change

main.tex

@@ -230,7 +230,7 @@ metasurfaces~\cite{iyer2015reconfigurable, shcherbakov2015ultrafast,
 In these works on all-dielectric nonlinear nanostructures, the
 building blocks (nanoparticles) were considered as objects with
 dielectric permittivity \textit{homogeneously} distributed over
-nanoparticle. Therefore, in order to manipulate the propagation angle
+nanoparticle (NP). Therefore, in order to manipulate the propagation angle
 of the transmitted light it was proposed to use complicated
 nanostructures with reduced symmetry~\cite{albella2015switchable,
   baranov2016tuning, shibanuma2016unidirectional}.
@@ -244,36 +244,36 @@ distributions in silicon nanoparticle around a magnetic resonance.}
 
 On the other hand, plasma explosion imaging technique has been used to
 observe electron-hole plasmas (EHP), produced by femtosecond lasers,
-inside nanoparticles~\cite{Hickstein2014}. Particularly, a strongly
+inside NPs~\cite{Hickstein2014}. Particularly, a strongly
 localized EHP in the front side\footnote{The incident wave propagates
-  in positive direction of $z$ axis. For the nanoparticle with
+  in positive direction of $z$ axis. For the NP with
   geometric center located at $z=0$ front side corresponds to the
   volume $z>0$ and back side for $z<0$} of NaCl nanocrystals of
 $R = 100$ nm was revealed. The forward ejection of ions in this case
-was attributed to a nanolensing effect inside the nanoparticle and the
+was attributed to a nanolensing effect inside the NP and the
 intensity enhancement as low as $10\%$ on the far side of the
-nanoparticle. Much stronger enhancements can be achieved near electric
+NP. Much stronger enhancements can be achieved near electric
 and magnetic dipole resonances excited in single semiconductor
-nanoparticles, such as silicon (Si), germanium (Ge) etc.
+NPs, such as silicon (Si), germanium (Ge) etc.
 
 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
+NP leads to a strongly inhomogeneous carrier
 distribution. To reveal and study this effect, we perform a full-wave
 numerical simulation of the intense femtosecond (\textit{fs}) laser
-pulse interaction with a silicon nanoparticle supporting Mie
+pulse interaction with a silicon NP 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
+dielectric permittivity is calculated for NPs of several
 sizes. The obtained results propose a novel strategy to create
 complicated non-symmetrical nanostructures by using single photo-excited
-spherical silicon nanoparticles. Moreover, we show that a dense
+spherical silicon NPs. Moreover, we show that a dense
 EHP can be generated at deeply subwavelength scale
 ($\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
+metalized parts inside the NP. In fact, such effects
+transform an all-dielectric NP to a hybrid one strongly
 extending functionality of the ultrafast optical nanoantennas.
 
 
@@ -316,7 +316,7 @@ the critical density and above, silicon acquires metallic properties
 ultrashort laser irradiation.
 
 The process of three-dimensional photo-generation of the EHP in
-silicon nanoparticles has not been modeled before in
+silicon NPs 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.
@@ -325,7 +325,7 @@ taking into 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
+laser interaction with the NP. The created electron-hole
 plasma then will recombine, however, as its existence modifies both
 laser-particle interaction and, hence, the following particle
 evolution.
@@ -333,7 +333,7 @@ evolution.
 \subsection{Light propagation}
 
 Ultra-short laser interaction and light propagation inside the silicon
-nanoparticle are modeled by solving the system of Maxwell's equations
+NP 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})} \\
@@ -360,7 +360,7 @@ 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
+NP 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
@@ -398,7 +398,7 @@ plasma as described below.
 % \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) $30\:f\!s$  b) $10\:f\!s$ before the pulse peak, c) at the pulse peak, d) $10\:f\!s$ e) $30\:f\!s$  after the pulse peak. Pulse duration $50\:f\!s$ (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.}
+% \caption{\label{fig2} Free carrier density snapshots of electron plasma evolution inside Si NP taken a) $30\:f\!s$  b) $10\:f\!s$ before the pulse peak, c) at the pulse peak, d) $10\:f\!s$ e) $30\:f\!s$  after the pulse peak. Pulse duration $50\:f\!s$ (FWHM). Wavelength $800$ nm in air. Radius of the NP $R \approx 105$ 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 NP. $n_{cr} = 5\cdot{10}^{21}$ cm$^{-3}$ is the critical plasma resonance electron density for silicon.}
 % \end{figure*}
 
 
@@ -530,23 +530,23 @@ license.
 %\subsection{Effect of the irradiation intensity on EHP generation}
 
