tidy3d.FieldProjectionAngleMonitor

class FieldProjectionAngleMonitor

Bases: AbstractFieldProjectionMonitor

Monitor that samples electromagnetic near fields in the frequency domain and projects them at given observation angles.

Parameters:

• center (Attribute: center) –

  Type	Tuple[float, float, float]
  Default	= (0.0, 0.0, 0.0)
  Units	um
  Description	Center of object in x, y, and z.

• size (Attribute: size) –

  Type	Tuple[NonNegativeFloat, NonNegativeFloat, NonNegativeFloat]
  Default
  Units	um
  Description	Size in x, y, and z directions.

• name (Attribute: name) –

  Type	ConstrainedStrValue
  Default
  Description	Unique name for monitor.

• interval_space (Attribute: interval_space) –

  Type	Tuple[PositiveInt, PositiveInt, PositiveInt]
  Default	= (1, 1, 1)
  Description	Number of grid step intervals at which near fields are recorded for projection to the far field, along each direction. If equal to 1, there will be no downsampling. If greater than 1, the step will be applied, but the first and last point of the monitor grid are always included. Using values greater than 1 can help speed up server-side far field projections with minimal accuracy loss, especially in cases where it is necessary for the grid resolution to be high for the FDTD simulation, but such a high resolution is unnecessary for the purpose of projecting the recorded near fields to the far field.

• colocate (Attribute: colocate) –

  Type	Literal[True]
  Default	= True
  Description	Defines whether fields are colocated to grid cell boundaries (i.e. to the primal grid) on-the-fly during a solver run. Can be toggled for field recording monitors and is hard-coded for other monitors depending on their specific function.

• freqs (Attribute: freqs) –

  Type	Union[Tuple[float, …], ArrayLike[dtype=float, ndim=1]]
  Default
  Units	Hz
  Description	Array or list of frequencies stored by the field monitor.

• apodization (Attribute: apodization) –

  Type	ApodizationSpec
  Default	= ApodizationSpec(startNone, endNone, widthNone, type’ApodizationSpec’)
  Description	Sets parameters of (optional) apodization. Apodization applies a windowing function to the Fourier transform of the time-domain fields into frequency-domain ones, and can be used to truncate the beginning and/or end of the time signal, for example to eliminate the source pulse when studying the eigenmodes of a system. Note: apodization affects the normalization of the frequency-domain fields.

• normal_dir (Attribute: normal_dir) –

  Type	Optional[Literal[‘+’, ‘-‘]]
  Default	= None
  Description	Direction of the surface monitor’s normal vector w.r.t. the positive x, y or z unit vectors. Must be one of '+' or '-'. Applies to surface monitors only, and defaults to '+' if not provided.

• exclude_surfaces (Attribute: exclude_surfaces) –

  Type	Optional[Tuple[Literal[‘x-’, ‘x+’, ‘y-’, ‘y+’, ‘z-’, ‘z+’], …]]
  Default	= None
  Description	Surfaces to exclude in the integration, if a volume monitor.

• custom_origin (Attribute: custom_origin) –

  Type	Optional[Tuple[float, float, float]]
  Default	= None
  Units	um
  Description	Local origin used for defining observation points. If None, uses the monitor’s center.

• far_field_approx (Attribute: far_field_approx) –

  Type	bool
  Default	= True
  Description	Whether to enable the far field approximation when projecting fields. If True, terms that decay as O(1/r^2) are ignored, as are the radial components of fields. Typically, this should be set to True only when the projection distance is much larger than the size of the device being modeled, and the projected points are in the far field of the device.

• window_size (Attribute: window_size) –

  Type	Tuple[NonNegativeFloat, NonNegativeFloat]
  Default	= (0, 0)
  Description	Size of the transition region of the windowing function used to ensure that the recorded near fields decay to zero near the edges of the monitor. The two components refer to the two tangential directions associated with each surface. For surfaces with the normal along x, the two components are (y, z). For surfaces with the normal along y, the two components are (x, z). For surfaces with the normal along z, the two components are (x, y). Each value must be between 0 and 1, inclusive, and denotes the size of the transition region over which fields are scaled to less than a thousandth of the original amplitude, relative to half the size of the monitor in that direction. A value of 0 turns windowing off in that direction, while a value of 1 indicates that the window will be applied to the entire monitor in that direction. This field is applicable for surface monitors only, and otherwise must remain (0, 0).

