Fixes suggested by Päivi up to sect. 3.2

Former-commit-id: 65d31b97bb6aa8feae9118d34ededbd3092e128a

lepaper/Tmatrix.bib

@@ -243,6 +243,15 @@
   number = {6}
 }
 
+@book{harrington_field_1993,
+  title = {Field {{Computation}} by {{Moment Methods}} ({{IEEE Press Series}} on {{Electromagnetic Wave Theory}})},
+  author = {Harrington, Roger F.},
+  year = {1993},
+  publisher = {{Wiley-IEEE Press}},
+  isbn = {978-0-7803-1014-8},
+  series = {The {{IEEE PRESS Series}} in {{Electromagnetic Waves}} ({{Donald G}}. {{Dudley}}, {{Editor}})}
+}
+
 @article{homola_surface_1999,
   title = {Surface Plasmon Resonance Sensors: Review},
   shorttitle = {Surface Plasmon Resonance Sensors},
@@ -261,6 +270,24 @@
   number = {1}
 }
 
+@article{hsu_bound_2016,
+  title = {Bound States in the Continuum},
+  author = {Hsu, Chia Wei and Zhen, Bo and Stone, A. Douglas and Joannopoulos, John D. and Solja{\v c}i{\'c}, Marin},
+  year = {2016},
+  month = jul,
+  volume = {1},
+  pages = {1--13},
+  publisher = {{Nature Publishing Group}},
+  issn = {2058-8437},
+  doi = {10.1038/natrevmats.2016.48},
+  abstract = {Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work.},
+  copyright = {2016 Macmillan Publishers Limited},
+  file = {/home/mmn/.zotero/zotero/w4aj0ekp.default/zotero/storage/WZUM4EMS/Hsu ym. - 2016 - Bound states in the continuum.pdf;/home/mmn/.zotero/zotero/w4aj0ekp.default/zotero/storage/7U67A75X/natrevmats201648.html},
+  journal = {Nature Reviews Materials},
+  language = {en},
+  number = {9}
+}
+
 @book{jackson_classical_1998,
   title = {Classical {{Electrodynamics Third Edition}}},
   author = {Jackson, John David},

lepaper/finite.lyx

@@ -306,8 +306,8 @@ outgoing
 , respectively, defined as follows:
 \begin_inset Formula 
 \begin{align}
-\vswfrtlm1lm\left(\kappa\vect r\right) & =j_{l}\left(\kappa r\right)\vsh1lm\left(\uvec r\right),\nonumber \\
+\vswfrtlm 1lm\left(\kappa\vect r\right) & =j_{l}\left(\kappa r\right)\vsh 1lm\left(\uvec r\right),\nonumber \\
-\vswfrtlm2lm\left(\kappa\vect r\right) & =\frac{1}{\kappa r}\frac{\ud\left(\kappa rj_{l}\left(\kappa r\right)\right)}{\ud\left(\kappa r\right)}\vsh2lm\left(\uvec r\right)+\sqrt{l\left(l+1\right)}\frac{j_{l}\left(\kappa r\right)}{\kappa r}\vsh3lm\left(\uvec r\right),\label{eq:VSWF regular}
+\vswfrtlm 2lm\left(\kappa\vect r\right) & =\frac{1}{\kappa r}\frac{\ud\left(\kappa rj_{l}\left(\kappa r\right)\right)}{\ud\left(\kappa r\right)}\vsh 2lm\left(\uvec r\right)+\sqrt{l\left(l+1\right)}\frac{j_{l}\left(\kappa r\right)}{\kappa r}\vsh 3lm\left(\uvec r\right),\label{eq:VSWF regular}
 \end{align}
 
