Per-particle absorption • terms

Objective

This example illustrates the calculation of orientation-averaged absorption spectra in homogeneous spheres, with three different methods. The structure consists of two gold spheres in water.

This simulation uses the following input file

ModeAndScheme 2 2
MultipoleCutoff 12
Wavelength 300 800 100
Incidence file incidence 2
Medium 1.7689 # for water
Verbosity 2
OutputFormat HDF5 cross_sections
ScattererCentredCrossSections

Scatterers 2
Au  0 0 0 20
Au  55 0 0 30

Show incidence file (click to open)

26 
 0.00000000  1.57079633  0.00000000  0.04761905
 3.14159265  1.57079633  0.00000000  0.04761905
 1.57079633  1.57079633  0.00000000  0.04761905
-1.57079633  1.57079633  0.00000000  0.04761905
 1.57079633  0.00000000  0.00000000  0.04761905
 1.57079633  3.14159265  0.00000000  0.04761905
 1.57079633  0.78539816  0.00000000  0.03809524
 1.57079633  2.35619449  0.00000000  0.03809524
-1.57079633  0.78539816  0.00000000  0.03809524
-1.57079633  2.35619449  0.00000000  0.03809524
 0.00000000  0.78539816  0.00000000  0.03809524
 0.00000000  2.35619449  0.00000000  0.03809524
 3.14159265  0.78539816  0.00000000  0.03809524
 3.14159265  2.35619449  0.00000000  0.03809524
 0.78539816  1.57079633  0.00000000  0.03809524
-0.78539816  1.57079633  0.00000000  0.03809524
 2.35619449  1.57079633  0.00000000  0.03809524
-2.35619449  1.57079633  0.00000000  0.03809524
 0.78539816  0.95531662  0.00000000  0.03214286
 0.78539816  2.18627604  0.00000000  0.03214286
-0.78539816  0.95531662  0.00000000  0.03214286
-0.78539816  2.18627604  0.00000000  0.03214286
 2.35619449  0.95531662  0.00000000  0.03214286
 2.35619449  2.18627604  0.00000000  0.03214286
-2.35619449  0.95531662  0.00000000  0.03214286
-2.35619449  2.18627604  0.00000000  0.03214286

Total cross-sections

We first retrieve the total cross-sections, as usual,

Rows: 303
Columns: 8
$ wavelength  <dbl> 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355…
$ crosstype   <chr> "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "A…
$ variable    <chr> "total", "total", "total", "total", "total", "total", "tot…
$ dichroism   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
$ average     <dbl> 7365.917, 7336.871, 7308.710, 7282.909, 7260.810, 7243.532…
$ scatterer   <chr> "both", "both", "both", "both", "both", "both", "both", "b…
$ region      <chr> "total_avg", "total_avg", "total_avg", "total_avg", "total…
$ calculation <chr> "total", "total", "total", "total", "total", "total", "tot…

Mackowski’s partial cross-sections

Formulas derived by Mackowski provide partial absorptions for individual spheres, which we average with a numerical cubature.

Rows: 202
Columns: 8
Groups: scatterer, wavelength, polarisation [202]
$ polarisation <chr> "4L", "4L", "4L", "4L", "4L", "4L", "4L", "4L", "4L", "4L…
$ scatterer    <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
$ wavelength   <dbl> 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 35…
$ partial_0    <dbl> 1910.220, 1880.418, 1853.695, 1830.292, 1810.320, 1793.76…
$ crosstype    <chr> "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "…
$ calculation  <chr> "Mackowski", "Mackowski", "Mackowski", "Mackowski", "Mack…
$ region       <chr> "total", "total", "total", "total", "total", "total", "to…
$ value        <dbl> 1910.220, 1880.418, 1853.695, 1830.292, 1810.320, 1793.76…

Stout’s per-particle cross-sections

In the Stout scheme, orientation-averaged quantities are obtained for each scatterer individually, using scatterer-centred formulas. This allows us to separate the absorption in different scatterers.

Rows: 303
Columns: 7
$ wavelength  <dbl> 300, 300, 300, 305, 305, 305, 310, 310, 310, 315, 315, 315…
$ crosstype   <chr> "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "Abs", "A…
$ name        <chr> "both", "1", "2", "both", "1", "2", "both", "1", "2", "bot…
$ value       <dbl> 7323.890, 1910.245, 5413.644, 7300.426, 1880.440, 5419.986…
$ scatterer   <chr> "both", "1", "2", "both", "1", "2", "both", "1", "2", "bot…
$ region      <chr> "total_avg", "total_avg", "total_avg", "total_avg", "total…
$ calculation <chr> "Stout", "Stout", "Stout", "Stout", "Stout", "Stout", "Sto…

Comparison

Last run: 05 December, 2023