Configuring for polarized radiation

This topic describes how SKIRT can be configured to track the polarization state of radiation during its interaction with certain media. The discussion is organized in the following sections:

• Describing the polarization state
• Configuring SKIRT with polarization
• Scattering in spherical media (dust grains, electrons, or atoms)
• Emission from aligned spheroidal dust grains
• Polarized primary emission

Describing the polarization state

The polarization state of electromagnetic radiation is commonly described by the Stokes vector, $\mathit{S}$,

$$\mathit{S}=\left(\begin{array}{c}I\\ Q\\ U\\ V\end{array}\right),$$

where $I$ represents the intensity of the radiation, $Q$ and $U$ describe linear polarization, and $V$ describes circular polarization. The degree of linear polarization, $P_{\text{L}}$, can be written as a function of the Stokes parameters,

$$P_{\text{L}}=\frac{\sqrt{Q^2+U^2}}{I}.$$

The (linear) polarization angle, $\gamma$, can be written as

$$\gamma =\frac{1}{2}{\arctan }_2\left(\frac{U}{Q}\right),$$

where ${\arctan }_2$ denotes the inverse tangent function that preserves the quadrant.

The polarization angle $\gamma$ describes the angle between the direction of linear polarization and a given reference direction in the plane orthogonal to the propagation direction. When considering a given observer frame, the reference direction is chosen to be the vertical axis, and the polarization angle is measured counter-clockwise when looking toward the source.

SKIRT defines the Stokes vector as described above, following the recommendations of the International Astronomical Union. Historically, however, authors have used various conventions for the signs of the Stokes parameters $U$ and $V$. For example, the polarization angle $\gamma$ is sometimes measured while looking toward the observer rather than toward the source, flipping the sign of both $U$ and $V$. Reversing the definition of circular polarization handedness also flips the sign of $V$. Assuming that the adopted conventions are properly documented, translating the values of the Stokes parameters from one convention into another can be accomplished by flipping the signs appropriately.

Configuring SKIRT with polarization

Enabling support for polarized radiation in a SKIRT simulation is straightforward. Most importantly, all material mixes associated with the medium components in the simulation must support polarization and have polarization enabled. Once this condition is satisfied, the polarization state will be tracked for all photon packets. Next, one should configure at least one of the instruments to record and output the accumulated polarization state of the detected photon packets (i.e. the four components of the Stokes vector). If not, the polarization state would be tracked but not "observed" by any of the instruments. Finally, some sources can be configured to emit polarized radiation.

The material mixes supporting polarization are discussed below in Scattering in spherical media (dust grains, electrons, or atoms) and Emission from aligned spheroidal dust grains. Note that SKIRT does not allow configurations where media with and without polarization would be mixed.

To cause an instrument to record and output the Stokes vector components, set its recordPolarization option to "true"; see the Instrument and FluxRecorder classes.

Polarized emission is further discussed below in Emission from aligned spheroidal dust grains and Polarized primary emission.

Scattering in spherical media (dust grains, electrons, or atoms)

SKIRT supports the effects on the radiation polarization state by scattering on spherical dust grains, on electrons, and on Lyman-alpha atoms.

The MeanTrustBenchmarkDustMix class implements representative grain polarization properties for a mixture of bare graphite, silicate and PAH dust grains. In other words, the optical properties are integrated over the size distribution and summed over the material types. This is perfectly fine for a treatment of scattering in the optical range. Make sure to set the scatteringType property to "SphericalPolarization".

When dust emission is included in the simulation, the calculation requires specific information for multiple grain size bins. This is especially true for small grains that are not in local thermal equilibrium. For this purpose, SKIRT includes the PolarizedGraphiteGrainComposition and PolarizedSilicateGrainComposition classes that provide optical polarization properties for graphite and silicate grains as a function of grain size. These classes can be configured through the ConfigurableDustMix class as in the following example:

<ConfigurableDustMix scatteringType="SphericalPolarization">
    <populations type="GrainPopulation">
        <GrainPopulation numSizes="10" normalizationType="FactorOnSizeDistribution" dustMassPerHydrogenAtom="0 Msun"
                         dustMassPerHydrogenMass="0" factorOnSizeDistribution="7.762471166e-31">
            <composition type="GrainComposition">
                <PolarizedSilicateGrainComposition/>
            </composition>
            <sizeDistribution type="GrainSizeDistribution">
                <PowerLawGrainSizeDistribution minSize="0.005 micron" maxSize="0.25 micron" exponent="3.5"/>
            </sizeDistribution>
        </GrainPopulation>
        <GrainPopulation numSizes="10" normalizationType="FactorOnSizeDistribution" dustMassPerHydrogenAtom="0 Msun"
                         dustMassPerHydrogenMass="0" factorOnSizeDistribution="7.413102413e-31">
            <composition type="GrainComposition">
                <PolarizedGraphiteGrainComposition/>
            </composition>
            <sizeDistribution type="GrainSizeDistribution">
                <PowerLawGrainSizeDistribution minSize="0.005 micron" maxSize="0.25 micron" exponent="3.5"/>
            </sizeDistribution>
        </GrainPopulation>
    </populations>
</ConfigurableDustMix>

The ElectronMix class implements wavelength-independent Thomson scattering on electrons with optional support for polarization. Make sure to set the includePolarization property to "true".

The LyaNeutralHydrogenGasMix class implements resonant Lyman-alpha line scattering with optional support for polarization. Make sure to set the includePolarization property to "true".

Emission from aligned spheroidal dust grains

The SpheroidalSilicateGrainComposition and SpheroidalGraphiteGrainComposition classes represent the optical and calorimetric properties of spheroidal silicate and graphite dust grains with support for polarized thermal emission by (partially) aligned spheroidal grains. There is currently no support for scattering and absorption interactions with aligned spheroidal grains; for these interactions the implementation behaves as if the grains are spherical.

These classes can be configured through the ConfigurableDustMix class in a way similar to the example for the polarized grain compositions in the previous section Scattering in spherical media (dust grains, electrons, or atoms). This time though, set the scatteringType property of the ConfigurableDustMix to "SpheroidalPolarization".

When including spheroidal grains, it is mandatory to also include a magnetic field in the simulation to determine the degree and direction of grain alignment at every location in the spatial domain. For a GeometricMedium instance, this can be accomplished by setting the magneticFieldStrength property to a nonzero value and providing a vector field for the magneticFieldDistribution property. For an ImportedMedium instance, set the importMagneticField property to "true" and provide the three magnetic field vector components on each row in the import file.

For more details, refer to the documentation of the SpheroidalSilicateGrainComposition and SpheroidalGraphiteGrainComposition classes.

Polarized primary emission

Secondary emission from aligned spheroidal dust grains is discussed in the previous section Emission from aligned spheroidal dust grains.

On the primary emission side, the PointSource class offers the option to emit polarized radiation by configuring the polarizationProfile property with a polarization profile other than NoPolarizationProfile. At the time of writing, just a single polarization profile is provided by the SineSquarePolarizationProfile class, intended primarily for testing. It should be straightforward to add other polarization profiles as needed for specific applications.