Top level modules¶
smuthi.simulation¶
smuthi.initial_field¶
This module defines classes to represent the initial excitation.

class
smuthi.initial_field.
DipoleCollection
(vacuum_wavelength, k_parallel_array='default', azimuthal_angles_array='default', angular_resolution=None, compute_swe_by_pwe=False, compute_dissipated_power_by_pwe=False)¶ Class for the representation of a set of point dipole sources. Use the append method to add DipoleSource objects.
Parameters:  vacuum_wavelength (float) – vacuum wavelength (length units)
 k_parallel_array (numpy.ndarray or str) – Inplane wavenumber. If ‘default’, use smuthi.fields.default_initial_field_k_parallel_array
 azimuthal_angles_array (numpy.ndarray or str) – Azimuthal angles for plane wave expansions If ‘default’, use smuthi.fields.default_azimuthal_angles
 angular_resolution (float) – If provided, angular arrays are generated with this angular resolution over the default angular range
 compute_swe_by_pwe (bool) – If True, the initial field coefficients are computed through a plane wave expansion of the whole dipole collection field. This is slower for few dipoles and particles, but can become faster than the default for many dipoles and particles (default=False).
 compute_dissipated_power_by_pwe (bool) – If True, evaluate dissipated power through a plane wave expansion of the whole scattered field. This is slower for few dipoles, but can be faster than the default for many dipoles (default=False).

append
(dipole)¶ Add dipole to collection.
Parameters: dipole (DipoleSource) – Dipole object to add.

dissipated_power
(particle_list, layer_system, k_parallel='default', azimuthal_angles='default', angular_resolution=None)¶ Compute the power that the dipole collection feeds into the system.
It is computed according to
\[P = \sum_i P_{0, i} + \frac{\omega}{2} \mathrm{Im} (\mathbf{\mu}_i^* \cdot \mathbf{E}_i(\mathbf{r}_i))\]where \(P_{0,i}\) is the power that the ith dipole would feed into an infinte homogeneous medium with the same refractive index as the layer that contains that dipole, \(\mathbf{r}_i\) is the location of the ith dipole, \(\omega\) is the angular frequency, \(\mathbf{\mu}_i\) is the dipole moment and \(\mathbf{E}_i\) includes the reflections of the dipole field from the layer interfaces, as well as the scattered field from all particles and the fields from all other dipoles. In contrast to dissipated_power_alternative, this routine uses the particle coupling routines and might be faster for many particles and few dipoles.
Parameters:  particle_list (list of smuthi.particles.Particle objects) – scattering particles
 layer_system (smuthi.layers.LayerSystem) – stratified medium
 k_parallel (ndarray or str) – array of inplane wavenumbers for plane wave expansions. If ‘default’, use smuthi.fields.default_initial_field_k_parallel_array
 azimuthal_angles (ndarray or str) – array of azimuthal angles for plane wave expansions. If ‘default’, use smuthi.fields.default_azimuthal_angles
 angular_resolution (float) – If provided, angular arrays are generated with this angular resolution over the default angular range
Returns: dissipated power of each dipole (list of floats)

dissipated_power_alternative
(particle_list, layer_system, k_parallel='default', azimuthal_angles='default', angular_resolution=None)¶ Compute the power that the dipole collection feeds into the system.
It is computed according to
\[P = \sum_i P_{0, i} + \frac{\omega}{2} \mathrm{Im} (\mathbf{\mu}_i^* \cdot \mathbf{E}_i(\mathbf{r}_i))\]where \(P_{0,i}\) is the power that the ith dipole would feed into an infinte homogeneous medium with the same refractive index as the layer that contains that dipole, \(\mathbf{r}_i\) is the location of the ith dipole, \(\omega\) is the angular frequency, \(\mathbf{\mu}_i\) is the dipole moment and \(\mathbf{E}_i\) includes the reflections of the dipole field from the layer interfaces, as well as the scattered field from all particles and the fields from all other dipoles. In contrast to dissipated_power, this routine uses the scattered field piecewise expansion and might be faster for few particles or many dipoles.
Parameters:  particle_list (list of smuthi.particles.Particle objects) – scattering particles
 layer_system (smuthi.layers.LayerSystem) – stratified medium
 k_parallel (ndarray or str) – array of inplane wavenumbers for plane wave expansions. If ‘default’, use smuthi.fields.default_initial_field_k_parallel_array
 azimuthal_angles (ndarray or str) – array of azimuthal angles for plane wave expansions. If ‘default’, use smuthi.fields.default_azimuthal_angles
 angular_resolution (float) – If provided, angular arrays are generated with this angular resolution over the default angular range
Returns: dissipated power of each dipole (list of floats)

