small modif

main.tex

@@ -215,11 +215,11 @@ baranov2016nonlinear, baranov2016tuning} and
 metasurfaces~\cite{iyer2015reconfigurable, shcherbakov2015ultrafast,
 yang2015nonlinear}.
 
-In all this works on all-dielectric nonlinear nanostructures, the
+In these works on all-dielectric nonlinear nanostructures, the
 building blocks (nanoparticles) were considered as objects with
 dielectric permittivity homogeneously distributed over
-nanoparticle. Therefore, in order to manipulate by propagation angle
-of transmitted light it is necessary to use complicated nanostructures
+nanoparticle. Therefore, in order to manipulate the propagation angle
+of the transmitted light it is necessary to use complicated nanostructures
 with reduced symmetry~\cite{albella2015switchable, baranov2016tuning,
 shibanuma2016unidirectional}.
 
@@ -236,16 +236,16 @@ 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 ($f\!s$) laser pulse interaction with a silicon
+femtosecond ($\,f\!s$) 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
+single spherical silicon nanoparticles. Moreover, we show that a dense EHP can
 be generated at deeply subwavelength scale
-($\approx$$\lambda$$^3$/100) supporting formation of small metalized
-parts inside the nanoparticle, which transforms all-dielectric
-nanoparticle to a hybrid one that extends functionality of the ultrafast
+($\approx$$\lambda$$^3$/100) supporting the formation of small metalized
+parts inside the nanoparticle. In fact, such effects transform an all-dielectric
+nanoparticle to a hybrid one strongly extending functionality of the ultrafast
 optical nanoantennas.
 
 
@@ -272,7 +272,7 @@ optical nanoantennas.
 \section{Modeling details}
  
 
-We focus out attention on silicon because this material is promising
+We focus attention on silicon because this material is promising
 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
@@ -309,7 +309,7 @@ where $\theta$ is the temporal pulse width at the half maximum (FWHM), $t_0$ is
 
 \subsection{Material ionization}
 
-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
+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 described below.
 % \begin{figure*}[ht!]
 % \centering
 % \includegraphics[width=120mm]{fig2.png}
@@ -331,10 +331,22 @@ where $I=\frac{n}{2}\sqrt{\frac{\epsilon_0}{\mu_0}}\left|\vec{E}\right|^2$ is th
 \begin{tabular*}{0.76\textwidth}{ c@{\extracolsep{\fill}} c@{\extracolsep{\fill}} c@{\extracolsep{\fill}} c@{\extracolsep{\fill}} c}
 $-80\:f\!s$&$-60\:f\!s$&$-30\:f\!s$&$ -20\:f\!s$&$ -10\:f\!s$\\
 \end{tabular*}
+{\setlength\topsep{-1pt}
+\begin{flushleft}
+$R=75$~nm
+\end{flushleft}}
 \includegraphics[width=0.9\textwidth]{2nm_75}
+{\setlength\topsep{-1pt}
+\begin{flushleft}
+$R=100$~nm
+\end{flushleft}}
 \includegraphics[width=0.9\textwidth]{2nm_100}
+{\setlength\topsep{-1pt}
+\begin{flushleft}
+$R=115$~nm
+\end{flushleft}}
 \includegraphics[width=0.9\textwidth]{2nm_115}
-\caption{\label{plasma-105nm} Evolution of lectron density $n_e$ (using $10^{\,20} \ {\rm cm}^{-3}$ units) for  (a--e)~$R=75$, (f--j)~$R=100$~nm, and (k--o)~$R=115$~nm. Gaussian pulse duration $80\:f\!s$, snapshot are taken before the pulse maxima, the corresponding time-shifts are shown in the top of each column.}
+\caption{\label{plasma-105nm} Evolution of electron density $n_e$ (using $10^{\,20} \ {\rm cm}^{-3}$ units) for  (a$\,$--$\,$e)~$R=75$~nm, (f$\,$--$\,$j$\,$)~$R=100$~nm, and ($\,$k$\,$--$\,$o)~$R=115$~nm. Gaussian pulse duration $80\:f\!s$, snapshots are taken before the pulse maxima, the corresponding time-shifts are shown in the top of each column. Laser irradiation fluences are (a-e) $0.12$ J/cm$^2$, (f-o) $0.16$ J/cm$^2$.}
 \end{figure*}
 
 The changes of the real and imaginary parts of the permittivity associated with the time-dependent free carrier response \cite{Sokolowski2000} can be derived from equations (\ref{Maxwell}, \ref{Drude}) and are written as follows
@@ -384,10 +396,7 @@ 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
+\subsection{Effects of nanoparticle size and scattering efficiency factor
 on scattering directions}
 
 % \begin{figure}[ht] \centering