Last

main.tex

@@ -532,8 +532,8 @@ license.
  $G_I = (I^{front}-I^{back})/(I^{front}+I^{back})$, 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
+ determined in a similar way by using volume integrals of squared
+ intensity to predict EHP asymmetry due to
  two-photon absorption.  Fig.~\ref{mie-fdtd}(b) shows $G$ factors
  as a function of the NP size. For the NPs of
  sizes below the first magnetic dipole resonance, the intensity is
@@ -541,14 +541,16 @@ license.
  $G_I > 0$. 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 NP as
- demonstrated in Fig.~\ref{mie-fdtd}(d). In fact, the similar EHP
+ demonstrated in Fig.~\ref{mie-fdtd}(d). In fact, very similar EHP
  distributions can be obtained by applying Maxwell's equations coupled
  with the rate equation for relatively weak excitation
  $N_e \approx 10^{20}$ cm$^{-3}$. The optical properties do not change
- considerably due to excitation according to (\ref{Index}). Therefore,
+ considerably due to the excitation according to (\ref{Index}). Therefore,
  the excitation processes follow the intensity distribution. However,
- such coincidence was achieved in quasi-stationary conditions, after the
- electric field made enough oscillations inside the Si NP. To achieve
+ such coincidence was achieved under quasi-stationary conditions, after the
+ electric field made enough oscillations inside the Si NP. 
+ 
+ To achieve
  a qualitative description of the EHP distribution, we introduced
  another asymmetry factor
  $G_{N_e} = (N_e^{front}-N_e^{back})/(N_e^{front}+N_e^{back})$
@@ -556,8 +558,8 @@ license.
  front and in the back parts of the NP. This way, $G_{N_e} = 0$ corresponds
  to the quasi-homogeneous case and the assumption of the NP
  homogeneous EHP distribution can be made to investigate the optical
- response of the excited Si NP. However, in case $G_{N_e}$ significantly
- differs from $0$, this assumption could not be proposed. In what
+ response of the excited Si NP. When $G_{N_e}$ significantly
+ differs from $0$, this assumption, however, could not be justified. In what
  follows, we discuss the results of the numerical modeling revealing
  the EHP evolution stages during pulse duration shown in
  Fig.~\ref{fig2} and the temporal/EHP dependent evolution of the
@@ -581,7 +583,7 @@ license.
 
 
 
- In order to describe all stages of strong interaction of light with
+ To describe all the stages of powerful enough light interaction with
  Si NP, we present the calculation results obtained by using Maxwell's
  equations coupled with electron kinetics equations for different
  radii for resonant and non-resonant conditions. In this case, the
@@ -596,12 +598,9 @@ license.
  whereas electric one (\textit{a1}) has $Q \approx$4. The larger
  particle supporting magnetic quadrupole resonance (\textit{b2})
  demonstrates \textit{Q} $\approx$ 40. As soon as the electromagnetic
- wave period at $\lambda$~=~800~nm is 2.6~\textit{fs}, we need about 10~\textit{fs}
- pulse to pump the electric dipole, 20~\textit{fs} for the magnetic dipole, and
- about 100~\textit{fs} for the magnetic quadrupole.
-
- According to these estimations, the first optical cycles taking place
- on few-femtosecond scale result in the excitation of the
+ wave period at $\lambda$~=~800~nm is 2.6~\textit{fs}, one needs about 10~\textit{fs}
+ to pump the electric dipole, 20~\textit{fs} for the magnetic dipole, and
+ about 100~\textit{fs} for the magnetic quadrupole. According to these considerations, the first optical cycles taking place on few-femtosecond scale result in the excitation of the
  low-\textit{Q} electric dipole resonance independently on the exact
  size of NPs and with the EHP concentration mostly on the front side
  of the NPs. We address to this phenomena as \textit{'Stage 1'}, as
@@ -612,26 +611,26 @@ license.
  is, the higher the NP asymmetry $G_{N_e}$ is achieved.
 
  \textit{'Stage 2'} corresponds to further electric field oscillations
- ($t \approx 2--15$) leading to unstationery nature of the EHP evolution
- with a maximum of the EHP distribution on the front side of the Si NP
- owing to starting excitation of MD and MQ resonances, requiring more
- time to be excited. At this stage, density of EHP ($N_e < 10^{20}$cm$^2$)
- is still not high enough to affect significantly optical properties
- of the Si NP.
+ ($t \approx 2--15$) leading to the unstationery EHP evolution
+ with a maximum of the EHP distribution in the front side of the Si NP
+ owing to the starting excitation of MD and MQ resonances that require more
+ time to be excited. At this stage, the density of EHP ($N_e < 10^{20}$cm$^2$)
+ is still not high enough to significantly affect the optical properties
+ of the NP.
 
  A number of optical cycles ($>$10 or $t>$25~\textit{fs}) is necessary to
  achieve the stationary intensity pattern corresponding to the
  Mie-based intensity distribution at the \textit{'Stage $3$'} (see
- Fig.~\ref{fig3}). The EHP density is still relatively not high to
- influence the EHP evolution and strong diffusion rates but already
- enough to change the optical properties locally. Below the magnetic
+ Fig.~\ref{fig3}). The EHP density is still relatively small to
+ affect the EHP evolution or for diffusion, but is already high
+ enough to change the local optical properties. Below the magnetic
  dipole resonance $R \approx 100$~nm, the EHP is mostly localized in
  the front side of the NP as shown in Fig.~\ref{fig2}(c). The highest
  stationary asymmetry factor $G_{N_e} \approx 0.5--0.6$ is achieved in this case. At the magnetic dipole
  resonance conditions, the EHP distribution has a toroidal shape and
- is much closer to homogeneous distribution. In contrast, above the
- magnetic dipole resonant size for $R = 115$~nm, the $G_{N_e} < 0$ due
- to dominantly EHP localized in the back side of the NP.
+ is much closer to the homogeneous distribution. In contrast, above the
+ magnetic dipole resonant size for $R = 115$~nm, and the $G_{N_e} < 0$ due
+ to the fact that EHP is dominantly localized in the back side of the NP.
 
  For the higher excitation conditions, the optical properties of
  silicon change significantly according to the equations
@@ -804,12 +803,12 @@ homogenization.
 % 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 NP
-nanomashining/manipulation at nanoscale, catalysis as well as
+nanomashining/manipulation at nanoscale, in catalysis as well as numerous
 nano-bio-applications.  The observed plasma-induced breaking symmetry
 can be also useful for beam steering, or for the enhanced second
 harmonics generation.
 
-\section{Acknowledgments} A. R. gratefully acknowledges support from The French Ministry of Science and Education. S. V. M. is thankful to ITMO Fellowship Program and T. E. I. to the ITMO Research Professorship Program and to the CINES of CNRS for computer support. The work was partially supported by Russian Foundation for Basic Researches (grants 17-03-00621, 17-02-00538, 16-29-05317).
+\section{Acknowledgments} A. R. and T. E. I. gratefully acknowledge the CINES of CNRS for computer support. S. V. M. is thankful to ITMO Fellowship Program. This work was partially supported by Russian Foundation for Basic Researches (grants 17-03-00621, 17-02-00538, 16-29-05317).