Nanosphere

This tutorial example simulates light scattering off a spherical particle above a substrate. The particle is illuminated with plane waves at oblique incidence, with S- and P-polarization. JCMsuite computes the near-field solution. Post-processes are used to compute absorption and scattering cross-sections, and to export field profiles.

_images/snapshot_010_log_intensity_field1.png

Near field intensity (pseudo-color, log-scale) in two cross-sections and triangular mesh of the geometry.

Definition of the geometry:

  • layout.jcm [ASCII]

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
    Layout2D {
  UnitOfLength = 1e-09
  MeshOptions {
    MaximumSideLength = 100
  }
  CoordinateSystem = Cylindrical
  BoundaryConditions {
    Boundary {
      Direction = All 
      Class = Transparent
    }
  }
  Objects {
    Parallelogram {
      Name = "CD"
      Height = 900
      Width = 450
      Port = West
      GlobalPosition = [0 0]
      DomainId = 1
      Priority = ComputationalDomain      
    }
    CircleSector {
      Radius = 400
      AngleRange = [-90 90]
      GlobalPosition = [0 0]
      DomainId = 2
      Priority = 1
      RefineAll = 4
      MeshOptions {
        MaximumSideLength = 50
      }
    }
    
    Parallelogram {
      Height = 900
      Width = 450
      Port = North
      Alignment {
        Parent {
          Domain = "CD"
          Port = South
        }
        Displacement = [-0 -60]
        Orientation = AntiParallel
      }
      DomainId = 3
      Priority = 2
      
    }
  }
}

The computational domain is defined by a parallelogram in the x-y-plane. In line 6 the coordinate system is chosen which defines the y-axis as rotational symmetry axis. The sphere is defined by a (rotated) circle sector (lines 23-33), and the substrate is defined by a (rotated) parallelogram.

The refractive indices, resp. relative permittivities, of the various geometrical domains are defined here:

  • materials.jcm [ASCII]

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
    Material {
  DomainId = 1
  RelPermittivity = 1
  RelPermeability = 1
}
Material {
  DomainId = 2
  RelPermittivity = (8.99, 0.6)
  RelPermeability = 1
}
Material {
  DomainId = 3
  RelPermittivity = 2.25
  RelPermeability = 1
}

The illumination with two independent, S- and P-polarized plane waves is defined in the following:

  • sources.jcm [ASCII]

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
    
SourceBag {
  Source {
    ElectricFieldStrength {
      PlaneWave {
        Lambda0 = 4e-07
        ThetaPhi = [20 0]
        Incidence = FromAbove
        3DTo2D = yes
        SP = [1 0]
        
      }
    }
  }
}
SourceBag {
  Source {
    ElectricFieldStrength {
      PlaneWave {
        Lambda0 = 4e-07
        ThetaPhi = [20 0]
        Incidence = FromAbove
        3DTo2D = yes
        SP = [0 1]
      }
    }
  }
}

Project type, accuracy settings and several post-processes are defined in the project file:

  • project.jcmp [ASCII]

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
    Project {
  Electromagnetics {
    TimeHarmonic {
      Scattering {
        FieldComponents = Electric
        Accuracy {
          FiniteElementDegree = 3         
        }
      }
    }
  }
}
PostProcess {
  DensityIntegration {
    FieldBagPath = "project_results/fieldbag.jcm"
    OutputFileName = "project_results/energy.jcm"
    OutputQuantity = ElectricFieldEnergy
  }
}
PostProcess {
  FluxIntegration {
    FieldBagPath = "project_results/fieldbag.jcm"
    OutputFileName = "project_results/scattered_energy_flux.jcm"
    OutputQuantity = ElectromagneticFieldEnergyFlux
    InterfaceType = ExteriorDomain
  }
}
PostProcess {
  ExportFields {
    FieldBagPath = "project_results/fieldbag.jcm"
    OutputFileName = "project_results/c_xy.jcm"
    Cartesian {
      GridPointsX = [-447.5e-9 : 5e-9 : 450e-9]
      GridPointsY = [-450.0e-9 : 5e-9 : 450e-9]
      GridPointsZ = 0
    }
  }
}
PostProcess {
  ExportFields {
    FieldBagPath = "project_results/fieldbag.jcm"
    OutputFileName = "project_results/c_xz.jcm"
    Cartesian {
      GridPointsX = [-447.5e-9 : 5e-9 : 450e-9]
      GridPointsZ = [-450.0e-9 : 5e-9 : 450e-9]
      GridPointsY = 0
    }
  }
}

