Detectors

class Photodiode(NA, gamma_offset, phi_offset, mean_coupling=False, coherent=False, cache_NA=<Quantity(0.0, 'dimensionless')>, sampling=<Quantity(200, 'dimensionless')>, polarization_filter=<Quantity(nan, 'degree')>, medium_refractive_index=<Quantity(1.0, 'refractive_index_unit')>)

Bases: BaseDetector

Detector class representing a photodiode with a non-coherent light coupling mechanism. This means it is independent of the phase of the impinging scattered light field.

Parameters:

• NA (Quantity) – Numerical aperture of the imaging system.

• cache_NA (Quantity) – Numerical aperture of the detector cache.

• gamma_offset (Quantity) – Angle [Degree] offset of the detector in the direction perpendicular to polarization.

• phi_offset (Quantity) – Angle [Degree] offset of the detector in the direction parallel to polarization.

• sampling (Quantity) – Sampling rate of the far-field distribution. Default is 200.

• polarization_filter (Optional[Quantity]) – Angle [Degree] of the polarization filter in front of the detector.

• mean_coupling (bool)

• coherent (bool)

• medium_refractive_index (Quantity | None)

NA: Quantity

cache_NA: Quantity | None = <Quantity(0.0, 'dimensionless')>

coherent: bool = False

coupling(scatterer)

Compute the light coupling between the detector and a scatterer.

The coupling quantifies the interaction between the field captured by the detector and the scattered field produced by the scatterer. Mathematically, the coupling is calculated as:

\[|\iint_{\Omega} \Phi_{det} \, \Psi_{scat}^* \, d \Omega|^2\]

Where:

• ( Phi_{det} ): The capturing field of the detector, representing the sensitivity of the detector to the incoming scattered field.

• ( Psi_{scat} ): The scattered field produced by the scatterer.

• ( Omega ): The solid angle over which the integration is performed, typically covering the full ( 4pi ) steradians around the scatterer.

• ( dOmega ): The differential solid angle element.

This integral computes the overlap between the detector’s sensitivity pattern and the scattered field, which is then squared to represent the power coupled into the detector.

Parameters:

scatterer (BaseScatterer) – The scatterer object that interacts with the incident light, producing the scattered field.

Returns:

The power coupling between the detector and the scatterer, expressed in watts (W). This value represents the amount of scattered power that is captured by the detector.

Return type:

Quantity

Notes

• The method internally invokes the appropriate binding method based on the type of scatterer (e.g., Sphere, Cylinder) to calculate the coupling.

• The coupling depends on both the geometry of the detector and the nature of the scattered field, making it essential for evaluating the efficiency of light collection in scattering experiments.

Example

A common use case is to evaluate how much of the scattered light from a nanoparticle is captured by a photodiode or integrating sphere. The result can be used to estimate the efficiency of light collection for scattering measurements.

gamma_offset: Quantity

get_energy_flow(scatterer, distance=<Quantity(1, 'meter')>)

Calculate the total energy flow (or radiated power) from the scatterer based on the Poynting vector.

The energy flow is computed using the following relationship between the scattered energy and the incident intensity:

\[\begin{split}W_a &= \sigma_{sca} \cdot I_{inc} \\[10pt] P &= \int_{A} I \, dA \\[10pt] I &= \frac{c n \epsilon_0}{2} \, |E|^2\end{split}\]

Where:

• ( W_a ): Energy flow (W)

• ( sigma_{sca} ): Scattering cross section (m²)

• ( I_{inc} ): Incident intensity (W/m²)

• ( P ): Radiated power (W)

• ( I ): Energy density (W/m²)

• ( c ): Speed of light in vacuum (m/s)

• ( n ): Refractive index of the surrounding medium

• ( epsilon_0 ): Permittivity of free space (F/m)

• ( E ): Electric field (V/m)

The total power is computed by integrating the intensity over the surface area of the scatterer.

Parameters:

• scatterer (BaseScatterer) – The scatterer object, which contains information about the scattering properties of the particle, such as geometry and material.

• distance (Quantity) – The distance at which the Poynting vector is computed. It should change the computed total power.

Returns:

The total energy flow (radiated power) from the scatterer, expressed in watts.

