Scatterers

class Sphere

Bases: BaseScatterer

add_to_scene(self: PyMieSim.single.scatterer.Sphere, scene: object, **kwargs) → None

property an

III.88 of B&B:

\[a_n = \frac{ \mu_{sp} \Psi_n(\alpha) \Psi_n^\prime(\beta) - \mu M \Psi_n^\prime(\alpha) \Psi_n(\beta) }{ \mu_{sp} \xi_n(\alpha) \Psi_n^\prime(\beta) - \mu M \xi_n^\prime (\alpha) \Psi_n(\beta) }\]

With \(M = \frac{k_{sp}}{k}\) (Eq:I.103)

Returns:

A list of ‘an’ scattering coefficients used in the spherical wave expansion.

Return type:

list

Type:

Returns \(a_n\) coefficient as defined in Eq

property bn

III.89 of B&B:

\[b_n = \frac{ \mu M \Psi_n(\alpha) \Psi_n^\prime(\beta) - \mu_{sp} \Psi_n^\prime(\alpha) \Psi_n(\beta) }{ \mu M \xi_n(\alpha) \Psi_n^\prime(\beta) - \mu_{sp} \xi_n^\prime (\alpha) \Psi_n(\beta) }\]

With \(M = \frac{k_{sp}}{k}\) (Eq:I.103)

Returns:

A list of ‘bn’ scattering coefficients used in the spherical wave expansion.

Return type:

list

Type:

Returns \(b_n\) coefficient as defined in Eq

property cn

For future purpose only! Returns \(c_n\) coefficient as defined in Eq:III.90 of B&B:

\[c_n = \frac{ \mu_{sp} M \big[ \xi_n(\alpha) \Psi_n^\prime(\alpha) - \xi_n^\prime(\alpha) \Psi_n(\alpha) \big] }{ \mu_{sp} \xi_n(\alpha) \Psi_n^\prime(\beta) - \mu M \xi_n^\prime (\alpha) \Psi_n(\beta) }\]

With \(M = \frac{k_{sp}}{k}\) (Eq:I.103)

Returns:

A list of ‘cn’ scattering coefficients used in the spherical wave expansion.

Return type:

list

compute_an_bn(self: PyMieSim.single.scatterer.BaseScatterer, max_order: SupportsInt | SupportsIndex = 0) → None

Computes the coefficients an and bn for the scatterer. :param max_order: The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter). :type max_order: int, optional

compute_cn_dn(self: PyMieSim.single.scatterer.BaseScatterer, max_order: SupportsInt | SupportsIndex = 0) → None

Computes the coefficients cn and dn for the scatterer.

Parameters:

max_order (int, optional) – The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter).

property diameter

Diameter of the sphere.

property dn

For future purpose only! Returns \(d_n\) coefficient as defined in Eq:III.91 of B&B:

\[d_n = \frac{ \mu M^2 \big[ \xi_n(\alpha) \Psi_n^\prime(\alpha) - \xi_n^\prime(\alpha) \Psi_n(\alpha) \big] }{ \mu M \xi_n(\alpha) \Psi_n^\prime(\beta) - \mu_{sp} M \xi_n^\prime (\alpha) \Psi_n(\beta) }\]

With \(M = \frac{k_{sp}}{k}\) (Eq:I.103)

Returns:

A list of ‘dn’ scattering coefficients used in the spherical wave expansion.

Return type:

list

get_coefficient(self: PyMieSim.single.scatterer.BaseScatterer, type: str, order: SupportsInt | SupportsIndex) → complex

Returns a specific scattering coefficient for a given type and order.

Parameters:

• type (str) – The type of coefficient (‘an’, ‘bn’, ‘cn’, ‘dn’).

• order (int) – The order of the scattering coefficient.

Returns:

The value of the specified scattering coefficient.

Return type:

float

init(self: PyMieSim.single.scatterer.BaseScatterer, source: BaseSource, max_order: SupportsInt | SupportsIndex = 0) → None

Initializes the scatterer by computing size parameter, cross section, and scattering coefficients.

Parameters:

• source (BaseSource) – The source of the electromagnetic field, used to determine incident field properties for scatterer initialization.

