Tmatrix classes¶

This section describes the Tmatrix classes currently implemented in the toolbox.

Tmatrix
TmatrixEbcm
TmatrixMie
TmatrixPm
TmatrixSmarties
TmatrixDda

Tmatrix ¶

class ott.Tmatrix(data, type)¶

Class representing the T-matrix of a scattering particle or lens. This class can either be instantiated directly or used as a base class for defining custom T-matrix types.

This class is the base class for all other T-matrix object, you should inherit from this class when defining your own T-matrix creation methods. This class doesn’t inherit from double or single, instead the internal array type can be set at creation allowing the use of different data types such as sparse or gpuArray.

This class is not a handle class, therefore, when using the class methods you need to store the resulting T-matrix output, for example:

tmatrix = ott.Tmatrix();
new_tmatrix = tmatrix.scattered();

Properties

data – The T-matrix this class encapsulates
type (enum) – Type of T-matrix (total or scattered)

Methods

total() – Convert to a total-field T-matrix
scattered() – Convert to a scattered-field T-matrix
real – Extract real part of T-matrix
imag – Extract imaginary part of T-matrix

Static methods

simple() – Construct a simple particle T-matrix

See also Tmatrix, simple, ott.TmatrixMie.

Tmatrix(data, type)¶

Construct a new T-matrix object.

Usage

TMATRIX() leaves the data uninitialised.

TMATRIX(data, type) initializes the data with the matrix data.

Parameters

data (numeric) – The T-matrix data. Typically a sparse or full matrix.
type (enum) – Type of T-matrix. Must be ‘internal’, ‘scattered’ or ‘total’.

Example

The following example creates an identity T-matrix which represents a particle which doesn’t scatter light:

data = eye(16);
tmatrix = ott.Tmatrix(data, 'total');

static simple(shape, varargin)¶

Constructs a T-matrix for different simple particle shapes. This method creates an instance of one of the other T-matrix classes and is here only as a helper method.

Usage

SIMPLE(shape) constructs a new simple T-matrix for the given ott.shapes.Shape object.

SIMPLE(name, parameters) constructs a new T-matrix for the shape described by the name and parameters.

Supported shape names [parameters]

‘sphere’ – Spherical (or layered sphere) [ radius ]
‘cylinder’ – z-axis aligned cylinder [ radius height ]
‘ellipsoid’ – Ellipsoid [ a b c]
‘superellipsoid’ – Superellipsoid [ a b c e n ]
‘cone-tipped-cylinder’ – [ radius height cone_height ]
‘cube’ – Cube [ width ]
‘axisym’ – Axis-symetric particle [ rho(:) z(:) ]

Optional named arguments

method (enum) – Allows you to choose the preferred method to use for T-matrix calculation. Supported methods are ‘mie’, smarties’, ‘dda’, ‘ebcm’, and ‘pm’. Default: ‘’.
method_tol (numeric) – Specifies the error tolerances, a number between (0, 1] to use for method selection. Smaller values correspond to more accurate methods. Default: [].

Example

The following example creates a T-matrix for a cube with side length of 1 micron using a guess at the best available method. Illumination wavelength is 1064 nm, relative index 1.5/1.33:

tmatrix = ott.Tmatrix.simple('cube', 1.0e-6, ...
  'wavelength0', 1064e-9, ...
  'index_medium', 1.33, 'index_particle', 1.5);

TmatrixEbcm ¶

Constructs a T-matrix using extended boundary conditions method.

class ott.TmatrixEbcm(rtp, normals, ds, varargin)¶

Constructs a T-matrix using extended boundary conditions method. Inherits from ott.Tmatrix.

TmatrixEbcm properties:: k_medium Wavenumber in the surrounding medium k_particle Wavenumber of the particle

This class is based on tmatrix_ebcm_axisym.m from ottv1.

TmatrixMie ¶

Construct T-matrix from Mie scattering coefficients.

class ott.TmatrixMie(radius, varargin)¶

TmatrixMie construct T-matrix from Mie scattering coefficients

TmatrixMie properties:: radius The radius of the sphere the T-matrix represents k_medium Wavenumber in the trapping medium k_particle Wavenumber of the particle

This class is based on tmatrix_mie.m and tmatrix_mie_layered.m from ottv1.

TmatrixPm ¶

Constructs a T-matrix using the point matching method.

class ott.TmatrixPm(rtp, normals, varargin)¶

TmatrixPm constructs a T-matrix using the point matching method

TmatrixPm properties:: k_medium Wavenumber in the surrounding medium k_particle Wavenumber of the particle
TmatrixPm methods:: getInternal Get the internal T-matrix

This class is based on tmatrix_pm.m from ottv1.

TmatrixSmarties ¶

class ott.TmatrixSmarties(a, c, varargin)¶

Constructs a T-matrix using SMARTIES. Inherits from ott.Tmatrix

SMARTIES is a method for calculating T-matrices for spheroids.

This class requires the SMARTIES toolbox has been loaded onto the path. Details about the toolbox can be found in:

Somerville, Auguié, Le Ru. JQSRT, Volume 174, May 2016, Pages 39-55. https://doi.org/10.1016/j.jqsrt.2016.01.005

TmatrixDda ¶

class ott.TmatrixDda(xyz, varargin)¶

Constructs a T-matrix using discrete dipole approximation. Inherits from ott.Tmatrix.

To construct a T-matrix with DDA, either the simple interface or the class constructor can be used. Using the simple interface, the following should produce something similar to TmatrixMie:

Tmatrix = ott.TmatrixDda.simple('sphere', 0.1, 'index_relative', 1.2);

The DDA method requires a lot of memory to calculate the T-matrix. Most small desktop computers will be unable to calculate T-matrices for large particles (i.e., particles larger than a couple of wavelengths in diameter using 20 dipoles per wavelength). For these particles, consider using Geometric Optics or Finite Difference Time Domain method.

Tmatrix classes¶

Tmatrix¶

TmatrixEbcm¶

TmatrixMie¶

TmatrixPm¶

TmatrixSmarties¶

TmatrixDda¶