 \end_inset
@@ -315,8 +315,8 @@ outgoing
 
 \begin_inset Formula 
 \begin{align}
-\vswfouttlm1lm\left(\kappa\vect r\right) & =h_{l}^{\left(1\right)}\left(\kappa r\right)\vsh1lm\left(\uvec r\right),\nonumber \\
+\vswfouttlm 1lm\left(\kappa\vect r\right) & =h_{l}^{\left(1\right)}\left(\kappa r\right)\vsh 1lm\left(\uvec r\right),\nonumber \\
-\vswfouttlm2lm\left(\kappa\vect r\right) & =\frac{1}{kr}\frac{\ud\left(\kappa rh_{l}^{\left(1\right)}\left(\kappa r\right)\right)}{\ud\left(\kappa r\right)}\vsh2lm\left(\uvec r\right)+\sqrt{l\left(l+1\right)}\frac{h_{l}^{\left(1\right)}\left(\kappa r\right)}{\kappa r}\vsh3lm\left(\uvec r\right),\label{eq:VSWF outgoing}\\
+\vswfouttlm 2lm\left(\kappa\vect r\right) & =\frac{1}{kr}\frac{\ud\left(\kappa rh_{l}^{\left(1\right)}\left(\kappa r\right)\right)}{\ud\left(\kappa r\right)}\vsh 2lm\left(\uvec r\right)+\sqrt{l\left(l+1\right)}\frac{h_{l}^{\left(1\right)}\left(\kappa r\right)}{\kappa r}\vsh 3lm\left(\uvec r\right),\label{eq:VSWF outgoing}\\
  & \tau=1,2;\quad l=1,2,3,\dots;\quad m=-l,-l+1,\dots,+l,\nonumber 
 \end{align}
 
@@ -360,7 +360,7 @@ outgoing
 \emph on
 positive
 \emph default
- imaginary part, and gainy materials will have it negative and, for example,
+ imaginary part, and gain materials will have it negative and, for example,
  Drude-Lorenz model of a lossy medium will have poles in the lower complex
  half-plane.
 \end_layout
@@ -387,9 +387,9 @@ vector spherical harmonics
 
 \begin_inset Formula 
 \begin{align}
-\vsh1lm\left(\uvec r\right) & =\frac{1}{\sqrt{l\left(l+1\right)}}\nabla\times\left(\vect r\ush lm\left(\uvec r\right)\right)=\frac{1}{\sqrt{l\left(l+1\right)}}\nabla\ush lm\left(\uvec r\right)\times\vect r,\nonumber \\
+\vsh 1lm\left(\uvec r\right) & =\frac{1}{\sqrt{l\left(l+1\right)}}\nabla\times\left(\vect r\ush lm\left(\uvec r\right)\right)=\frac{1}{\sqrt{l\left(l+1\right)}}\nabla\ush lm\left(\uvec r\right)\times\vect r,\nonumber \\
-\vsh2lm\left(\uvec r\right) & =\frac{1}{\sqrt{l\left(l+1\right)}}r\nabla\ush lm\left(\uvec r\right),\nonumber \\
+\vsh 2lm\left(\uvec r\right) & =\frac{1}{\sqrt{l\left(l+1\right)}}r\nabla\ush lm\left(\uvec r\right),\nonumber \\
-\vsh3lm\left(\uvec r\right) & =\uvec r\ush lm\left(\uvec r\right).\label{eq:vector spherical harmonics definition}
+\vsh 3lm\left(\uvec r\right) & =\uvec r\ush lm\left(\uvec r\right).\label{eq:vector spherical harmonics definition}
 \end{align}
 
 \end_inset
@@ -408,7 +408,7 @@ electric dipolar
 \end_inset
 
  waves 
-\begin_inset Formula $\vswfrtlm21m$
+\begin_inset Formula $\vswfrtlm 21m$
 \end_inset
 
 , they vanish.
@@ -646,11 +646,11 @@ The single-particle scattering problem at frequency
 \end_inset
 
  can be posed as follows: Let a scatterer be enclosed inside the ball 
-\begin_inset Formula $\closedball{R^{<}}{\vect 0}$
+\begin_inset Formula $\closedball{R^{<}}{\vect0}$
 \end_inset
 
  and let the whole volume 
-\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect 0}$
+\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect0}$
 \end_inset
 
  be filled with a homogeneous isotropic medium with wave number 
@@ -659,7 +659,7 @@ The single-particle scattering problem at frequency
 
 .
  Inside 
-\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect 0}$
+\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect0}$
 \end_inset
 
 , the electric field can be expanded as
@@ -681,7 +681,7 @@ doplnit frekvence a polohy
 \end_inset
 