• max_order (int, optional) – The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter).

property material

Material of the sphere.

property medium

Medium surrounding the sphere.

print_properties(self: PyMieSim.single.scatterer.Sphere, arg0: SupportsInt | SupportsIndex) → None

Prints the properties of the sphere.

property_names = ['size_parameter', 'cross_section', 'g', 'g_with_farfields', 'Qsca', 'Qext', 'Qabs', 'Qback', 'Qratio', 'Qforward', 'Qpr', 'Csca', 'Cext', 'Cabs', 'Cback', 'Cratio', 'Cforward', 'Cpr']

property radius

Radius of the sphere.

property volume

Volume of the sphere.

class InfiniteCylinder

Bases: BaseScatterer

property a1n

Returns \(a_{1n}\) coefficient as defined in ref[5]:

\[a_{1n} = \frac{ m_t J_n(m_t x) J_n^\prime (m x) - m J_n^\prime (m_t x) J_n(m x) }{ m_t J_n(m_t x) H_n^\prime (m x) - m J_n^\prime (m_t x) H_n(m x) }\]

With \(m\) being the refractive index of the medium and \(m_t\) being the refractive index of the scatterer.

Returns:

A list of a1n scattering coefficients for the cylinder. These coefficients describe the scattering behavior of the cylinder in the first mode of the spherical wave expansion.

Return type:

list

property a2n

Returns \(a_{2n}\) coefficient as defined in ref[5]:

\[a_{2n} = \frac{ m_t J_n(m_t x) J_n^\prime (m x) - m J_n^\prime (m_t x) J_n(m x) }{ m_t J_n(m_t x) H_n^\prime (m x) - m J_n^\prime (m_t x) H_n(m x) }\]

With \(m\) being the refractive index of the medium and \(m_t\) being the refractive index of the scatterer.

Returns:

A list of a2n scattering coefficients for the cylinder. These coefficients describe the scattering behavior of the cylinder in the second mode of the spherical wave expansion.

Return type:

list

add_to_scene(self: PyMieSim.single.scatterer.InfiniteCylinder, scene: object, **kwargs) → None

property b1n

Returns \(b_{1n}\) coefficient as defined in ref[5]:

\[b_{1n} = \frac{ m J_n(m_t x) J_n^\prime (m x) - m_t J_n^\prime (m_t x) J_n(m x) }{ m J_n(m_t x) H_n^\prime (m x) - m_t J_n^\prime (m_t x) H_n(m x) }\]

With \(m\) being the refractive index of the medium and \(m_t\) being the refractive index of the scatterer.

Returns:

A list of b1n scattering coefficients for the cylinder. These coefficients describe the scattering behavior of the cylinder in the first mode of the spherical wave expansion.

Return type:

list

property b2n

Returns \(b_{2n}\) coefficient as defined in ref[5]:

\[b_{2n} = \frac{ m J_n(m_t x) J_n^\prime (m x) - m_t J_n^\prime (m_t x) J_n(m x) }{ m J_n(m_t x) H_n^\prime (m x) - m_t J_n^\prime (m_t x) H_n(m x) }\]

With \(m\) being the refractive index of the medium and \(m_t\) being the refractive index of the scatterer.

Returns:

A list of b2n scattering coefficients for the cylinder. These coefficients describe the scattering behavior of the cylinder in the second mode of the spherical wave expansion.

Return type:

list

compute_an_bn(self: PyMieSim.single.scatterer.BaseScatterer, max_order: SupportsInt | SupportsIndex = 0) → None

Computes the coefficients an and bn for the scatterer. :param max_order: The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter). :type max_order: int, optional

compute_cn_dn(self: PyMieSim.single.scatterer.BaseScatterer, max_order: SupportsInt | SupportsIndex = 0) → None

Computes the coefficients cn and dn for the scatterer.

Parameters:

max_order (int, optional) – The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter).

property diameter

Diameter of the cylinder.

get_coefficient(self: PyMieSim.single.scatterer.BaseScatterer, type: str, order: SupportsInt | SupportsIndex) → complex

Returns a specific scattering coefficient for a given type and order.