electric_field
(x, y, z, layer_system)¶ Evaluate the complex electric field of the dipole collection.
Parameters:  x (array like) – Array of xvalues where to evaluate the field (length unit)
 y (array like) – Array of yvalues where to evaluate the field (length unit)
 z (array like) – Array of zvalues where to evaluate the field (length unit)
 layer_system (smuthi.layer.LayerSystem) – Stratified medium
 Returns
 Tuple (E_x, E_y, E_z) of electric field values

magnetic_field
(x, y, z, layer_system)¶ Evaluate the complex magnetic field of the dipole collection.
Parameters:  x (array like) – Array of xvalues where to evaluate the field (length unit)
 y (array like) – Array of yvalues where to evaluate the field (length unit)
 z (array like) – Array of zvalues where to evaluate the field (length unit)
 layer_system (smuthi.layer.LayerSystem) – Stratified medium
 Returns
 Tuple (H_x, H_y, H_z) of magnetic field values

piecewise_field_expansion
(layer_system)¶ Compute a piecewise field expansion of the dipole collection..
Parameters: layer_system (smuthi.layer.LayerSystem) – stratified medium Returns: smuthi.field_expansion.PiecewiseWaveExpansion object

plane_wave_expansion
= functools.partial(<bound method Memoize.__call__ of <smuthi.utility.memoizing.Memoize object>>, None)¶

spherical_wave_expansion
(particle, layer_system)¶ Regular spherical wave expansion of the dipole collection including layer system response, at the locations of the particles. If self.compute_swe_by_pwe is True, use the dipole collection plane wave expansion, otherwise use the individual dipoles spherical_wave_expansion method.
Parameters:  particle (smuthi.particles.Particle) – particle relative to which the swe is computed
 layer_system (smuthi.layer.LayerSystem) – stratified medium
Returns: regular smuthi.field_expansion.SphericalWaveExpansion object

class
smuthi.initial_field.
DipoleSource
(vacuum_wavelength, dipole_moment, position, k_parallel_array='default', azimuthal_angles_array='default')¶ Class for the representation of a single point dipole source.
Parameters:  vacuum_wavelength (float) – vacuum wavelength (length units)
 dipole_moment (list or tuple) – (x, y, z)coordinates of dipole moment vector
 position (list or tuple) – (x, y, z)coordinates of dipole position
 k_parallel_array (numpy.ndarray or str) – Inplane wavenumber. If ‘default’, use smuthi.fields.default_initial_field_k_parallel_array
 azimuthal_angles_array (numpy.ndarray or str) – Azimuthal angles for plane wave expansions If ‘default’, use smuthi.fields.default_azimuthal_angles

check_dissipated_power_homogeneous_background
(layer_system)¶

current
()¶ The current density takes the form
\[\mathbf{j}(\mathbf{r}) = \delta(\mathbf{r}  \mathbf{r}_D) \mathbf{j}_D,\]where \(\mathbf{j}_D = j \omega \mathbf{\mu}\), \(\mathbf{r}_D\) is the location of the dipole, \(\omega\) is the angular frequency and \(\mathbf{\mu}\) is the dipole moment. For further details, see ‘Principles of nano optics’ by Novotny and Hecht.
Returns: List of [x, y, z]components of current density vector \(\mathbf{j}_D\)

