Summary
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@ -1054,7 +1054,28 @@ literal "true"
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\end_layout
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\begin_layout Section
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\begin_layout Section
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Acknowledgements
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Summary
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\begin_layout Standard
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We presented two major enhancements of the electromagnetic multiple-scattering
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\begin_inset Formula $T$
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-matrix method: 1) Employing Ewald summation techniques enables very efficient
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computation of lattice modes and optical response of infinite periodic
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nanoparticle structures.
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2) Exploiting possible symmetries of the system by transformation into
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symmetry adapted basis reduces the requirements on computational resources
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considerably, enabling simulations of finite systems with dozens of thousands
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of scatterers.
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These enhancements are included into the QPMS software suite, which we
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hereby make publicly available under the GNU General Public License.
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\end_layout
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\begin_layout Section
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Acknowledgments
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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@ -107,7 +107,7 @@ name "sec:Introduction"
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\begin_layout Standard
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\begin_layout Standard
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The problem of electromagnetic response of a system consisting of many relativel
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The problem of electromagnetic response of a system consisting of many relativel
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y small, compact scatterers in various geometries, and its numerical solution,
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y small, compact scatterers in various geometries, and its numerical solution,
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is relevant to many branches of nanophotonics.
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is relevant to several branches of nanophotonics.
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In practice, the scatterers often form some ordered structure, such as
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In practice, the scatterers often form some ordered structure, such as
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metalic or dielectric nanoparticle arrays
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metalic or dielectric nanoparticle arrays
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\begin_inset CommandInset citation
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\begin_inset CommandInset citation
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@ -203,15 +203,22 @@ literal "false"
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couplings between each pair of DoF.
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couplings between each pair of DoF.
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Therefore, a common (frequency-domain) approach to get an approximate solution
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Therefore, a common (frequency-domain) approach to get an approximate solution
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of the scattering problem for many small particles has been the coupled
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of the scattering problem for many small particles has been the coupled
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dipole approximation (CDA) where a drastic reduction of the number of DoF
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dipole approximation (CD)
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is achieved by approximating individual scatterers to electric dipoles
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\begin_inset CommandInset citation
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(characterised by a polarisability tensor) coupled to each other through
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LatexCommand cite
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Green's functions.
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key "zhao_extinction_2003"
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literal "false"
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\end_inset
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where a drastic reduction of the number of DoF is achieved by approximating
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individual scatterers to electric dipoles (characterised by a polarisability
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tensor) coupled to each other through Green's functions.
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\end_layout
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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CDA is easy to implement and demands relatively little computational resources
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CD is easy to implement and demands relatively little computational resources
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but suffers from at least two fundamental drawbacks.
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but suffers from at least two fundamental drawbacks.
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The obvious one is that the dipole approximation is too rough for particles
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The obvious one is that the dipole approximation is too rough for particles
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with diameter larger than a small fraction of the wavelength, which results
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with diameter larger than a small fraction of the wavelength, which results
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@ -242,11 +249,11 @@ literal "false"
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\end_inset
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– and CDA by definition fails to capture such modes.
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– and CD by definition fails to capture such modes.
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\end_layout
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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The natural way to overcome both limitations of CDA mentioned above is to
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The natural way to overcome both limitations of CD mentioned above is to
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take higher multipoles into account.
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take higher multipoles into account.
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Instead of a polarisability tensor, the scattering properties of an individual
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Instead of a polarisability tensor, the scattering properties of an individual
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particle are then described with more general
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particle are then described with more general
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@ -336,7 +343,8 @@ literal "false"
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\end_inset
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\end_inset
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, which also a rare example is in this field of a code with a clear licence.
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, which also a rare example is in this field of a publicly available code
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with a clear licence.
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\end_layout
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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@ -355,6 +363,18 @@ However, the potential of MSTMM reaches far beyond its past implementations.
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on computational resources, hence speeding up the computations and allowing
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on computational resources, hence speeding up the computations and allowing
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for finite size simulations of systems with particle numbers practically
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for finite size simulations of systems with particle numbers practically
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impossible to reliably simulate with any other method.
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impossible to reliably simulate with any other method.
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Furthemore, the method can be combined with other integral methods, which
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removes the limitation to systems with compact scatterers only, and enables
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e.g.
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including a substrate
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\begin_inset CommandInset citation
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LatexCommand cite
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key "czajkowski_multipole_2020"
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literal "false"
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\end_inset
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.
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\begin_inset Note Note
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\begin_inset Note Note
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status open
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status open
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@ -493,15 +513,14 @@ TODO před odesláním zkontrolovat, co všechno to v danou chvíli umí.
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\end_inset
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\end_inset
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It includes extensive Doxygen documentation, together with description
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It includes Doxygen documentation together with description of the API.
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of the API.
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It has been written with customisability and extendibility in mind, so
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It has been written with customisability and extendibility in mind, so
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that including e.g.
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that including e.g.
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alternative methods of
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alternative methods of
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\begin_inset Formula $T$
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\begin_inset Formula $T$
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\end_inset
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\end_inset
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-matrix calculations of a single matrix are as easy as possible.
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-matrix calculations of a single particle's matrix are as easy as possible.
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\end_layout
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\end_layout
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\begin_layout Standard
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\begin_layout Standard
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