Comment on using Beyn's algorithm.

+ literature reference update


Former-commit-id: aa3050b8cd95b4bd15b120be243298779a31b16a

lepaper/Tmatrix.bib

@@ -252,19 +252,6 @@
   file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/9E7R7IRX/Mackowski - 2001 - An effective medium method for calculation of the .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/D75CJ78C/S002240730100022X.html}
 }
 
-@article{hakala_bose-einstein_2017,
-  title = {Bose-{{Einstein Condensation}} in a {{Plasmonic Lattice}}},
-  abstract = {Bose-Einstein condensation is a remarkable manifestation of quantum statistics and macroscopic quantum coherence. Superconductivity and superfluidity have their origin in Bose-Einstein condensation. Ultracold quantum gases have provided condensates close to the original ideas of Bose and Einstein, while condensation of polaritons and magnons have introduced novel concepts of non-equilibrium condensation. Here, we demonstrate a Bose-Einstein condensate (BEC) of surface plasmon polaritons in lattice modes of a metal nanoparticle array. Interaction of the nanoscale-confined surface plasmons with a room-temperature bath of dye molecules enables thermalization and condensation in picoseconds. The ultrafast thermalization and condensation dynamics are revealed by an experiment that exploits itinerant thermalization and the open cavity character of the system. A crossover from BEC to usual lasing is realized by tailoring the band structure. This new condensate is a manifestation of macroscopic quantum coherence in unprecedented time-scales, with promise for future technologies due to its room-temperature and on-chip nature.},
-  urldate = {2017-08-31},
-  journal = {arXiv:1706.01528, in review in Nature Physics},
-  url = {http://arxiv.org/abs/1706.01528},
-  author = {Hakala, T. K. and Moilanen, A. J. and V{\"a}kev{\"a}inen, A. I. and Guo, R. and Martikainen, J.-P. and Daskalakis, K. S. and Rekola, H. T. and Julku, A. and T{\"o}rm{\"a}, P.},
-  month = jun,
-  year = {2017},
-  keywords = {Condensed Matter - Quantum Gases,Physics - Optics,Quantum Physics},
-  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/V2ZCKC7E/Hakala et al. - 2017 - Bose-Einstein Condensation in a Plasmonic Lattice.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/VJSF4X3I/1706.html}
-}
-
 @book{dresselhaus_group_2008,
   title = {Group {{Theory}}: {{Application}} to the {{Physics}} of {{Condensed Matter}}},
   isbn = {978-3-540-32899-5},
@@ -277,6 +264,23 @@
   file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/GFGPVB4A/Mildred_S._Dresselhaus,_Gene_Dresselhaus,_Ado_Jorio_Group_theory_application_to_the_physics_of_condensed_matter.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/E78682CJ/9783540328971.html}
 }
 
+@article{wang_rich_2018,
+  title = {The Rich Photonic World of Plasmonic Nanoparticle Arrays},
+  volume = {21},
+  issn = {1369-7021},
+  abstract = {Metal nanoparticle arrays that support surface lattice resonances have emerged as an exciting platform for manipulating light\textendash{}matter interactions at the nanoscale and enabling a diverse range of applications. Their recent prominence can be attributed to a combination of desirable photonic and plasmonic attributes: high electromagnetic field enhancements extended over large volumes with long-lived lifetimes. This Review will describe the design rules for achieving high-quality optical responses from metal nanoparticle arrays, nanofabrication advances that have enabled their production, and the theory that inspired their experimental realization. Rich fundamental insights will focus on weak and strong coupling with molecular excitons, as well as semiconductor excitons and the lattice resonances. Applications related to nanoscale lasing, solid-state lighting, and optical devices will be discussed. Finally, prospects and future open questions will be described.},
+  number = {3},
+  urldate = {2018-05-14},
+  journal = {Materials Today},
+  doi = {10.1016/j.mattod.2017.09.002},
+  url = {http://www.sciencedirect.com/science/article/pii/S1369702117306727},
+  author = {Wang, Weijia and Ramezani, Mohammad and V{\"a}kev{\"a}inen, Aaro I. and T{\"o}rm{\"a}, P{\"a}ivi and Rivas, Jaime G{\'o}mez and Odom, Teri W.},
+  month = apr,
+  year = {2018},
+  pages = {303-314},
+  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/QZXJBPIT/Wang et al. - 2018 - The rich photonic world of plasmonic nanoparticle .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/IHJ6YXLB/S1369702117306727.html}
+}
+
 @article{linton_lattice_2010,
   title = {Lattice {{Sums}} for the {{Helmholtz Equation}}},
   volume = {52},
@@ -353,8 +357,8 @@
 
 @article{NIST:DLMF,
   title = {{{NIST Digital Library}} of {{Mathematical Functions}}},
-  url = {http://dlmf.nist.gov/},
   key = {DLMF},
+  url = {http://dlmf.nist.gov/},
   note = {F.~W.~J. Olver, A.~B. Olde Daalhuis, D.~W. Lozier, B.~I. Schneider, R.~F. Boisvert, C.~W. Clark, B.~R. Miller and B.~V. Saunders, eds.}
 }
 