dissipated_power
(particle_list, layer_system, show_progress=True)¶ Compute the power that the dipole feeds into the system.
It is computed according to
\[P = P_0 + \frac{\omega}{2} \mathrm{Im} (\mathbf{\mu}^* \cdot \mathbf{E}(\mathbf{r}_D))\]where \(P_0\) is the power that the dipole would feed into an infinte homogeneous medium with the same refractive index as the layer that contains the dipole, \(\mathbf{r}_D\) is the location of the dipole, \(\omega\) is the angular frequency, \(\mathbf{\mu}\) is the dipole moment and \(\mathbf{E}\) includes the reflections of the dipole field from the layer interfaces, as well as the scattered field from all particles.
Parameters:  particle_list (list of smuthi.particles.Particle objects) – scattering particles
 layer_system (smuthi.layers.LayerSystem) – stratified medium
 show_progress (bool) – if true, display progress
Returns: dissipated power as float

dissipated_power_alternative
(particle_list, layer_system)¶ Compute the power that the dipole feeds into the system.
It is computed according to
\[P = P_0 + \frac{\omega}{2} \mathrm{Im} (\mathbf{\mu}^* \cdot \mathbf{E}(\mathbf{r}_D))\]where \(P_0\) is the power that the dipole would feed into an infinte homogeneous medium with the same refractive index as the layer that contains the dipole, \(\mathbf{r}_D\) is the location of the dipole, \(\omega\) is the angular frequency, \(\mathbf{\mu}\) is the dipole moment and \(\mathbf{E}\) includes the reflections of the dipole field from the layer interfaces, as well as the scattered field from all particles. In contrast to dissipated_power, this routine relies on the scattered field piecewise expansion and and might thus be slower.
Parameters:  particle_list (list of smuthi.particles.Particle objects) – scattering particles
 layer_system (smuthi.layers.LayerSystem) – stratified medium
Returns: dissipated power as float

dissipated_power_homogeneous_background
(layer_system)¶ Compute the power that the dipole would radiate in an infinite homogeneous medium of the same refractive index as the layer that contains the dipole.
\[P_0 = \frac{\mathbf{\mu} k \omega^3}{12 \pi}\]Parameters: layer_system (smuthi.layers.LayerSystem) – stratified medium Returns: power (float)

electric_field
(x, y, z, layer_system, include_direct_field=True, include_layer_response=True)¶ Evaluate the complex electric field of the dipole source.
Parameters:  x (array like) – Array of xvalues where to evaluate the field (length unit)
 y (array like) – Array of yvalues where to evaluate the field (length unit)
 z (array like) – Array of zvalues where to evaluate the field (length unit)
 layer_system (smuthi.layer.LayerSystem) – Stratified medium
 include_direct_field (bool) – if True (default), the direct dipole field is included. otherwise, only the layer response of the dipole field is returned.
 include_layer_response (bool) – if True (default), the layer response of the dipole field is included. otherwise, only the direct dipole field is returned.
 Returns
 Tuple (E_x, E_y, E_z) of electric field values

magnetic_field
(x, y, z, layer_system, include_direct_field=True, include_layer_response=True)¶ Evaluate the complex magnetic field of the dipole source.
Parameters:  x (array like) – Array of xvalues where to evaluate the field (length unit)
 y (array like) – Array of yvalues where to evaluate the field (length unit)
 z (array like) – Array of zvalues where to evaluate the field (length unit)
 layer_system (smuthi.layer.LayerSystem) – Stratified medium
 include_direct_field (bool) – if True (default), the direct dipole field is included. otherwise, only the layer response of the dipole field is returned.
 include_layer_response (bool) – if True (default), the layer response of the dipole field is included. otherwise, only the direct dipole field is returned.
 Returns
 Tuple (H_x, H_y, H_z) of electric field values

outgoing_spherical_wave_expansion
(layer_system)¶ The dipole field as an expansion in spherical vector wave functions.
Parameters: layer_system (smuthi.layers.LayerSystem) – stratified medium Returns: outgoing smuthi.field_expansion.SphericalWaveExpansion object

piecewise_field_expansion
(layer_system, include_direct_field=True, include_layer_response=True)¶ Compute a piecewise field expansion of the dipole field.
Parameters:  layer_system (smuthi.layer.LayerSystem) – stratified medium
 include_direct_field (bool) – if True (default), the direct dipole field is included. otherwise, only the layer response of the dipole field is returned.
 include_layer_response (bool) – if True (default), the layer response of the dipole field is included. otherwise, only the direct dipole field is returned.
Returns: smuthi.field_expansion.PiecewiseWaveExpansion object