The density integration post-process can be used to compute the absorption cross-section. The flux integration post-process can be used to compute the scattering cross-section. (Alternatively, also far-field computation / Fourier transform post-process can be used for obtaining angular dependent scattering amplitudes.) ExportFields post-processes are used for visualization purposes in this case.

The data_analysis folder contains also a script where geometrical, material, source, and computational parameters can be set, and where a wavelength scan is performed, yielding computation of the wavelength dependent absorption and scattering cross-sections (with corresponding template files layout.jcmt, sources.jcmt, materials.jcmt, project.jcmpt). Please note that in this case JCMsuite is used in Daemon mode, allowing for parallel execution of the various wavelengths of the wavelength scan. With appropriate hardware and license, all wavelength responses can be computed at the same time, allowing for fast computation of the whole parameter scan.

  • data_analysis/run_simulation.m [ASCII]

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
    local_jcm_path = getenv('JCMROOT'); addpath(fullfile(local_jcm_path, 'ThirdPartySupport', 'Matlab'));
jcmwave_startup; jcmwave_set_num_threads(1); jcmwave_daemon_shutdown();
jcmwave_daemon_add_workstation('Multiplicity', 2, 'NThreads', 1); 

% geometry
keys.uol = 1.e-9;                                
keys.radius_scatterer = 400.0;
keys.contains_substrate = true;
keys.offset_sphere = -10.0; % offset between sphere and substrate in uol

% refractive indices
keys.n_1 = 1.0; % background
keys.n_2 = 3.0 + 0.1i; % sphere
keys.n_3 = 1.5; % substrate

% S&P plane waves incidence angle
keys.theta = 20;

keys.fem_degree = 3;
keys.n_steps = 0;

c0 = 299792458; mu0 = 4*pi*1e-7; eps0 = 1/(mu0*c0^2); Z0 = sqrt(mu0/eps0);
geo_cross_section = pi*(keys.radius_scatterer*keys.uol)^2; p_in = 0.5*keys.n_1/Z0*geo_cross_section; 

% parameter scan
job_ids = []; results = []; simulation_results = []; counter = 0;

wavelengths = [400:2:600]*1e-9;

for ii = 1:length(wavelengths)
  counter = counter + 1;
  keys.vacuum_wavelength = wavelengths(ii);

  job_ids(end + 1) = jcmwave_solve('project.jcmp', keys, 'workingdir', fullfile('tmp', ['s_' num2str(counter, '%05i')]));

  results(counter, 1) = keys.vacuum_wavelength;
  results(counter, 6) = keys.fem_degree;
  results(counter, 7) = keys.n_steps;
end;

[simulation_results, logs] = jcmwave_daemon_wait(job_ids);

for ii = 1:length(job_ids)
  this_result = simulation_results{ii};
  field_energy = cell2mat(this_result{2}.ElectricFieldEnergy);
  omega = 2*pi*c0/keys.vacuum_wavelength;         
  absorption = -2*omega*imag(field_energy(2, :))/p_in;
  flux_scat = cell2mat(this_result{4}.ElectromagneticFieldEnergyFlux);
  scattering = sum(real(flux_scat), 1)/p_in;
  results(ii, 2:3) = absorption;
  results(ii, 4:5) = scattering;
end

filename = ['results_' datestr(now,'yyyymmdd_HHMMSS') '.txt']; 
save ('-ascii', '-double', filename, 'results'); copyfile(filename, 'results.txt');
display_results;
_images/wavelength_scan.png

Wavelength-dependent absorption and scattering off a nanosphere on top of a substrate.