Return type:

Quantity

Notes

This method computes the energy flow by calculating the Poynting vector (which represents the directional energy flux) and summing it over the surface mesh of the scatterer. The final result is the total radiated power.

get_footprint(scatterer)

Generate the footprint of the scattered light coupling with the detector.

\[\big| \mathscr{F}^{-1} \big\{ \tilde{ \psi } (\xi, \nu),\ \tilde{ \phi}_{l,m}(\xi, \nu) \big\} (\delta_x, \delta_y) \big|^2\]

Where:

\(\Phi_{det}\) is the capturing field of the detector and

\(\Psi_{scat}\) is the scattered field.

Args:

scatterer (BaseScatterer): The scatterer object.

Returns:

Footprint: The scatterer footprint with this detector.

Parameters:

scatterer (BaseScatterer)

Return type:

Footprint

get_poynting_vector(scatterer, distance=<Quantity(1, 'meter')>)

Compute the Poynting vector norm, representing the energy flux density of the electromagnetic field.

The Poynting vector describes the directional energy transfer per unit area for an electromagnetic wave. It is defined as:

\[\vec{S} = \epsilon_0 c^2 \, \vec{E} \times \vec{B}\]

Where:

• ( vec{S} ): Poynting vector (W/m²)

• ( epsilon_0 ): Permittivity of free space (F/m)

• ( c ): Speed of light in vacuum (m/s)

• ( vec{E} ): Electric field vector (V/m)

• ( vec{B} ): Magnetic field vector (T)

The cross product of the electric and magnetic field vectors results in the Poynting vector, which represents the flow of electromagnetic energy in space.

Parameters:

• scatterer (BaseScatterer) – The scatterer object that interacts with the incident electromagnetic wave, affecting the fields and energy flow.

• distance (Quantity) – The distance at which the Poynting vector is computed.

Returns:

The norm of the Poynting vector, which gives the magnitude of the energy flux density in watts per square meter (W/m²).

Return type:

Quantity

Notes

The Poynting vector is computed over a 3D mesh of voxels that cover the entire solid angle of ( 4pi ) steradians. This method calculates the local energy flux at each voxel and returns the norm, which represents the magnitude of energy flow at each point in space around the scatterer.

The Poynting vector is fundamental in understanding how energy is transmitted through space in the form of electromagnetic waves.

Example

This method is used to assess the distribution of energy around a scatterer. The total energy flow can be obtained by integrating the Poynting vector over the surface enclosing the scatterer.

get_structured_scalarfield(sampling=100)

Generate a structured scalar field as a numpy array.

Parameters:

sampling (int) – The sampling rate for the scalar field. Default is 100.

Returns:

A 2D array representing the structured scalar field.

Return type:

numpy.ndarray

mean_coupling: bool = False

medium_refractive_index: Quantity | None = <Quantity(1.0, 'refractive_index_unit')>

mode_number: str = 'NC00'

phi_offset: Quantity

plot(unit_size=(600, 600), background_color='black', show_axis_label=False, colormap=<matplotlib.colors.LinearSegmentedColormap object>, save_name=None)

Plot the real and imaginary parts of the scattered fields in a 3D scene.

This method creates a 3D plot of the scattered fields, displaying the real part of the field as colored points in the scene. It also adds a translucent sphere and a directional cone to represent additional geometrical information.

Parameters:

• unit_size (Tuple[float, float]) – The size of the plot window (width, height). Default is (600, 600).

• background_color (str) – The background color of the plot. Default is ‘black’.

• show_axis_label (bool) – If True, axis labels will be shown. Default is False.

• colormap (str) – The colormap to use for the scalar field. Default is ‘blue_black_red’.

• Returns – None: This method does not return a value. It displays the 3D plot.

• save_name (str)

Return type:

None

polarization_filter: Quantity | None = <Quantity(nan, 'degree')>

rotation: Quantity = <Quantity(0, 'degree')>

sampling: Quantity | None = <Quantity(200, 'dimensionless')>

class CoherentMode(mode_number, NA, gamma_offset, phi_offset, mean_coupling=True, coherent=True, cache_NA=<Quantity(0.0, 'dimensionless')>, sampling=<Quantity(200, 'dimensionless')>, polarization_filter=<Quantity(nan, 'degree')>, rotation=<Quantity(90, 'degree')>, medium_refractive_index=<Quantity(1.0, 'refractive_index_unit')>)

Bases: BaseDetector

Detector class representing a laser Hermite-Gauss mode with a coherent light coupling mechanism. This means it depends on the phase of the impinging scattered light field.