plane_wave_expansion
(layer_system, i, k_parallel_array=None, azimuthal_angles_array=None)¶ Plane wave expansion of the dipole field.
Parameters:  layer_system (smuthi.layer.LayerSystem) – stratified medium
 i (int) – layer number in which to evaluate the expansion
 k_parallel_array (numpy.ndarray) – inplane wavenumber array for the expansion. if none specified, self.k_parallel_array is used
 azimuthal_angles_array (numpy.ndarray) – azimuthal angles for the expansion. if none specified, self.azimuthal_angles_array is used
Returns: tuple of to smuthi.field_expansion.PlaneWaveExpansion objects, one for upgoing and one for downgoing component

spherical_wave_expansion
(particle, layer_system)¶ Regular spherical wave expansion of the wave including layer system response, at the locations of the particles.
Parameters:  particle (smuthi.particles.Particle) – particle relative to which the swe is computed
 layer_system (smuthi.layer.LayerSystem) – stratified medium
Returns: regular smuthi.field_expansion.SphericalWaveExpansion object

class
smuthi.initial_field.
GaussianBeam
(vacuum_wavelength, polar_angle, azimuthal_angle, polarization, beam_waist, k_parallel_array='default', azimuthal_angles_array='default', amplitude=1, reference_point=None)¶ Class for the representation of a Gaussian beam as initial field.

initial_intensity
(layer_system)¶ Evaluate the incoming intensity of the initial field.
Parameters: layer_system (smuthi.layers.LayerSystem) – Stratified medium Returns: A smuthi.field_expansion.FarField object holding the initial intensity information.

plane_wave_expansion
(layer_system, i, k_parallel_array=None, azimuthal_angles_array=None)¶ Plane wave expansion of the Gaussian beam.
Parameters:  layer_system (smuthi.layer.LayerSystem) – stratified medium
 i (int) – layer number in which to evaluate the expansion
 k_parallel_array (numpy.ndarray) – inplane wavenumber array for the expansion. if none specified, self.k_parallel_array is used
 azimuthal_angles_array (numpy.ndarray) – azimuthal angles for the expansion. if none specified, self.azimuthal_angles_array is used
Returns: tuple of to smuthi.field_expansion.PlaneWaveExpansion objects, one for upgoing and one for downgoing component

propagated_far_field
(layer_system)¶ Evaluate the far field intensity of the reflected / transmitted initial field.
Parameters: layer_system (smuthi.layers.LayerSystem) – Stratified medium Returns: A tuple of smuthi.field_expansion.FarField objects, one for forward (i.e., into the top hemisphere) and one for backward propagation (bottom hemisphere).


class
smuthi.initial_field.
InitialField
(vacuum_wavelength)¶ Base class for initial field classes

angular_frequency
()¶ Angular frequency.
Returns: Angular frequency (float) according to the vacuum wavelength in units of c=1.

get_azimuthal_angles_array
()¶ Get azimuthal angles array which is either the default array or the one stored in the object

get_k_parallel_array
()¶ Get k_parallel array which is either the default array or the one stored in the object

piecewise_field_expansion
(layer_system)¶

plane_wave_expansion
(layer_system, i)¶ Virtual method to be overwritten.

spherical_wave_expansion
(particle, layer_system)¶ Virtual method to be overwritten.


class
smuthi.initial_field.
InitialPropagatingWave
(vacuum_wavelength, polar_angle, azimuthal_angle, polarization, amplitude=1, reference_point=None)¶ Base class for plane waves and Gaussian beams
Parameters:  vacuum_wavelength (float) –
 polar_angle (float) – polar propagation angle (0 means, parallel to zaxis)
 azimuthal_angle (float) – azimuthal propagation angle (0 means, in xz plane)
 polarization (int) – 0 for TE/s, 1 for TM/p
 amplitude (float or complex) – Electric field amplitude
 reference_point (list) – Location where electric field of incoming wave equals amplitude