@@ -374,7 +378,7 @@
   author = {Reid, M. T. Homer and Johnson, Steven G.},
   month = aug,
   year = {2015},
-  keywords = {Physics - Classical Physics,Physics - Computational Physics},
+  keywords = {Physics - Computational Physics,Physics - Classical Physics},
   pages = {3588-3598},
   file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/I2DXTKUF/Reid ja Johnson - 2015 - Efficient Computation of Power, Force, and Torque .pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/LG7AVZDH/1307.html}
 }
@@ -392,7 +396,7 @@
   month = jan,
   year = {2019},
   pages = {013901},
-  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/TDGW4CZ5/Guo ym. - 2019 - Lasing at $K$ Points of a Honeycomb Plasmonic Latt.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/8BW4R9F6/PhysRevLett.122.html}
+  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/T84XGIQP/supplemental.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/TDGW4CZ5/Guo ym. - 2019 - Lasing at $K$ Points of a Honeycomb Plasmonic Latt.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/8BW4R9F6/PhysRevLett.122.html}
 }
 
 @article{mie_beitrage_1908,
@@ -504,7 +508,26 @@
   author = {Ewald, P. P.},
   year = {1921},
   pages = {253-287},
-  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/TL9NGJTR/Ewald - 1921 - Die Berechnung optischer und elektrostatischer Git.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/HXX7A93Q/andp.html}
+  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/8J7H5EVE/ewald1921.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/TL9NGJTR/Ewald - 1921 - Die Berechnung optischer und elektrostatischer Git.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/HXX7A93Q/andp.html}
+}
+
+@article{hakala_boseeinstein_2018,
+  title = {Bose\textendash{{Einstein}} Condensation in a Plasmonic Lattice},
+  volume = {14},
+  copyright = {2018 The Author(s)},
+  issn = {1745-2481},
+  abstract = {Surface plasmon polaritons in an array of metallic nanoparticles evolve quickly into the band minimum by interacting with a molecule bath, forming a Bose\textendash{}Einstein condensate at room temperature within picoseconds.},
+  language = {en},
+  number = {7},
+  urldate = {2019-11-13},
+  journal = {Nature Phys},
+  doi = {10.1038/s41567-018-0109-9},
+  url = {https://www.nature.com/articles/s41567-018-0109-9},
+  author = {Hakala, Tommi K. and Moilanen, Antti J. and V{\"a}kev{\"a}inen, Aaro I. and Guo, Rui and Martikainen, Jani-Petri and Daskalakis, Konstantinos S. and Rekola, Heikki T. and Julku, Aleksi and T{\"o}rm{\"a}, P{\"a}ivi},
+  month = jul,
+  year = {2018},
+  pages = {739-744},
+  file = {/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/THHLXPYG/Hakala ym. - 2018 - Bose–Einstein condensation in a plasmonic lattice.pdf;/u/46/necadam1/unix/.mozilla/firefox/6m8fw48s.default/zotero/storage/VF4E9DUP/s41567-018-0109-9.html}
 }
 
 

lepaper/infinite.lyx

@@ -570,7 +570,12 @@ noprefix "false"
 \end_inset
 
 .
- Another, more robust approach is Beyn's contour integral algorithm 
+ 
+\end_layout
+
+\begin_layout Standard
+An alternative, more robust approach to generic minimisation algorithms
+ is Beyn's contour integral method 
 \begin_inset CommandInset citation
 LatexCommand cite
 key "beyn_integral_2012"
@@ -582,7 +587,42 @@ literal "false"
 \begin_inset Formula $M\left(\omega,\vect k\right)=0$
 \end_inset
 
- in a given frequency contour.
+ inside an area enclosed by a given complex frequency plane contour, assuming
+ that 
+\begin_inset Formula $M\left(\omega,\vect k\right)$
+\end_inset
+
+ is an analytical function of 
+\begin_inset Formula $\omega$
+\end_inset
+
+ inside the contour.
+ A necessary prerequisite for this is that all the ingredients of 
+\begin_inset Formula $M\left(\omega,\vect k\right)$
+\end_inset
+
+ are analytical as well.
+ It practice, this usually means that interpolation cannot be used in a
+ straightforward way for material properties or 
+\begin_inset Formula $T$
+\end_inset
+
+-matrices.
+ For material response, constant permittivity or Drude-Lorentz models suit
+ this purpose well.
+ The need to evaluate the 
+\begin_inset Formula $T$
+\end_inset
+
+-matrices precisely (without the speedup provided by interpolation) at many
+ points might cause a performance bottleneck for scatterers with more complicate
+d shapes.
+ And finally, the integration contour has to evade any branch cuts appearing
+ in the lattice-summed translation operator 
+\begin_inset Formula $W\left(\omega,\vect k\right)$
+\end_inset
+
+, as described in the following.
 \end_layout
 
 \begin_layout Subsection

lepaper/intro.lyx

@@ -149,7 +149,7 @@ s used in nanophotonics: there are modes in which the particles' electric
  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_bose-einstein_2017"
+key "guo_lasing_2019,pourjamal_lasing_2019,hakala_lasing_2017,yang_real-time_2015,hakala_boseeinstein_2018"
 literal "false"
 
 \end_inset