Parameters:

• mode_number (str) – String representing the HG mode to be initialized (e.g., ‘LP01’, ‘HG11’, ‘LG22’).

• NA (float) – Numerical aperture of the imaging system.

• cache_NA (Quantity) – Numerical aperture of the detector cache.

• gamma_offset (float) – Angle [Degree] offset of the detector in the direction perpendicular to polarization.

• phi_offset (float) – Angle [Degree] offset of the detector in the direction parallel to polarization.

• sampling (int) – Sampling rate of the far-field distribution. Default is 200.

• polarization_filter (Union[float, None]) – Angle [Degree] of the polarization filter in front of the detector.

• mean_coupling (bool) – Indicates if the coupling mechanism is point-wise (True) or mean-wise (False). Default is False.

• coherent (bool) – Indicates if the coupling mechanism is coherent. Default is True.

• rotation (float) – Rotation angle of the field along the axis of propagation. Default is 90.

• medium_refractive_index (Quantity | None)

NA: Quantity

cache_NA: Quantity | None = <Quantity(0.0, 'dimensionless')>

coherent: bool = True

coupling(scatterer)

Compute the light coupling between the detector and a scatterer.

The coupling quantifies the interaction between the field captured by the detector and the scattered field produced by the scatterer. Mathematically, the coupling is calculated as:

\[|\iint_{\Omega} \Phi_{det} \, \Psi_{scat}^* \, d \Omega|^2\]

Where:

• ( Phi_{det} ): The capturing field of the detector, representing the sensitivity of the detector to the incoming scattered field.

• ( Psi_{scat} ): The scattered field produced by the scatterer.

• ( Omega ): The solid angle over which the integration is performed, typically covering the full ( 4pi ) steradians around the scatterer.

• ( dOmega ): The differential solid angle element.

This integral computes the overlap between the detector’s sensitivity pattern and the scattered field, which is then squared to represent the power coupled into the detector.

Parameters:

scatterer (BaseScatterer) – The scatterer object that interacts with the incident light, producing the scattered field.

Returns:

The power coupling between the detector and the scatterer, expressed in watts (W). This value represents the amount of scattered power that is captured by the detector.

Return type:

Quantity

Notes

• The method internally invokes the appropriate binding method based on the type of scatterer (e.g., Sphere, Cylinder) to calculate the coupling.

• The coupling depends on both the geometry of the detector and the nature of the scattered field, making it essential for evaluating the efficiency of light collection in scattering experiments.

Example

A common use case is to evaluate how much of the scattered light from a nanoparticle is captured by a photodiode or integrating sphere. The result can be used to estimate the efficiency of light collection for scattering measurements.

gamma_offset: Quantity

get_energy_flow(scatterer, distance=<Quantity(1, 'meter')>)

Calculate the total energy flow (or radiated power) from the scatterer based on the Poynting vector.

The energy flow is computed using the following relationship between the scattered energy and the incident intensity:

\[\begin{split}W_a &= \sigma_{sca} \cdot I_{inc} \\[10pt] P &= \int_{A} I \, dA \\[10pt] I &= \frac{c n \epsilon_0}{2} \, |E|^2\end{split}\]

Where:

• ( W_a ): Energy flow (W)

• ( sigma_{sca} ): Scattering cross section (m²)

• ( I_{inc} ): Incident intensity (W/m²)

• ( P ): Radiated power (W)

• ( I ): Energy density (W/m²)

• ( c ): Speed of light in vacuum (m/s)

• ( n ): Refractive index of the surrounding medium

• ( epsilon_0 ): Permittivity of free space (F/m)

• ( E ): Electric field (V/m)

The total power is computed by integrating the intensity over the surface area of the scatterer.

Parameters:

• scatterer (BaseScatterer) – The scatterer object, which contains information about the scattering properties of the particle, such as geometry and material.