electric_field
(x, y, z, layer_system)¶ Evaluate the complex electric field corresponding to the wave.
Parameters:  x (array like) – Array of xvalues where to evaluate the field (length unit)
 y (array like) – Array of yvalues where to evaluate the field (length unit)
 z (array like) – Array of zvalues where to evaluate the field (length unit)
 layer_system (smuthi.layer.LayerSystem) – Stratified medium
 Returns
 Tuple (E_x, E_y, E_z) of electric field values

magnetic_field
(x, y, z, layer_system)¶ Evaluate the complex magnetic field corresponding to the wave.
Parameters:  x (array like) – Array of xvalues where to evaluate the field (length unit)
 y (array like) – Array of yvalues where to evaluate the field (length unit)
 z (array like) – Array of zvalues where to evaluate the field (length unit)
 layer_system (smuthi.layer.LayerSystem) – Stratified medium
 Returns
 Tuple (H_x, H_y, H_z) of magnetic field values

piecewise_field_expansion
(layer_system)¶ Compute a piecewise field expansion of the initial field.
Parameters: layer_system (smuthi.layer.LayerSystem) – stratified medium Returns: smuthi.field_expansion.PiecewiseWaveExpansion object

spherical_wave_expansion
(particle, layer_system)¶ Regular spherical wave expansion of the wave including layer system response, at the locations of the particles.
Parameters:  particle (smuthi.particles.Particle) – particle relative to which the swe is computed
 layer_system (smuthi.layer.LayerSystem) – stratified medium
Returns: regular smuthi.field_expansion.SphericalWaveExpansion object

class
smuthi.initial_field.
PlaneWave
(vacuum_wavelength, polar_angle, azimuthal_angle, polarization, amplitude=1, reference_point=None)¶ Class for the representation of a plane wave as initial field.
Parameters:  vacuum_wavelength (float) –
 polar_angle (float) – polar angle of kvector (0 means, k is parallel to zaxis)
 azimuthal_angle (float) – azimuthal angle of kvector (0 means, k is in xz plane)
 polarization (int) – 0 for TE/s, 1 for TM/p
 amplitude (float or complex) – Plane wave amplitude at reference point
 reference_point (list) – Location where electric field of incoming wave equals amplitude

plane_wave_expansion
(layer_system, i)¶ Plane wave expansion for the plane wave including its layer system response. As it already is a plane wave, the plane wave expansion is somehow trivial (containing only one partial wave, i.e., a discrete plane wave expansion).
Parameters:  layer_system (smuthi.layers.LayerSystem) – Layer system object
 i (int) – layer number in which the plane wave expansion is valid
Returns: Tuple of smuthi.field_expansion.PlaneWaveExpansion objects. The first element is an upgoing PWE, whereas the second element is a downgoing PWE.
smuthi.layers¶
Provide class for the representation of planar layer systems.

class
smuthi.layers.
LayerSystem
(thicknesses=None, refractive_indices=None)¶ Stack of planar layers.
Parameters:  thicknesses (list) – layer thicknesses, first and last are semi inf and set to 0 (length unit)
 refractive_indices (list) – complex refractive indices in the form n+jk

is_degenerate
()¶ Returns True if the layer system consists of only two layers of the same material. This function is useful for detecting if layer mediated coupling can be omitted when calculating the coupling between particles.
Returns: True if layer system is degenerate. False otherwise.

layer_number
(z)¶ Return number of layer that contains point [0,0,z]
If z is on the interface, the higher layer number is selected.
Parameters: z (float) – zcoordinate of query point (length unit) Returns: number of layer containing z

lower_zlimit
(i)¶ Return the zcoordinate of lower boundary
The coordinate system is defined such that z=0 corresponds to the interface between layer 0 and layer 1.
Parameters: i (int) – index of layer in question (must be between 0 and number_of_layers1) Returns: zcoordinate of lower boundary

number_of_layers
()¶ Return total number of layers
Returns: number of layers

reference_z
(i)¶ Return the anchor point’s zcoordinate.
The coordinate system is defined such that z=0 corresponds to the interface between layer 0 and layer 1.
Parameters: i (int) – index of layer in question (must be between 0 and number_of_layers1) Returns: anchor point’s zcoordinate

