Chain with large separation • terms

Objective

This example compares the calculation of cross-sections based on a common origin (Scheme 3) vs Stout’s particle-centred scheme (2). The structure consists of a small chain of 4 gold spheres in water, with a variable (large) separation.

This simulation uses the following input file

ModeAndScheme 2 {scheme}
MultipoleCutoff 8
Wavelength 300 700 100
Medium 1.7689 # epsilon of water
Incidence  0.0 0.0 0.0 
# only dipoles, similar outcome
# MultipoleSelections 1
# EE1:1_EM2:1_ME2:1_MM2:1  blocks
OutputFormat HDF5 xsec_{separation}_{comment_centred}_{scheme}

{comment}ScattererCentredCrossSections

Scatterers 4  
Au  0 0    {-3*separation/2}  30
Au  0 0    {-separation/2}  30
Au  0 0    {+separation/2}  30
Au  0 0    {+3*separation/2}  30

where {comment_centred} comments out (#) or not the keyword ScattererCentredCrossSections in each separate run, {scheme} is in 0,1,2,3, and {separation} is replaced by 200, 500, 1000 nm. The results are stored in separate output folders and collated for comparison.

Rows: 65,448
Columns: 11
$ separation      <dbl> 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200,…
$ comment_centred <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ scheme          <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ file            <chr> "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1",…
$ wavelength      <dbl> 300, 300, 300, 300, 300, 300, 300, 300, 300, 304, 304,…
$ crosstype       <chr> "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs"…
$ variable        <chr> "total", "I1", "I2", "I3", "I4", "I5", "I6", "I7", "I8…
$ polarisation1   <dbl> 2.553716e+04, 2.388653e+04, 1.610496e+03, 3.972004e+01…
$ polarisation2   <dbl> 2.553716e+04, 2.388653e+04, 1.610496e+03, 3.972004e+01…
$ dichroism       <dbl> 0.000000e+00, 0.000000e+00, 0.000000e+00, -2.842171e-1…
$ average         <dbl> 2.553716e+04, 2.388653e+04, 1.610496e+03, 3.972004e+01…

Fixed-orientation results

We compare the fixed-orientation cross-sections, with the results of Scheme = 0, ScattererCentred replotted in every panel for comparison (dotted lines and shaded areas, assumed here to be “ground truth”).

We observe that Mackowski’s scheme (3) produces incorrect results at large inter-particle separations. For Stout’s schemes (1 and 2) the use of ScattererCentredCrossSections is required for correct results in these conditions.

Last run: 05 December, 2023