 If there were no scatterer and 
-\begin_inset Formula $\closedball{R^{<}}{\vect 0}$
+\begin_inset Formula $\closedball{R^{<}}{\vect0}$
 \end_inset
 
  were filled with the same homogeneous medium, the part with the outgoing
@@ -690,7 +690,7 @@ If there were no scatterer and
 \end_inset
 
  due to sources outside 
-\begin_inset Formula $\openball{R^{>}}{\vect 0}$
+\begin_inset Formula $\openball{R^{>}}{\vect0}$
 \end_inset
 
  would remain.
@@ -836,7 +836,12 @@ literal "false"
 \end_inset
 
 .
- In general, simulating scattering of a regular spherical wave 
+ In general, elements of the 
+\begin_inset Formula $T$
+\end_inset
+
+-matrix can be obtained by simulating scattering of a regular spherical
+ wave 
 \begin_inset Formula $\vswfrtlm{\tau}lm$
 \end_inset
 
@@ -879,23 +884,49 @@ literal "false"
 \end_inset
 
 .
- Note that older versions of SCUFF-EM contained a bug that rendered almost
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+Note that the upstream versions of SCUFF-EM contain a bug that renders almost
  all 
 \begin_inset Formula $T$
 \end_inset
 
--matrix results wrong; we found and fixed the bug and from upstream version
+-matrix results wrong; we found and fixed the bug in our fork available
- xxx
+ at 
-\begin_inset Marginal
+\begin_inset CommandInset href
-status open
+LatexCommand href
+target "https://github.com/texnokrates/scuff-em"
+literal "false"
+
+\end_inset
+
+ in revision 
+\begin_inset CommandInset href
+LatexCommand href
+name "g78689f5"
+target "https://github.com/texnokrates/scuff-em/commit/78689f5514072853aa5cad455ce15b3e024d163d"
+literal "false"
+
+\end_inset
+
+.
+ However, the 
+\begin_inset CommandInset href
+LatexCommand href
+name "bugfix"
+target "https://github.com/HomerReid/scuff-em/pull/197"
+literal "false"
+
+\end_inset
+
+ has not been merged into upstream by the time of writing this article.
  
-\begin_layout Plain Layout
-Not yet merged to upstream.
 \end_layout
 
 \end_inset
 
- onwards, it should behave correctly.
 
 \end_layout
 
@@ -1168,7 +1199,7 @@ where
 \end_inset
 
 , respectively.
- 
+ Here 
 \family roman
 \series medium
 \shape up
@@ -1819,8 +1850,8 @@ expansion coefficients
 they
 \emph default
  transform under translation.
- Let us assume the field can be in terms of regular waves everywhere, and
+ We assume the field can be expressed in terms of regular waves everywhere,
- expand it in two different origins 
+ and expand it in two different origins 
 \begin_inset Formula $\vect r_{p},\vect r_{q}$
 \end_inset
 
@@ -1980,7 +2011,7 @@ and analogously the elements of the singular operator
 \begin_inset Formula $h_{l}^{(1)}=j_{l}+iy_{l}$
 \end_inset
 
-) in the radial part instead of the regular bessel functions,
+) in the radial part instead of the regular Bessel functions,
 \begin_inset Note Note
 status collapsed
 

lepaper/infinite.lyx

@@ -200,7 +200,7 @@ noprefix "false"
 \end_inset
 
  inside the unit cell; any particle of the periodic system can thus be labeled
- by a multiindex from 
+ by a multi-index from 
 \begin_inset Formula $\mathcal{P}=\ints^{d}\times\mathcal{P}_{1}$
 \end_inset
 
@@ -271,6 +271,9 @@ noprefix "false"
 \end_inset
 
 , and eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -327,6 +330,9 @@ noprefix "false"
 
 \begin_layout Standard
 As in the case of a finite system, eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -346,6 +352,9 @@ noprefix "false"
 \end_inset
 
  Eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -445,8 +454,14 @@ noprefix "false"
 \end_inset
 