response
(pwe, from_layer, to_layer)¶ Evaluate the layer system response to an electromagnetic excitation inside the layer system.
Parameters:  pwe (tuple or smuthi.field_expansion.PlaneWaveExpansion) – Either specify a PlaneWaveExpansion object that that represents the electromagnetic excitation, or a tuple of two PlaneWaveExpansion objects representing the upwards and downwards propagating partial waves of the excitation.
 from_layer (int) – Layer number in which the excitation is located
 to_layer (int) – Layer number in which the layer response is to be evaluated
Returns: Tuple (pwe_up, pwe_sown) of PlaneWaveExpansion objects representing the layer system response to the excitation.

upper_zlimit
(i)¶ Return the zcoordinate of upper boundary.
The coordinate system is defined such that z=0 corresponds to the interface between layer 0 and layer 1.
Parameters: i (int) – index of layer in question (must be between 0 and number_of_layers1) Returns: zcoordinate of upper boundary

wavenumber
(layer_number, vacuum_wavelength)¶ Parameters:  layer_number (int) – number of layer in question
 vacuum_wavelength (float) – vacuum wavelength
Returns: wavenumber in that layer as float

smuthi.layers.
fresnel_r
(pol, kz1, kz2, n1, n2)¶ Fresnel reflection coefficient.
Parameters:  pol (int) – polarization (0=TE, 1=TM)
 kz1 (float or array) – incoming wave’s zwavenumber (k*cos(alpha1))
 kz2 (float or array) – transmitted wave’s zwavenumber (k*cos(alpha2))
 n1 (float or complex) – first medium’s complex refractive index (n+ik)
 n2 (float or complex) – second medium’s complex refractive index (n+ik)
Returns: Complex Fresnel reflection coefficient (float or array)

smuthi.layers.
fresnel_t
(pol, kz1, kz2, n1, n2)¶ Fresnel transmission coefficient.
Parameters:  pol (int) – polarization (0=TE, 1=TM)
 kz1 (float or array) – incoming wave’s zwavenumber (k*cos(alpha1))
 kz2 (float or array) – transmitted wave’s zwavenumber (k*cos(alpha2))
 n1 (float or complex) – first medium’s complex refractive index (n+ik)
 n2 (float or complex) – second medium’s complex refractive index (n+ik)
Returns: Complex Fresnel transmission coefficient (float or array)

smuthi.layers.
interface_transition_matrix
(pol, kz1, kz2, n1, n2)¶ Interface transition matrix to be used in the Transfer matrix algorithm.
Parameters:  pol (int) – polarization (0=TE, 1=TM)
 kz1 (float or array) – incoming wave’s zwavenumber (k*cos(alpha1))
 kz2 (float or array) – transmitted wave’s zwavenumber (k*cos(alpha2))
 n1 (float or complex) – first medium’s complex refractive index (n+ik)
 n2 (float or complex) – second medium’s complex refractive index (n+ik)
Returns: Interface transition matrix as 2x2 numpy array or as 2x2 mpmath.matrix

smuthi.layers.
layer_propagation_matrix
(kz, d)¶ Layer propagation matrix to be used in the Transfer matrix algorithm.
Parameters:  kz (float or complex) – zwavenumber (k*cos(alpha))
 d (float) – thickness of layer
Returns: Layer propagation matrix as 2x2 numpy array or as 2x2 mpmath.matrix

smuthi.layers.
layersystem_scattering_matrix
(pol, layer_d, layer_n, kpar, omega)¶ Scattering matrix of a planarly layered medium.
Parameters:  pol (int) – polarization(0=TE, 1=TM)
 layer_d (list) – layer thicknesses
 layer_n (list) – complex layer refractive indices
 kpar (float) – inplane wavenumber
 omega (float) – angular frequency in units of c=1: omega=2*pi/lambda
Returns: Scattering matrix as 2x2 numpy array or as 2x2 mpmath.matrix