Parameters:

• type (str) – The type of coefficient (‘an’, ‘bn’, ‘cn’, ‘dn’).

• order (int) – The order of the scattering coefficient.

Returns:

The value of the specified scattering coefficient.

Return type:

float

init(self: PyMieSim.single.scatterer.BaseScatterer, source: BaseSource, max_order: SupportsInt | SupportsIndex = 0) → None

Initializes the scatterer by computing size parameter, cross section, and scattering coefficients.

Parameters:

• source (BaseSource) – The source of the electromagnetic field, used to determine incident field properties for scatterer initialization.

• max_order (int, optional) – The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter).

property material

Material of the cylinder.

property medium

Medium of the cylinder.

print_properties(self: PyMieSim.single.scatterer.InfiniteCylinder, arg0: SupportsInt | SupportsIndex) → None

Prints the properties of the cylinder.

property_names = ['size_parameter', 'cross_section', 'g_with_farfields', 'Qsca', 'Qext', 'Qabs', 'Csca', 'Cext', 'Cabs']

property radius

Radius of the cylinder.

class CoreShell

Bases: BaseScatterer

add_to_scene(*args, **kwargs)

Overloaded function.

1. add_to_scene(self: PyMieSim.single.scatterer.CoreShell, arg0: object, **kwargs) -> None

2. add_to_scene(self: PyMieSim.single.scatterer.CoreShell, scene: object, **kwargs) -> None

property an

Returns the ‘an’ scattering coefficients.

\[a_n = \frac{ \Psi_n (y) \left[ \dot{\Psi}_n (\tilde{m}_{2} y) - A_n (x) \dot{\xi}_n (\tilde{m}_{2} y) \right] - \tilde{m}_{2} \dot{\Psi}_n (y) \left[ \Psi_n (\tilde{m}_{2} y) - A_n (x) \xi_n (\tilde{m}_{2} y) \right] }{ \xi_n (y) \left[ \dot{\Psi}_n (\tilde{m}_{2} y) - A_n (x) \dot{\xi}_n (\tilde{m}_{2} y) \right] - \tilde{m}_{2} \dot{\xi}_n (y) \left[ \Psi_n (\tilde{m}_{2} y) - A_n (x) \xi_n (\tilde{m}_{2} y) \right] }\]

with:

\[\begin{split}A_n = \frac{ \tilde{m}_{2} \Psi_n (\tilde{m}_{2} x) \dot{\Psi}_n (\tilde{m}_{1} x) - \tilde{m}_{1} \dot{\Psi}_n (\tilde{m}_{2} x) \Psi_n (\tilde{m}_{1} x) }{ \tilde{m}_{2} \xi_n (\tilde{m}_{2} x) \dot{\Psi}_n (\tilde{m}_{1} x) - \tilde{m}_{1} \dot{\xi}_n (\tilde{m}_{2} x) \Psi_n (\tilde{m}_{1} x) } \\ B_n = \frac{ \tilde{m}_{2} \psi_n (\tilde{m}_{1} x) \dot{\psi}_n (\tilde{m}_{2} x) - \tilde{m}_{1} \psi_n (\tilde{m}_{2} x) \dot{\psi}_n (\tilde{m}_{1} x) }{ \tilde{m}_{2} \psi_n (\tilde{m}_{1} x) \dot{\xi}_n (\tilde{m}_{2} x) - \tilde{m}_{1} \xi_n (\tilde{m}_{2} x) \dot{\psi}_n (\tilde{m}_{1} x) }\end{split}\]

Returns:

A list of ‘an’ scattering coefficients used in the spherical wave expansion.