• distance (Quantity) – The distance at which the Poynting vector is computed. It should change the computed total power.

Returns:

The total energy flow (radiated power) from the scatterer, expressed in watts.

Return type:

Quantity

Notes

This method computes the energy flow by calculating the Poynting vector (which represents the directional energy flux) and summing it over the surface mesh of the scatterer. The final result is the total radiated power.

get_footprint(scatterer)

Generate the footprint of the scattered light coupling with the detector.

\[\big| \mathscr{F}^{-1} \big\{ \tilde{ \psi } (\xi, \nu),\ \tilde{ \phi}_{l,m}(\xi, \nu) \big\} (\delta_x, \delta_y) \big|^2\]

Where:

\(\Phi_{det}\) is the capturing field of the detector and

\(\Psi_{scat}\) is the scattered field.

Args:

scatterer (BaseScatterer): The scatterer object.

Returns:

Footprint: The scatterer footprint with this detector.

Parameters:

scatterer (BaseScatterer)

Return type:

Footprint

get_poynting_vector(scatterer, distance=<Quantity(1, 'meter')>)

Compute the Poynting vector norm, representing the energy flux density of the electromagnetic field.

The Poynting vector describes the directional energy transfer per unit area for an electromagnetic wave. It is defined as:

\[\vec{S} = \epsilon_0 c^2 \, \vec{E} \times \vec{B}\]

Where:

• ( vec{S} ): Poynting vector (W/m²)

• ( epsilon_0 ): Permittivity of free space (F/m)

• ( c ): Speed of light in vacuum (m/s)

• ( vec{E} ): Electric field vector (V/m)

• ( vec{B} ): Magnetic field vector (T)

The cross product of the electric and magnetic field vectors results in the Poynting vector, which represents the flow of electromagnetic energy in space.

Parameters:

• scatterer (BaseScatterer) – The scatterer object that interacts with the incident electromagnetic wave, affecting the fields and energy flow.

• distance (Quantity) – The distance at which the Poynting vector is computed.

Returns:

The norm of the Poynting vector, which gives the magnitude of the energy flux density in watts per square meter (W/m²).

Return type:

Quantity

Notes

The Poynting vector is computed over a 3D mesh of voxels that cover the entire solid angle of ( 4pi ) steradians. This method calculates the local energy flux at each voxel and returns the norm, which represents the magnitude of energy flow at each point in space around the scatterer.

The Poynting vector is fundamental in understanding how energy is transmitted through space in the form of electromagnetic waves.

Example

This method is used to assess the distribution of energy around a scatterer. The total energy flow can be obtained by integrating the Poynting vector over the surface enclosing the scatterer.

get_structured_scalarfield(sampling=100)

Generate a structured scalar field as a numpy array.

Parameters:

sampling (int) – The sampling rate for the scalar field. Default is 100.

Returns:

A 2D array representing the structured scalar field.

Return type:

numpy.ndarray

mean_coupling: bool = True

medium_refractive_index: Quantity | None = <Quantity(1.0, 'refractive_index_unit')>

mode_number: str

phi_offset: Quantity

plot(unit_size=(600, 600), background_color='black', show_axis_label=False, colormap=<matplotlib.colors.LinearSegmentedColormap object>, save_name=None)

Plot the real and imaginary parts of the scattered fields in a 3D scene.

This method creates a 3D plot of the scattered fields, displaying the real part of the field as colored points in the scene. It also adds a translucent sphere and a directional cone to represent additional geometrical information.

Parameters:

• unit_size (Tuple[float, float]) – The size of the plot window (width, height). Default is (600, 600).

• background_color (str) – The background color of the plot. Default is ‘black’.

• show_axis_label (bool) – If True, axis labels will be shown. Default is False.

• colormap (str) – The colormap to use for the scalar field. Default is ‘blue_black_red’.

• Returns – None: This method does not return a value. It displays the 3D plot.

• save_name (str)

Return type:

None

polarization_filter: Quantity | None = <Quantity(nan, 'degree')>

rotation: Quantity | None = <Quantity(90, 'degree')>

sampling: Quantity | None = <Quantity(200, 'dimensionless')>