smuthi.layers.
layersystem_transfer_matrix
(pol, layer_d, layer_n, kpar, omega)¶ Transfer matrix of a planarly layered medium.
Parameters:  pol (int) – polarization(0=TE, 1=TM)
 layer_d (list) – layer thicknesses
 layer_n (list) – complex layer refractive indices
 kpar (float) – inplane wavenumber
 omega (float) – angular frequency in units of c=1: omega=2*pi/lambda
Returns: Transfer matrix as 2x2 numpy array or as 2x2 mpmath.matrix

smuthi.layers.
matrix_inverse
(m)¶ Parameters: m (mpmath.matrix or numpy.ndarray) – matrix to invert Returns: inverse of m with same data type as m1 and m2

smuthi.layers.
matrix_product
(m1, m2)¶ Parameters:  m1 (mpmath.matrix or numpy.ndarray) – first matrix
 m2 (mpmath.matrix or numpy.ndarray) – second matrix
Returns: matrix product m1 * m2 with same data type as m1 and m2

smuthi.layers.
set_precision
(prec=None)¶ Set the numerical precision of the layer system response. You can use this to evaluate the layer response of unstable systems, for example in the case of evanescent waves in very thick layers. Calculations take longer time if the precision is set to a value other than None (default).
Parameters: prec (None or int) – If None, calculations are done using standard double precision. If int, that many decimal digits are considered in the calculations, using the mpmath package.
smuthi.particles¶
Classes for the representation of scattering particles.

class
smuthi.particles.
AnisotropicSphere
(position=None, euler_angles=None, polar_angle=0, azimuthal_angle=0, refractive_index=(1+0j), radius=1, refractive_index_z=(2+0j), l_max=None, m_max=None, n_rank=None)¶ Particle subclass for anisotropic spheres.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 euler_angles (list) – Euler angles [alpha, beta, gamma] in (zy’z’’convention) in radian. Alternatively, you can specify the polar and azimuthal angle of the axis of revolution.
 polar_angle (float) – Polar angle of axis of revolution.
 azimuthal_angle (float) – Azimuthal angle of axis of revolution.
 refractive_index (complex) – Complex refractive index of particle in xy plane (if not rotated)
 refractive_index_z (complex) – Complex refractive index of particle along zaxis (if not rotated)
 radius (float) – Sphere radius
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field
 n_rank (int) – Maximal multipole order used for in NFMDS (default: l_max + 5)

circumscribing_sphere_radius
()¶ Virtual method to be overwritten

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray

class
smuthi.particles.
CustomParticle
(position=None, euler_angles=None, polar_angle=0, azimuthal_angle=0, refractive_index=(1+0j), geometry_filename=None, scale=1, l_max=None, m_max=None, n_rank=None)¶ Particle subclass for custom particle shapes defined via FEM file.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 euler_angles (list) – Euler angles [alpha, beta, gamma] in (zy’z’’convention) in radian. Alternatively, you can specify the polar and azimuthal angle of the axis of revolution.
 polar_angle (float) – Polar angle of axis of revolution.
 azimuthal_angle (float) – Azimuthal angle of axis of revolution.
 geometry_filename (string) – Path to FEM file
 scale (float) – Scaling factor for particle dimensions (relative to provided dimensions)
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field
 n_rank (int) – Maximal multipole order used for in NFMDS (default: l_max + 5)

circumscribing_sphere_radius
()¶ Virtual method to be overwritten

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray

class
smuthi.particles.
FiniteCylinder
(position=None, euler_angles=None, polar_angle=0, azimuthal_angle=0, refractive_index=(1+0j), cylinder_radius=1, cylinder_height=1, l_max=None, m_max=None, n_rank=None, use_python_tmatrix=False, nint=100)¶ Particle subclass for finite cylinders.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 euler_angles (list) – Euler angles [alpha, beta, gamma] in (zy’z’’convention) in radian. Alternatively, you can specify the polar and azimuthal angle of the axis of revolution.
 polar_angle (float) – Polar angle of axis of revolution.
 azimuthal_angle (float) – Azimuthal angle of axis of revolution.
 refractive_index (complex) – Complex refractive index of particle
 cylinder_radius (float) – Radius of cylinder (length unit)
 cylinder_height (float) – Height of cylinder, in zdirection if not rotated (length unit)
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field
 n_rank (int) – Maximal multipole order used for in NFMDS (default: l_max + 5)
 use_python_tmatrix (bool) – If true, use Alan Zhan’s Python code to compute the Tmatrix rather than NFMDS
 nint (int) – Number of angles used in integral (only for python tmnatrix)

