and two-photon interband cross-sections \cite{Choi2002, Bristow2007, Derrien2013}, $n_a = 5\cdot{10}^{22} cm^{-3}$ is the saturation particle density \cite{Derrien2013}, $C = 3.8\cdot{10}^{-31}$ cm$^6$/s is the Auger recombination rate \cite{Van1987}, $\tau_{rec} = 6\cdot{10}^{-12}$s is the minimum Auger recombination time \cite{Yoffa1980}, and $\alpha = 21.2$ cm$^2$/J is the avalanche ionization coefficient \cite{Pronko1998} at the wavelength $800$ nm in air. As we have noted, free carrier diffusion is neglected during and shortly after the laser excitation \cite{Van1987, Sokolowski2000}.
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=0.495\textwidth]{mie-fdtd-3}
+\caption{\label{mie-fdtd} Mie and FDTD comparison. (c-f) Incident light goes from the left.}
+\end{figure}
+
 \begin{figure*}[ht!]
 \centering
 \includegraphics[width=0.9\textwidth]{Ne_105nm_800}
@@ -347,43 +340,45 @@ The changes of the real and imaginary parts of the permittivity associated with
 
 \subsection{Effect of the irradiation intensity on EHP generation}
 
-Fig. \ref{fig2} demonstrates EHP temporal evolution inside silicon
-nanoparticle of $R \approx 105$ nm during irradiation by
-high-intensity ultrashort laser Gaussian pulse. Snapshots of electron
-density taken at different times correspond to different total amount
-of deposited energy and, therefore, different intensities of
-irradiation. We introduce the parameter of EHP asymmetry $G$, defined
+Fig. \ref{fig2} demonstrates the temporal evolution of the EHP generated inside the silicon
+nanoparticle of $R \approx 105$ nm. Here, irradiation by
+high-intensity, $I\approx $ from XXX to YYY (???), ultrashort laser Gaussian pulse is considered. Snapshots of free carrier density taken at different times correspond to different total amount of the deposited energy (different laser intensities). 
+
+To better analyze the degree of inhomogeneity,  we introduce the EHP asymmetry parameter, $G$, which is defined
 as a relation between the average electron density generated in the
 front side of the nanoparticle and the average electron density in the
 back side, as shown in Fig. \ref{fig2}. During the femtosecond pulse
 interaction, this parameter significantly varies.
 
-Far before the pulse peak in Fig. \ref{fig2}(a), the excitation
+Far before the pulse peak shown in Fig. \ref{fig2}(a), the excitation
 processes follow the intensity distribution, generating a low-density
 electron plasma of a toroidal shape at magnetic dipole resonance
 conditions. For higher intensities, the optical properties of silicon
-change significantly according to equations (\ref{Index}), and
-nonresonant electric dipole contributes to the forward shifting of EHP
+change significantly according to the equations (\ref{Index}). As a result, the non-resonant electric dipole contributes to the forward shifting of EHP
 density maximum. Therefore, EHP is localized in the front part of the
 nanoparticle, increasing the asymmetry factor $G$ in
 Fig. \ref{fig2}(b). Approximately at the pulse peak, the critical
 electron density $n_{cr} = 5\cdot{10}^{21} cm^{-3}$ for silicon, which
 corresponds to the transition to quasi-metallic state $Re(\epsilon)
-\approx 0$ and to electron plasma resonance \cite{Sokolowski2000}, is overcome. At the same time, $G$ factor
+\approx 0$ and to the electron plasma resonance (so-called "volume plasmons", and/or "localized plasmons" typical for metallic nanoparticles !??) \cite{Sokolowski2000}, is overcome. 
+At the same time, $G$ factor
 reaches the maximum value close to $2.5$ in
-Fig. \ref{fig2}(c). Further irradiation leads to a decrease of the
-asymmetry parameter down to $1$ for higher electron densities in
+Fig. \ref{fig2}(c). Further irradiation leads to a decrease in the
+asymmetry parameter down to $1$ for higher electron densities, as one may observe in
 Fig. \ref{fig2}(d, e).
 
-It is worth noting, that it is possible to achieve a formation of
+It is worth noting that it is possible to achieve a formation of
 deeply subwavelength EHP regions due to high field localization. In
 particular, we observe very small EHP localization at magnetic dipole
 resonant conditions for $R \approx 105$ nm. The EHP distribution in
-Fig. \ref{fig2}(c) is the optimal for symmetry breaking in silicon
-nanoparticle, as results in the bigger asymmetry factor $G$ and higher
-electron densities $n_e$. We want to stress here that such regime
-could be still safe for nanoparticle due to small volume of such high
-EHP density, which should be diffused after some time.
+Fig. \ref{fig2}(c) is optimal for symmetry breaking in silicon
+nanoparticle, as it results in the larger asymmetry factor $G$ and higher
+electron densities $n_e$. We stress here that such regime
+could be still safe for nanoparticle due to the very small volume where such high
+EHP density is formed. 
+
+TODO: need to discuss this -
+Of cause, this plasma is expected to diffuse after the considered time and turn to the homogeneously distributed one over the nanoparticle volume with a smaller density. Part of the electrons can also be ejected/injected into the surrounding medium, the process known to depend on the Shottky barrier at the particle border.
 