Return type:

list

property bn

Returns the ‘bn’ scattering coefficients.

\[b_n = \frac{ \tilde{m}_{2} \Psi_n (y) \left[ \dot{\Psi}_n (\tilde{m}_{2} y) - B_n (x) \dot{\xi}_n (\tilde{m}_{2} y) \right] - \dot{\Psi}_n (y) \left[ \Psi_n (\tilde{m}_{2} y) - B_n (x) \xi_n (\tilde{m}_{2} y) \right] }{ \tilde{m}_{2} \xi_n (y) \left[ \dot{\Psi}_n (\tilde{m}_{2} y) - A_n (x) \dot{\xi}_n (\tilde{m}_{2} y) \right] - \dot{\xi}_n (y) \left[ \Psi_n (\tilde{m}_{2} y) - B_n (x) \xi_n (\tilde{m}_{2} y) \right] }\]

with:

\[\begin{split}A_n = \frac{ \tilde{m}_{2} \Psi_n (\tilde{m}_{2} x) \dot{\Psi}_n (\tilde{m}_{1} x) - \tilde{m}_{1} \dot{\Psi}_n (\tilde{m}_{2} x) \Psi_n (\tilde{m}_{1} x) }{ \tilde{m}_{2} \xi_n (\tilde{m}_{2} x) \dot{\Psi}_n (\tilde{m}_{1} x) - \tilde{m}_{1} \dot{\xi}_n (\tilde{m}_{2} x) \Psi_n (\tilde{m}_{1} x) } \\ B_n = \frac{ \tilde{m}_{2} \psi_n (\tilde{m}_{1} x) \dot{\psi}_n (\tilde{m}_{2} x) - \tilde{m}_{1} \psi_n (\tilde{m}_{2} x) \dot{\psi}_n (\tilde{m}_{1} x) }{ \tilde{m}_{2} \psi_n (\tilde{m}_{1} x) \dot{\xi}_n (\tilde{m}_{2} x) - \tilde{m}_{1} \xi_n (\tilde{m}_{2} x) \dot{\psi}_n (\tilde{m}_{1} x) }\end{split}\]

Returns:

A list of ‘bn’ scattering coefficients used in the spherical wave expansion.

Return type:

list

property cn

Returns the ‘cn’ scattering coefficients.

Returns:

A list of ‘cn’ scattering coefficients used in the spherical wave expansion.

Return type:

list

compute_an_bn(self: PyMieSim.single.scatterer.BaseScatterer, max_order: SupportsInt | SupportsIndex = 0) → None

Computes the coefficients an and bn for the scatterer. :param max_order: The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter). :type max_order: int, optional

compute_cn_dn(self: PyMieSim.single.scatterer.BaseScatterer, max_order: SupportsInt | SupportsIndex = 0) → None

Computes the coefficients cn and dn for the scatterer.

Parameters:

max_order (int, optional) – The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter).

property core_diameter

Diameter of the core shell.

property core_material

Material of the core shell.

property dn

Returns the ‘dn’ scattering coefficients.

Returns:

A list of ‘dn’ scattering coefficients used in the spherical wave expansion.

Return type:

list

get_coefficient(self: PyMieSim.single.scatterer.BaseScatterer, type: str, order: SupportsInt | SupportsIndex) → complex

Returns a specific scattering coefficient for a given type and order.

Parameters:

• type (str) – The type of coefficient (‘an’, ‘bn’, ‘cn’, ‘dn’).

• order (int) – The order of the scattering coefficient.

Returns:

The value of the specified scattering coefficient.

Return type:

float

init(self: PyMieSim.single.scatterer.BaseScatterer, source: BaseSource, max_order: SupportsInt | SupportsIndex = 0) → None

Initializes the scatterer by computing size parameter, cross section, and scattering coefficients.

Parameters:

• source (BaseSource) – The source of the electromagnetic field, used to determine incident field properties for scatterer initialization.

• max_order (int, optional) – The maximum order of the coefficients to compute (default is 0, which means it will be computed based on the size parameter).

print_properties(self: PyMieSim.single.scatterer.CoreShell, arg0: SupportsInt | SupportsIndex) → None

Prints the properties of the core-shell scatterer.

property_names = ['size_parameter', 'cross_section', 'g', 'g_with_farfields', 'Qsca', 'Qext', 'Qabs', 'Qback', 'Qratio', 'Qforward', 'Qpr', 'Csca', 'Cext', 'Cabs', 'Cback', 'Cratio', 'Cforward', 'Cpr']

property radius

Overall radius of the core-shell scatterer.

property shell_material

Material of the shell.

property shell_thickness

Thickness of the shell.

property volume

Volume of the core-shell scatterer.