circumscribing_sphere_radius
()¶ Virtual method to be overwritten

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray

class
smuthi.particles.
LayeredSpheroid
(position=None, euler_angles=None, polar_angle=0, azimuthal_angle=0, layer_refractive_indices=(1+0j), layer_semi_axes_c=1, layer_semi_axes_a=1, l_max=None, m_max=None, n_rank=None)¶ Particle subclass for layered spheroid.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 euler_angles (list) – Euler angles [alpha, beta, gamma] in (zy’z’’convention) in radian. Alternatively, you can specify the polar and azimuthal angle of the axis of revolution.
 polar_angle (float) – Polar angle of axis of revolution.
 azimuthal_angle (float) – Azimuthal angle of axis of revolution.
 layer_refractive_indices (complex) – Complex refractive index of particle
 layer_semi_axes_c (float) – Spheroid half axis in direction of axis of revolution (zaxis if not rotated)
 layer_semi_axes_a (float) – Spheroid half axis in lateral direction (x and yaxis if not rotated)
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field
 n_rank (int) – Maximal multipole order used in NFMDS (default: l_max + 5)

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray

class
smuthi.particles.
Particle
(position=None, euler_angles=None, refractive_index=(1+0j), l_max=None, m_max=None)¶ Base class for scattering particles.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 euler_angles (list) – Particle Euler angles in the format [alpha, beta, gamma]
 refractive_index (complex) – Complex refractive index of particle
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field

circumscribing_sphere_radius
()¶ Virtual method to be overwritten

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray

is_inside
(x, y, z)¶ Virtual method to be overwritten. Until all child classes implement it: return False

is_outside
(x, y, z)¶ Virtual method to be overwritten. Until all child classes implement it: return True

class
smuthi.particles.
Sphere
(position=None, refractive_index=(1+0j), radius=1, l_max=None, m_max=None)¶ Particle subclass for spheres.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 refractive_index (complex) – Complex refractive index of particle
 radius (float) – Particle radius (length unit)
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field

circumscribing_sphere_radius
()¶ Virtual method to be overwritten

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray

is_inside
(x, y, z)¶ Virtual method to be overwritten. Until all child classes implement it: return False

is_outside
(x, y, z)¶ Virtual method to be overwritten. Until all child classes implement it: return True

class
smuthi.particles.
Spheroid
(position=None, euler_angles=None, polar_angle=0, azimuthal_angle=0, refractive_index=(1+0j), semi_axis_c=1, semi_axis_a=1, l_max=None, m_max=None, n_rank=None)¶ Particle subclass for spheroids.
Parameters:  position (list) – Particle position in the format [x, y, z] (length unit)
 euler_angles (list) – Euler angles [alpha, beta, gamma] in (zy’z’’convention) in radian. Alternatively, you can specify the polar and azimuthal angle of the axis of revolution.
 polar_angle (float) – Polar angle of axis of revolution.
 azimuthal_angle (float) – Azimuthal angle of axis of revolution.
 refractive_index (complex) – Complex refractive index of particle
 semi_axis_c (float) – Spheroid half axis in direction of axis of revolution (zaxis if not rotated)
 semi_axis_a (float) – Spheroid half axis in lateral direction (x and yaxis if not rotated)
 l_max (int) – Maximal multipole degree used for the spherical wave expansion of incoming and scattered field
 m_max (int) – Maximal multipole order used for the spherical wave expansion of incoming and scattered field
 n_rank (int) – Maximal multipole order used in NFMDS (default: l_max + 5)

circumscribing_sphere_radius
()¶ Virtual method to be overwritten

compute_t_matrix
(vacuum_wavelength, n_medium)¶ Return the Tmatrix of a particle.
Parameters:  vacuum_wavelength (float) –
 n_medium (float or complex) – Refractive index of surrounding medium
 particle (smuthi.particles.Particle) – Particle object
Returns: Tmatrix as ndarray