tidy3d.FieldProjectionAngleMonitor#
- class FieldProjectionAngleMonitor[source]#
Bases:
AbstractFieldProjectionMonitor
Monitor
that samples electromagnetic near fields in the frequency domain and projects them at given observation angles.- Parameters:
center (Tuple[float, float, float] = (0.0, 0.0, 0.0)) – [units = um]. Center of object in x, y, and z.
size (Tuple[NonNegativeFloat, NonNegativeFloat, NonNegativeFloat]) – [units = um]. Size in x, y, and z directions.
name (ConstrainedStrValue) – Unique name for monitor.
interval_space (Tuple[PositiveInt, PositiveInt, PositiveInt] = (1, 1, 1)) – 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 (Literal[True] = True) – 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 (Union[Tuple[float, ...], ArrayLike[dtype=float, ndim=1]]) – [units = Hz]. Array or list of frequencies stored by the field monitor.
apodization (ApodizationSpec = ApodizationSpec(start=None, end=None, width=None, type='ApodizationSpec')) – 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 (Optional[Literal['+', '-']] = None) – 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 (Optional[Tuple[Literal['x-', 'x+', 'y-', 'y+', 'z-', 'z+'], ...]] = None) – Surfaces to exclude in the integration, if a volume monitor.
custom_origin (Optional[Tuple[float, float, float]] = None) – [units = um]. Local origin used for defining observation points. If
None
, uses the monitor’s center.far_field_approx (bool = True) – 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 toTrue
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 (Tuple[NonNegativeFloat, NonNegativeFloat] = (0, 0)) – 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 alongy
, the two components are (x
,z
). For surfaces with the normal alongz
, 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 (Union[Medium, AnisotropicMedium, PECMedium, PoleResidue, Sellmeier, Lorentz, Debye, Drude, FullyAnisotropicMedium, CustomMedium, CustomPoleResidue, CustomSellmeier, CustomLorentz, CustomDebye, CustomDrude, CustomAnisotropicMedium, PerturbationMedium, PerturbationPoleResidue, Medium2D] = None) – 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 custommedium
can be useful in some situations for advanced users, but we recommend trying to avoid using a non-defaultmedium
.proj_distance (float = 1000000.0) – [units = um]. Radial distance of the projection points from
local_origin
.theta (Union[Tuple[float, ...], ArrayLike[dtype=float, ndim=1]]) – [units = rad]. Polar angles with respect to the global z axis, relative to the location of
local_origin
, at which to project fields.phi (Union[Tuple[float, ...], ArrayLike[dtype=float, ndim=1]]) – [units = rad]. 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
andsize
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 byphi
,theta
, andproj_distance
, relative to thecustom_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 theSimulation
object as one of its monitors. Now, we no longer need to provide a separate near-fieldFieldMonitor
- the near fields will automatically be recorded based on the size and location of theFieldProjectionAngleMonitor
. 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
toTrue
, 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 settingfar_field_approx
toFalse
.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
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
toFalse
in theFieldProjectionAngleMonitor
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:
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)[source]#
Size of monitor storage given the number of points after discretization.
- __hash__()#
Hash method.