 , w.r.t.
- the distance; the gain might then balance the losses in particles, resulting
+\begin_inset space \space{}
+\end_inset
+
+the distance; the gain might then balance the losses in particles, resulting
  in sustained modes satisfying eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -498,6 +513,9 @@ noprefix "false"
 \end_inset
 
  is solved in the same way as eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -509,10 +527,7 @@ noprefix "false"
 \end_inset
 
  in the multipole degree truncated form.
-\end_layout
+ The lattice mode problem 
-
-\begin_layout Standard
-The lattice mode problem 
 \begin_inset CommandInset ref
 LatexCommand eqref
 reference "eq:lattice mode equation"
@@ -994,6 +1009,9 @@ scalar
 \end_inset
 
 : in eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -1483,6 +1501,9 @@ If the normal component
 \end_inset
 
  is zero, in the last sum in eq.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -1520,7 +1541,10 @@ noprefix "false"
 \end_inset
 
  can be evaluated e.g.
- using the Taylor series
+\begin_inset space \space{}
+\end_inset
+
+using the Taylor series
 \lang finnish
 
 \begin_inset Formula 
@@ -1810,6 +1834,9 @@ literal "false"
 
  variable to the positive imaginary half-axis.
  This moves the branch cuts w.r.t.
+\begin_inset space \space{}
+\end_inset
+
 
 \begin_inset Formula $\kappa$
 \end_inset

lepaper/intro.lyx

@@ -191,10 +191,10 @@ zkontroluj reference, přidej referenci na frequency domain fem
 
 ) include the field degrees of freedom (DoF) of the background medium (which
  can have very large volumes), whereas integral approaches such as the boundary
- element method (BEM, a.k.a the method of moments, MOM, 
+ element method (BEM, a.k.a the method of moments, MOM 
 \begin_inset CommandInset citation
 LatexCommand cite
-key "medgyesi-mitschang_generalized_1994,reid_efficient_2015"
+key "harrington_field_1993,medgyesi-mitschang_generalized_1994,reid_efficient_2015"
 literal "false"
 
 \end_inset
@@ -221,8 +221,20 @@ s used in nanophotonics: there are modes in which the particles' electric
  dipole moments completely vanish due to symmetry, and regardless of how
  small the particles are, the excitations have quadrupolar or higher-degree
  multipolar character.
- These modes typically appear at the band edges where interesting phenomena
+ These modes, belonging to a category that is sometimes called 
- such as lasing or Bose-Einstein condensation have been observed 
+\emph on
+optical bound states in the continuum (BIC)
+\emph default
+ 
+\begin_inset CommandInset citation
+LatexCommand cite
+key "hsu_bound_2016"
+literal "false"
+
+\end_inset
+
+, typically appear at the band edges where interesting phenomena such as
+ lasing or Bose-Einstein condensation have been observed 
 \begin_inset CommandInset citation
 LatexCommand cite
 key "guo_lasing_2019,pourjamal_lasing_2019,hakala_lasing_2017,yang_real-time_2015,hakala_boseeinstein_2018"
@@ -238,10 +250,14 @@ The natural way to overcome both limitations of CDA mentioned above is to
  take higher multipoles into account.
  Instead of a polarisability tensor, the scattering properties of an individual
  particle are then described with more general 
+\emph on
+transition matrix
+\emph default
+ (commonly known as 
 \begin_inset Formula $T$
 \end_inset
 
--matrix, and different particles' multipole excitations are coupled together
+-matrix), and different particles' multipole excitations are coupled together
  via translation operators, a generalisation of the Green's functions used
  in CDA.
  This is the idea behind the 
@@ -332,12 +348,12 @@ However, the potential of MSTMM reaches far beyond its past implementations.
  This enables, among other things, to use MSTMM for fast solving of the
  lattice modes of such periodic systems, and comparing them to their finite
  counterparts with respect to electromagnetic response, which is useful
- to isolate the bulk and finite-size phenomena of photonic arrays.
+ to isolate the bulk and finite-size phenomena of photonic lattices.
  Moreover, we exploit symmetries of the system to decompose the problem
  into several substantially smaller ones, which provides better understanding
  of modes, mainly in periodic systems, and substantially reduces the demands
  on computational resources, hence speeding up the computations and allowing
- for finite size simulations of systems with particle counts practically
+ for finite size simulations of systems with particle numbers practically
  impossible to reliably simulate with any other method.
 \begin_inset Note Note
 status open