  Firstly, we analyze Mie coefficients (Fig.~\ref{mie-fdtd}(b) ) and
- the intensity distribution inside the non-excited Si nanoparticle as
+ the intensity distribution inside the non-excited Si NP as
  a function of its size for a fixed laser wavelength $\lambda = 800$
  nm.  We introduce $G_I$ factor of asymmetry, corresponding to
  difference between the volume integral of intensity in the front side
- of the nanoparticle to that in the back side normalized to their sum:
+ of the NP to that in the back side normalized to their sum:
  $G_I = (I^{front}-I^{back})/(I^{front}+I^{back})$, where
  $I^{front}=\int_{(z>0)}|E|^2d{\mathrm{v}}$ and
  $I^{back}=\int_{(z<0)} |E|^2d{\mathrm{v}}$. The factor $G_{I^2}$ was
  introduced in a similar way using volume integrals of squared
  intensity as a better option to predict EHP asymmetry due to
  two-photon absorption.  Fig.~\ref{mie-fdtd}(b) shows $G$ factors
- as a function of the nanoparticle size. For the nanoparticles of
+ as a function of the NP size. For the NPs of
  sizes below the first magnetic dipole resonance, the intensity is
  enhanced in the front side as in Fig.~\ref{mie-fdtd}(c) and
  $G_I > 0$. The behavior changes near the size resonance value,
  corresponding to $R \approx 105$ nm. In contrast, for larger sizes,
- the intensity is enhanced in the back side of the nanoparticle as
+ the intensity is enhanced in the back side of the NP as
  demonstrated in Fig.~\ref{mie-fdtd}(d). In fact, the similar EHP
  distributions can be obtained by applying Maxwell's equations coupled
  with the rate equation for relatively weak excitation
@@ -570,7 +570,7 @@ license.
  asymmetry factor $G$ in Fig.~\ref{fig3}.
 
 % Fig. \ref{Mie} demonstrates the temporal evolution of the EHP
-% generated inside the silicon nanoparticle of $R \approx 105$
+% generated inside the silicon NP 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
@@ -580,7 +580,7 @@ license.
 %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
+% NP and the average electron density in the back side, as
 % shown in Fig. \ref{fig2}. During the femtosecond pulse interaction,
 % this parameter significantly varies.
 
@@ -672,32 +672,32 @@ license.
  that such regime could be still safe for NP due to the very small
  volume where such high EHP density is formed.
 
-% \subsection{Effects of nanoparticle size and scattering efficiency
+% \subsection{Effects of NP size and scattering efficiency
 % factor on scattering directions}
 
 % \begin{figure}[ht] \centering
 % \includegraphics[width=90mm]{fig3.png}
 % \caption{\label{fig3} a) Scattering efficiency factor $Q_{sca}$
-% dependence on the radius $R$ of non-excited silicon nanoparticle
+% dependence on the radius $R$ of non-excited silicon NP
 % calculated by Mie theory; b) Parameter of forward/backward scattering
 % dependence on the radius $R$ calculated by Mie theory for non-excited
-% silicon nanoparticle c) Optimization parameter $K$ dependence on the
+% silicon NP c) Optimization parameter $K$ dependence on the
 % average electron density $n_e^{front}$ in the front half of the
-% nanoparticle for indicated radii (1-7).}
+% NP for indicated radii (1-7).}
 % \end{figure}
 
-% We have discussed the EHP kinetics for a silicon nanoparticle of a
+% We have discussed the EHP kinetics for a silicon NP 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
+% influence of the NP 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
+% the initial intensity distribution inside the NP 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
+% forward/backward scattering for non-excited silicon NPs of
 % different radii calculated by Mie theory \cite{Mie1908}. Scattering
 % efficiency dependence gives us the value of resonant sizes of
-% nanoparticles, where the initial electric fields are significantly
+% NPs, where the initial electric fields are significantly
 % enhanced and, therefore, we can expect that the following conditions
 % will result in a stronger electron density gradients. Additionally,
 % in the case of maximum forward or backward scattering, the initial
@@ -714,30 +714,30 @@ license.
 % $G$ does not guarantee the optimal asymmetry of intensity
 % distribution, as the size of generated plasma and the value of the
 % electron density equally contribute to the change of the modified
-% nanoparticle optical response. For example, it is easier to localize
-% high electron densities inside smaller nanoparticles, however, due
+% NP optical response. For example, it is easier to localize
+% high electron densities inside smaller NPs, however, due
 % to the negligible size of the generated EHP with respect to laser
 % wavelength in media, the intensity distribution around the
-% nanoparticle will not change considerably. Therefore, we propose to
+% NP will not change considerably. Therefore, we propose to
 % introduce the optimization factor
 % $K = \frac{n_e(G-1)R^2}{n_{cr}G{R_0^2}}$, where $R_0 = 100$ nm,
 % $n_{cr} = 5\cdot{10}^{21} cm^{-3}$, and $G$ is asymmetry of EHP,
 % defined previously. The calculation results for different radii of
-% silicon nanoparticles and electron densities are presented in
+% silicon NPs and electron densities are presented in
 % Fig. \ref{fig3}(c). One can see, that the maximum value are achieved
-% for the nanoparticles, that satisfy both initial maximum forward
+% for the NPs, that satisfy both initial maximum forward
 % scattering and not far from the first resonant condition. For larger
-% nanoparticles, lower values of EHP asymmetry factor are obtained, as
+% NPs, 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.
+% the front side of the NP 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
+% intensity distribution around the NP for double-pulse
 % experiment. The first pulse of larger pulse energy and polarization
-% along $Ox$ generates asymmetric EHP inside silicon nanoparticle,
+% along $Ox$ generates asymmetric EHP inside silicon NP,
 % whereas the second pulse of lower pulse energy and polarization $Oz$
 % interacts with EHP after the first pulse is gone. The minimum
 % relaxation time of high electron density in silicon is
@@ -745,30 +745,30 @@ license.
 % electron density will not have time to decrease significantly for
 % subpicosecond pulse separations. In our simulations, we use
 % $\delta{t} = 200\:f\!s$ pulse separation. The intensity
-% distributions near the silicon nanoparticle of $R = 95$ nm,
+% distributions near the silicon NP of $R = 95$ nm,
 % corresponding to maxima value of $K$ optimization factor, without
 % plasma and with generated plasma are shown in Fig. \ref{fig4}. The
 % intensity distribution is strongly asymmetric in the case of EHP
-% presence. One can note, that the excited nanoparticle is out of
+% presence. One can note, that the excited NP is out of
 % quasi-resonant condition and the intensity enhancements in
 % Fig. \ref{fig4}(c) are weaker than in Fig. \ref{fig4}(b). Therefore,
 % the generated nanoplasma acts like a quasi-metallic nonconcentric
-% nanoshell inside the nanoparticle, providing a symmetry reduction
+% nanoshell inside the NP, providing a symmetry reduction
 % \cite{Wang2006}.
 
