References etc.

Former-commit-id: c89c6417e387b6aa228ccdafb4c66438908240d0

lepaper/finite.lyx

@@ -678,8 +678,33 @@ literal "false"
 
 \end_inset
 
-, but in general one can find them numerically by simulating scattering
+; for particles with smooth surfaces one can find them numerically using
- of a regular spherical wave 
+ the 
+\emph on
+null-field method
+\emph default
+ 
+\begin_inset CommandInset citation
+LatexCommand cite
+key "waterman_new_1969,waterman_symmetry_1971,kristensson_scattering_2016"
+literal "false"
+
+\end_inset
+
+ which works well in the most typical cases, but for less common parameter
+ ranges (such as concave shapes, extreme values of aspect ratios or relative
+ refractive index) they might suffer from serious numerical instabilities
+ 
+\begin_inset CommandInset citation
+LatexCommand cite
+after "Sect. 5.8.4"
+key "mishchenko_scattering_2002"
+literal "false"
+
+\end_inset
+
+.
+ In general, simulating scattering of a regular spherical wave 
 \begin_inset Formula $\vswfrtlm{\tau}lm$
 \end_inset
 
@@ -699,12 +724,21 @@ literal "false"
 \end_inset
 
 , see below.
+ 
+\end_layout
+
+\begin_layout Standard
 For the numerical evaluation of 
 \begin_inset Formula $T$
 \end_inset
 
--matrices we typically use the scuff-tmatrix tool from the free software
+-matrices for simple axially symmetric scatterers in QPMS, we typically
- SCUFF-EM suite 
+ use the null-field equations, and for more complicated scatterers we use
+ the 
+\family typewriter
+scuff-tmatrix
+\family default
+ tool from the free software SCUFF-EM suite 
 \begin_inset CommandInset citation
 LatexCommand cite
 key "reid_efficient_2015,SCUFF2"
@@ -744,11 +778,20 @@ The magnitude of the
 
 -matrix elements depends heavily on the scatterer's size compared to the
  wavelength.
- Fortunately, the 
+ Typically,
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+It has been proven that the 
 \begin_inset Formula $T$
 \end_inset
 
--matrix of a bounded scatterer is a compact operator 
+-matrix of a bounded scatterer is a compact operator for 
+\emph on
+acoustic
+\emph default
+ scattering problems 
 \begin_inset CommandInset citation
 LatexCommand cite
 key "ganesh_convergence_2012"
@@ -756,17 +799,14 @@ literal "false"
 
 \end_inset
 
-
+.
-\begin_inset Note Note
+ While we conjecture that this holds also for bounded electromagnetic scatterers
-status open
+, we are not aware of a definitive proof.
-
-\begin_layout Plain Layout
-TODO
 \end_layout
 
 \end_inset
 
-, so from certain multipole degree onwards, 
+ from certain multipole degree onwards, 
 \begin_inset Formula $l,l'>L$
 \end_inset
 
@@ -782,7 +822,7 @@ TODO
 \begin_inset Formula $L$
 \end_inset
 
- gives a good approximation of the actual infinite-dimensional itself.
+ gives a good approximation of the actual infinite-dimensional operator.
  If the incident field is well-behaved, i.e.
  the expansion coefficients 
 \begin_inset Formula $\rcoefftlm{\tau'}{l'}{m'}$
@@ -1015,7 +1055,7 @@ where
 \end_inset
 
  is well-defined only when 
-\begin_inset Formula $\eta$
+\begin_inset Formula $\kappa^{2}\eta$
 \end_inset
 
  is real.
@@ -1043,6 +1083,26 @@ where
 \end_inset
 
  is negative and its magnitude equals to power absorbed by the scatterer.
+ In other words, the hermitian operator 
+\begin_inset Formula $\Pi=\Tp{}^{\dagger}\Tp{}+\left(\Tp{}^{\dagger}+\Tp{}\right)/2$
+\end_inset
+
+ must be negative (semi-)definite for a particle without gain.
+ This provides a simple but very useful sanity check on the numerically
+ obtained 
+\begin_inset Formula $T$
+\end_inset
+
+-matrices: non-negligible positive eigenvalues of 
+\begin_inset Formula $\Pi$
+\end_inset
+
+ indicate either too drastic multipole truncation or another problem with
+ the 
+\begin_inset Formula $T$
+\end_inset
+
+-matrix.
 \end_layout
 
 \begin_layout Subsubsection

lepaper/infinite.lyx

@@ -959,6 +959,10 @@ W_{\alpha,\tau lm;\beta,\tau'l'm'}(\vect k) & =\sum_{\lambda=\left|l-l'\right|+1
 \end_inset
 
 
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
 \begin_inset Marginal
 status open
 
@@ -968,6 +972,11 @@ Check signs
 
 \end_inset
 
+
+\end_layout
+
+\end_inset
+
 where the constant factors are exactly the same as in 
 \begin_inset CommandInset ref
 LatexCommand eqref

lepaper/intro.lyx

@@ -260,6 +260,22 @@ superposition
 \end_inset
 
 -matrix method
+\emph default
+ 
+\begin_inset CommandInset citation
+LatexCommand cite
+key "litvinov_rigorous_2008"
+literal "false"
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\emph on
 \begin_inset Marginal
 status open
 
@@ -271,7 +287,10 @@ a.k.a.
 \end_inset
 
 
-\emph default
+\end_layout
+
+\end_inset
+
 , and it has been implemented previously for a limited subset of problems
 \begin_inset Marginal
 status open
@@ -284,6 +303,14 @@ Refs; list the limitations of available codes?
 
 .
  
+\begin_inset CommandInset citation
+LatexCommand cite
+key "markkanen_fast_2017,markkanen_fastmm_2017"
+literal "false"
+
+\end_inset
+
+ 
 \begin_inset Note Note
 status open
 
@@ -340,13 +367,29 @@ We hereby release our MSTMM implementation, the
 \emph on
 QPMS Photonic Multiple Scattering
 \emph default
- suite, as free software under the GNU General Public License version 3.
+ suite 
+\begin_inset CommandInset citation
+LatexCommand cite
+key "necada_qpms_2019"
+literal "false"
 
+\end_inset
+
+, as free software under the GNU General Public License version 3.
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
 \begin_inset Marginal
 status open
 
 \begin_layout Plain Layout
-TODO refs to the code repositories once it is published.
+(remember to clean / update the repos before submitting)
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -358,25 +401,16 @@ TODO refs to the code repositories once it is published.
 s.
  Moreover, it includes the improvements covered in this article, enabling
  to simulate even larger systems and also infinite structures with periodicity
- in one or two or three dimensions, which can be used e.g.
+ in one, two or three dimensions, which can be used e.g.
- for quickly evaluating dispersions of such structures.
+ for evaluating dispersions of such structures.
  The QPMS suite contains a core C library, Python bindings and several utilities
- for routine computations.
+ for routine computations, such as scattering cross sections under plane
-\begin_inset Marginal
+ wave irradiation or lattice modes of two-dimensional periodic arrays.
-status open
-
-\begin_layout Plain Layout
-Such as?
-\end_layout
-
-\end_inset
-
- 
 \begin_inset Note Note
 status open
 
 \begin_layout Plain Layout
-, such as TODO.
+TODO před odesláním zkontrolovat, co všechno to v danou chvíli umí.
 \end_layout
 
 \end_inset