Dipole Emission Study Plugin

The dipole emission plugin evaluates radiative emission from classical electric dipoles embedded in a passive optical structure. It reports angular radiation intensity per squared dipole moment for x-, y-, and z-oriented dipoles into a selected collection half-space. By default, the result is summed over all sampled dipole positions using position_weights. position_weights may represent emitter-density quadrature weights, and may provide one weight per position or one weight per position and dipole axis.

The main result is radiation_intensity with dimensions ("dipole_axis", "polarization", "angle", "f"):

• radiation_intensity is stored and includes the study source_time spectrum.

• radiation_intensity_transfer(bulk_refractive_index) is a derived method that normalizes by the total power the same dipoles would emit in a uniform medium at the given refractive index, yielding the cavity transfer in 1/sr. Integrating it over the study’s collection solid angle gives the half-space radiative contribution; for a bulk emitter a single study integrates to 1/2 (the full radiative Purcell factor requires both collection half-spaces).

Use store_position_indexes to additionally retain radiation intensity at selected individual positions. The stored optional array has dimensions ("index", "dipole_axis", "polarization", "angle", "f"), with a matching derived transfer method.

Both outputs are normalized per squared electric dipole moment, with dipole moment expressed in C*um. The emitted field is linear in the dipole moment d, so the radiated power scales as |d|**2. Multiplying radiation_intensity by the physical |d|**2 gives the corresponding angular power density in W/sr. The transfer methods are normalized ratios: the source_time spectrum and the dipole-moment scaling cancel between the radiated and bulk emitted powers. If the dipole strength varies with position or orientation, include those relative |d|**2 factors in position_weights.

Defining a Study

Use base_sim for the source-free optical environment and analysis_region for the region containing the emitters and the part of the structure whose scattering response contributes to the collected radiation. The normal_axis and direction of the analysis region select the collection side. For example, normal_axis=2 and direction="+" describes emission collected toward +z. base_sim must be three-dimensional; the radiation intensity is a per-solid-angle quantity, so 2D simulations (a zero-size dimension) are rejected.

Far-field directions are supplied as a SphericalAngleDataArray, with theta and phi in radians. theta is measured away from the selected collection normal and must satisfy abs(theta) < pi/2. The p polarization lies in the plane formed by the observation direction and collection normal; s is orthogonal to that plane. On the result, the per-direction angles are read from the DipoleEmissionStudyData.theta and .phi properties; the data arrays carry only an integer angle index.

import tidy3d as td
from tidy3d.plugins import dipole_emission

# Define base_sim as a source-free td.Simulation containing the optical structure.

positions = td.PointDataArray(
    [[0.0, 0.0, 0.0], [0.1, 0.0, 0.0]]
)

angles = td.SphericalAngleDataArray(
    [[0.0, 0.0], [0.3, 0.5]]
)

region = dipole_emission.EmissionAnalysisRegion(
    center=(0, 0, 0),
    size=(2, 2, 2),
    normal_axis=2,
    direction="+",
    dl=0.02,
)

study = dipole_emission.DipoleEmissionStudy(
    base_sim=base_sim,
    analysis_region=region,
    positions=positions,
    position_weights=[1.0, 1.0],
    store_position_indexes=(0,),
    source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),
    freqs=[freq0],
    angles=angles,
    polarizations=("p", "s"),
)

data = study.run(folder_name="dipole_emission")

Notes

Ordinary monitors in base_sim are copied into every angle and polarization task as diagnostics. Their data is available only from the returned batch data, for example with study.run(..., return_batch_data=True).

The study targets radiative emission into a continuum of far-field directions. Non-radiative channels, ohmic absorption, surface-plasmon coupling, and trapped guided-mode power are not included in the returned radiation intensity.

The v1 workflow is intended for open finite-domain collection geometries. Base simulations whose boundary conditions are incompatible with the generated reciprocal probes are rejected during ordinary Tidy3D validation.

API Reference

plugins.dipole_emission.EmissionAnalysisRegion	Region over which dipole emission is evaluated.
plugins.dipole_emission.DipoleEmissionStudy	Dipole-emission sweep definition.
plugins.dipole_emission.DipoleEmissionStudyData	Reduced result from a DipoleEmissionStudy.
plugins.dipole_emission.DipoleEmissionStudyDataArray	Angular radiation intensity per dipole moment squared.
plugins.dipole_emission.DipoleEmissionStudyPositionDataArray	Position-resolved angular radiation intensity per dipole moment squared.
SphericalAngleDataArray	Spherical angles as indexed (theta, phi) pairs.