changes

main.tex

@@ -467,7 +467,11 @@ license.
  \caption{\label{time-evolution} Temporal EHP (a, c, e) and asymmetry factor
    $G_{N_e}$ (b, d, f) evolution for different Si nanoparticle radii of
    (a, b) $R = 75$~nm, (c, d) $R = 100$~nm, and (e, f) $R = 115$~nm. Pulse
-   duration $50$~\textit{fs} (FWHM). Wavelength $800$~nm in air. (b,
+   duration $50$~\textit{fs} (FWHM). \red{\textbf{TODO:} on the plot
+     it looks more like 75 fs for FWHM!!! Anton? \textbf{TODO2:} in
+     text period of 800nm light is 2.6 fs, on the plot it is for sure
+    < 2 fs. Anton???}
+   Wavelength $800$~nm in air. (b,
    d, f) Different stages of EHP evolution shown in Fig.~\ref{plasma-grid}
    are indicated. The temporal evolution of Gaussian beam intensity is
    also shown. Peak laser fluence is fixed to be $0.125$~J/cm$^2$.}
@@ -506,7 +510,7 @@ license.
  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,
+ size. For the NPs of sizes below the first MD 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
@@ -538,7 +542,12 @@ license.
  EHP densities and the asymmetry factor $G_{N_e}$. It reveals the EHP
  evolution stages during pulse duration. Typical change of the
  permittivity corresponding to each stage is shown in
- Fig.~\ref{plasma-grid}.
+ Fig.~\ref{plasma-grid}.  For better visual representation of time
+ scale of the whole incident pulse and its single optical cycle we put a
+ squared electric field profile on all plots at
+ Fig.~\ref{time-evolution} in gray color as a backgroud image (note
+ linear time scale on the left column and logarithmic scale on the
+ right one).
 
  To describe all the stages of light non-linear interaction with Si
  NP, we present the calculation results obtained by using Maxwell's
@@ -546,30 +555,29 @@ license.
  radii for resonant and non-resonant conditions. In this case, the
  geometry of the EHP distribution can strongly deviate from the
  intensity distribution given by Mie theory. Two main reasons cause
- the deviation: (i) non-stationarity of the energy deposition and (ii)
- nonlinear effects, taking place due to transient optical changes in
- Si. The non-stationary intensity deposition results in different time
- delays for exciting electric and magnetic resonances inside Si NP
- because of different quality factors $Q$ of the resonances.
-
- In particular, magnetic dipole resonance (\textit{b1}) has
- $Q \approx 8$, 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},
- 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, after few
- optical cycles taking place on a 10~\textit{fs} scale it results in
- the excitation of the low-\textit{Q} electric dipole resonance
- independently on the exact size of NPs. Moreover, during the first
- optical cycle there is no multiple mode structure inside of NP, which
- results into a very similar field distribution for all size of NP
- under consideration. We address to this phenomena as
- \textit{'Stage~1'}, as shown in Figs.~\ref{plasma-grid}(a,e,i).
- and~\ref{plasma-grid}. The first stage at the first optical cycle
- demonstrates the initial penetration of electromagnetic fild into the
- NP.
+ the deviation: (i) non-stationarity of interaction between
+ electromagnetic pulse and NP (ii) nonlinear effects, taking place due
+ to transient optical changes in Si. The non-stationary intensity
+ deposition during \textit{fs} pulse results in different time delays
+ for exciting electric and magnetic resonances inside Si NP because of
+ different quality factors $Q$ of the resonances.
+
+ In particular, MD resonance (\textit{b1}) has $Q \approx 8$, whereas
+ electric one (\textit{a1}) has $Q \approx 4$. The larger particle
+ supporting MQ resonance (\textit{b2}) demonstrates $ Q \approx
+ 40$. As soon as the electromagnetic wave period at $\lambda = 800$~nm
+ is 2.6~\textit{fs}, one needs about 10~\textit{fs} to pump the ED,
+ 20~\textit{fs} for the MD, and about 100~\textit{fs} for the MQ.
+ According to these considerations, after few optical cycles taking
+ place on a 10~\textit{fs} scale it results in the excitation of the
+ low-\textit{Q} ED resonance, which dominates MD and МQ independently
+ on the exact size of NPs. Moreover, during the first optical cycle
+ there is no multiple mode structure inside of NP, which results into
+ a very similar field distribution for all size of NP under
+ consideration as shown in Figs.~\ref{plasma-grid}(a,e,i) . We address
+ to this phenomena as \textit{'Stage~1'}. This stage demonstrates the
+ initial penetration of electromagnetic field into the NP during the
+ first optical cycle.
  
  \textit{'Stage~2'} corresponds to further electric field oscillations
  ($t \approx 2\div15$) leading to the unstationery EHP evolution
@@ -584,19 +592,19 @@ license.
  Mie-based intensity distribution at the \textit{'Stage~3'} (see
  Fig.~\ref{time-evolution}). 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
+ change the local optical properties. Below the MD
  resonance $R \approx 100$~nm, the EHP is mostly localized in the
  front side of the NP as shown in Fig.~\ref{plasma-grid}(c). The highest
  stationary asymmetry factor $G_{N_e} \approx 0.5\div0.6$ is achieved
- in this case. At the magnetic dipole resonance conditions, the EHP
+ in this case. At the MD resonance conditions, the EHP
  distribution has a toroidal shape and is much closer to the
- homogeneous distribution. In contrast, above the magnetic dipole
+ homogeneous distribution. In contrast, above the MD
  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
- (\ref{Index}). As a result, the non-resonant electric dipole
+ (\ref{Index}). As a result, the non-resonant ED
  contributes to the forward shifting of EHP density
  maximum. Therefore, EHP is localized in the front part of the NP,
  influencing the asymmetry factor $G_{N_e}$ in
@@ -619,7 +627,7 @@ license.
  It is worth noting that it is possible to achieve a formation of
  deeply subwavelength EHP regions due to high field localization. The
  smallest EHP localization and the larger asymmetry factor are
- achieved below the magnetic dipole resonant conditions for $R < 100$~nm.
+ achieved below the MD resonant conditions for $R < 100$~nm.
  Thus, the EHP distribution in Fig.~\ref{plasma-grid}(c) is optimal for
  symmetry breaking in Si NP, as it results in the larger asymmetry
  factor $G_{N_e}$ and higher electron densities $N_e$. We stress here