• medium (Attribute: medium) –

  Type	Union[Medium, AnisotropicMedium, PECMedium, PoleResidue, Sellmeier, Lorentz, Debye, Drude, FullyAnisotropicMedium, CustomMedium, CustomPoleResidue, CustomSellmeier, CustomLorentz, CustomDebye, CustomDrude, CustomAnisotropicMedium, PerturbationMedium, PerturbationPoleResidue, Medium2D]
  Default	= None
  Description	Medium through which to project fields. Generally, the fields should be projected through the same medium as the one in which this monitor is placed, and this is the default behavior when medium=None. A custom medium can be useful in some situations for advanced users, but we recommend trying to avoid using a non-default medium.

• proj_distance (Attribute: proj_distance) –

  Type	float
  Default	= 1000000.0
  Units	um
  Description	Radial distance of the projection points from local_origin.

• theta (Attribute: theta) –

  Type	Union[Tuple[float, …], ArrayLike[dtype=float, ndim=1]]
  Default
  Units	rad
  Description	Polar angles with respect to the global z axis, relative to the location of local_origin, at which to project fields.

• phi (Attribute: phi) –

  Type	Union[Tuple[float, …], ArrayLike[dtype=float, ndim=1]]
  Default
  Units	rad
  Description	Azimuth angles with respect to the global z axis, relative to the location of local_origin, at which to project fields.

Notes

Parameters Caveats

The center and size parameters define where the monitor will be placed in order to record near fields, typically very close to the structure of interest. The near fields are then projected to far-field locations defined by phi, theta, and proj_distance, relative to the custom_origin.

Usage Caveats

The field projections make use of the analytical homogeneous medium Green’s function, which assumes that the fields are propagating in a homogeneous medium. Therefore, one should use PML / Absorber as boundary conditions in the part of the domain where fields are projected.

Server-side field projections will add to the monetary cost of the simulation. However, typically the far field projections have a very small computation cost compared to the FDTD simulation itself, so the increase in monetary cost should be negligibly small in most cases. For applications where the monitor is an open surface rather than a box that encloses the device, it is advisable to pick the size of the monitor such that the recorded near fields decay to negligible values near the edges of the monitor.

By default, if no proj_distance was provided, the fields are projected to a distance of 1m.

Server-side field projection Application

Provide the FieldProjectionAngleMonitor monitor as an input to the Simulation object as one of its monitors. Now, we no longer need to provide a separate near-field FieldMonitor - the near fields will automatically be recorded based on the size and location of the FieldProjectionAngleMonitor. Note also that in some cases, the server-side computations may be slightly more accurate than client-side ones, because on the server, the near fields are not downsampled at all.

We can re-project the already-computed far fields to a different distance away from the structure - we neither need to run another simulation nor re-run the FieldProjector.

Far-Field Approximation Selection

If the distance between the near and far field locations is much larger than the size of the device, one can typically set far_field_approx to True, which will make use of the far-field approximation to speed up calculations. If the projection distance is comparable to the size of the device, we recommend setting far_field_approx to False.

When selected, it is assumed that:

• The fields are measured at a distance much greater than the size of our simulation in the transverse direction.

• The geometric approximations imply that any quantity whose magnitude drops off as \(\frac{1}{r^2}\) or faster is ignored.

The advantages of these approximations are:

• The projections are computed relatively fast.

• The projections are cast in a simple mathematical form. which allows re-projecting the fields to different distance without the need to re-run a simulation or to re-run the FieldProjector.

In cases where we may want to project to intermediate distances where the far field approximation is no longer valid, simply include the class definition parameter far_field_approx to False in the FieldProjectionAngleMonitor instantiation. The resulting computations will be a bit slower, but the results will be significantly more accurate.

Example

>>> monitor = FieldProjectionAngleMonitor(
...     center=(1,2,3),
...     size=(2,2,2),
...     freqs=[250e12, 300e12],
...     name='n2f_monitor',
...     custom_origin=(1,2,3),
...     phi=[0, np.pi/2],
...     theta=np.linspace(-np.pi/2, np.pi/2, 100),
...     far_field_approx=True,
...     )

See also

Notebooks:

• Performing near field to far field projections

• Field projection for a zone plate: Realistic case study further demonstrating the accuracy of the field projections.

• Metalens in the visible frequency range: Realistic case study further demonstrating the accuracy of the field projections.

• Multilevel blazed diffraction grating: For far field projections in the context of perdiodic boundary conditions.

Attributes

Methods

storage_size(num_cells, tmesh)

Size of monitor storage given the number of points after discretization.

proj_distance

theta

phi

storage_size(num_cells, tmesh)

Size of monitor storage given the number of points after discretization.

__hash__()

Hash method.