 \subsection{Effects of nanoparticle size/scattering efficiency factor
 on scattering directions}
@@ -402,8 +397,8 @@ nanoparticle for indicated radii (1-7).}
 We have discussed the EHP kinetics for a silicon nanoparticle of a fixed radius $R \approx 105$ nm. In what follows, we investigate the influence of the nanoparticle size on
 the EHP patterns and temporal evolution during ultrashort laser
 irradiation. A brief analysis of the initial intensity distribution
-inside the nanoparticle given by Mie theory for a spherical
-homogenneous nanoparticle \cite{Mie1908} can be useful in
+inside the nanoparticle given by the classical Mie theory for 
+homogeneous spherical particles \cite{Mie1908} can be useful in
 this case. Fig. \ref{fig3}(a, b) shows the scattering efficiency and
 the asymmetry parameter for forward/backward scattering for
 non-excited silicon nanoparticles of different radii calculated by Mie
@@ -441,12 +436,15 @@ nanoparticles, lower values of EHP asymmetry factor are obtained, as
 the electron density evolves not only from the intensity patterns in
 the front side of the nanoparticle but also in the back side.
 
+TODO: 
+Need to discuss agreement/differences between Mie and FDTD+rate. Anton ?!
+
 To demonstrate the effect of symmetry breaking, we calculate the
 intensity distribution around the nanoparticle for double-pulse
 experiment. The first pulse of larger pulse energy and polarization
 along $Ox$ generates asymmetric EHP inside silicon nanoparticle,
 whereas the second pulse of lower pulse energy and polarization
-$Oz$interacts with EHP after the first pulse is gone. The minimum
+$Oz$ interacts with EHP after the first pulse is gone. The minimum
 relaxation time of high electron density in silicon is $\tau_{rec} =
 6\cdot{10}^{-12}$ s \cite{Yoffa1980}, therefore, the
 electron density will not have time to decrease significantly for
@@ -478,10 +476,7 @@ with electron plasma inside.}
 
 \subsection{Asymmetry analysis: effects of pulse duration, intensity
 and size} It is important to optimize asymmetry by varying pulse
-duration, intensity and size.  TEI: for Konstantin L.: please change
-Mie figure and add a discussion and how the results agree, what is the
-difference TEI: for Anton R.: please add a discussion of the previous
-experiments and how the results agree
+duration, intensity and size.  
 
 TODO Kostya: add some discusion on rise-on time for optical switching
 like this: Small size will give as a magnetic dipole b1 resonance with
@@ -496,14 +491,15 @@ switching applications this is a rise-on time.
 TODO Kostya: Add discussion about mode selection due to the formation
 of the plasma.
 
-\section{Conclusions} We have considered light interaction with a
+\section{Conclusions} We have considered ultra-short and sufficiently intense light interactions with a single
 semiconductor nanoparticle under different irradiation conditions and
 for various particle sizes. As a result of the presented
 self-consistent calculations, we have obtained spatio-temporal EHP
-evolution for different light intensities and pulse temporal
-widths. It has been demonstrated that EHP generation strongly affects
+evolution inside the particle for different laser intensities and  temporal
+pulse widths. It has been demonstrated that the EHP generation strongly affects
 nanoparticle scattering and, in particular, changes the preferable
-scattering direction. In particular, the scattering efficiency factor
+scattering direction. 
+In particular, the scattering efficiency factor
 is used to define the optimum nanoparticle size for preferential
 forward or backward scattering. Furthermore, a parameter has been
 introduced to describe the scattering asymmetry as a ratio of the EHP
@@ -514,23 +510,14 @@ photonics applications. The observed plasma-induced breaking symmetry
 can be also useful for beam steering, or for the enhanced second
 harmonics generation.
 
-\section{Acknowledgments} TEI: need to add Acknowledgements The
-authors gratefully acknowledge financial support from The French
-Ministry of Science and Education and from France-Russia PHC
-Kolmogorov project.  TEI: for Sergey M., please put Kivshar et al. and
-other Refs TEI: for Anton R., please put much more references that you
-have found describing experiments and previous calculations
-
+\section{Acknowledgments} We gratefully acknowledge support from The French
+Ministry of Science and Education, from the French Center of Scientific Research (CNRS) and from the PHC Kolmogorov project "FORMALAS".  
 
 
 
 
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