 % \begin{figure}[ht] \centering
 % \includegraphics[width=90mm]{fig4.png}
 % \caption{\label{fig4} a) Electron plasma distribution inside Si
-% nanoparticle $R \approx 95$ nm $50\:f\!s$ after the pulse peak;
+% NP $R \approx 95$ nm $50\:f\!s$ after the pulse peak;
 % (Kostya: Is it scattering field intensity snapshot $XXX\:f\!s$ after
 % the second pulse maxima passed the particle?) Intensity
-% distributions around and inside the nanoparticle b) without plasma,
+% distributions around and inside the NP b) without plasma,
 % c) with electron plasma inside.}
 % \end{figure}
 
 %\begin{figure} %\centering
 % \includegraphics[height=0.7\linewidth]{Si-flow-R140-XYZ-Eabs}
-% \caption{EHP distributions for nonres., MD, ED, and MQ nanoparticles
+% \caption{EHP distributions for nonres., MD, ED, and MQ NPs
 % at moderate photoexcitation. The aim is to show different possible
 % EHP patterns and how strong could be symmetry breaking.
 % \label{fgr:example}
@@ -786,12 +786,12 @@ 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 inside the
-nanoparticles and investigated the asymmetry of EHP distributions. % for different laser intensities. % and temporal pulse widths.
+NPs and investigated the asymmetry of EHP distributions. % 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
+%NP scattering and, in particular, changes the preferable
 %scattering direction. 
 Different pathways of EHP evolution from the front side to the back
-side have been revealed, depending on the nanoparticle sizes, and the
+side have been revealed, depending on the NP sizes, and the
 origins of different behavior have been explained by the
 non-stationarity of the energy deposition and different quality
 resonant factors for exciting the electric and magnetic dipole
@@ -799,21 +799,21 @@ resonances, intensity distribution by Mie theory and newly
 plasma-induced nonlinear effects. The effect of the strong broadband
 electric dipole resonance on the EHP asymmetric distribution during
 first optical cycles has been revealed for different size
-parameters. The higher EHP asymmetry is established for nanoparticles
+parameters. The higher EHP asymmetry is established for NPs
 of smaller sizes below the first magnetic dipole
 resonance. Essentially different EHP evolution and lower asymmetry is
-achieved for larger nanoparticles due to the stationary intensity
-enhancement in the back side of the nanoparticle. The EHP densities
+achieved for larger NPs due to the stationary intensity
+enhancement in the back side of the NP. The EHP densities
 above the critical value were shown to lead to the EHP distribution
 homogenization.
 % In particular, the scattering efficiency factor is used to define
-% the optimum nanoparticle size for preferential forward or backward
+% the optimum NP size for preferential forward or backward
 % scattering. Furthermore, a parameter has been introduced to describe
 % the scattering asymmetry as a ratio of the EHP density in the front
-% side to that in the back side of the nanoparticle. This parameter
+% side to that in the back side of the NP. This parameter
 % can be then used for two-dimensional scattering mapping, which is
 % particularly important in numerous photonics applications.
-The EHP asymmetry opens a wide range of applications in nanoparticle
+The EHP asymmetry opens a wide range of applications in NP
 nanomashining/manipulation at nanoscale, catalysis as well as
 nano-bio-applications.  The observed plasma-induced breaking symmetry
 can be also useful for beam steering, or for the enhanced second