Astrobite’s guide to polarimetry

By Briley Lewis

A brief introduction to polarized light

Light is an electromagnetic wave – and its electric field is not always oriented in the same direction. The orientation of the light’s electric field defines its “state of polarization”. In this guide, we’ll talk about what polarization is, how it’s generated by the cosmos, and how we can observe it.

We categorize polarization into three main categories: unpolarized light, linearly polarized light, and elliptically polarized light. Unpolarized light (aka natural light) is better described as randomly polarized light; That is, many light sources are a collection of emitters, where the polarization of the emitted light changes very frequently and randomly. This is an extreme, and Light often is partially kind of polarized. Linearly polarized light has a constant electric field orientation (although the magnitude of the wave can still vary). Elliptically polarized light has an electric field whose vector rotates and traces an ellipse. An example of this is circularly polarized light, in which both the x and y directions are the same size. Some of these cases are shown in the figure below.

With the help of matrices we can describe the polarization mathematically. Stokes vectors (aka Stokes parameters) are a useful way to do this. There are four parameters: I, Q, uand v. I is the total intensity, Q describes a linear polarization (horizontal or vertical, depending on the sign) and u describes polarization on a second set of orthogonal axes (+/-45 degrees), and v describes elliptical polarization (right-handed if >0, left-handed<0). They are defined as follows:

• I = S₁ = 2I₀ (where I₀ is the incident light)
• Q=S₂ = 2I₁ – 2I₀ (where I₁ is the light passing through a horizontal-axis linear polarizer)
• U=S₃ = 2I₂ – 2I₀ (where I₂ is the light passing through a linear polarizer with an axis at 45^O)
• V=S₄ = 2I₃ – 2I₀ (where I₃ is the light through a circular polarizer)

For fully polarized light I² = Q² + and² + v². For a partially polarized system, the degree of polarization is given by P = (Q² + and² + v²)^½ / I. See Hecht’s Table 8.5 for an illustrative example of Stokes vectors for different states of polarization. Similarly, the operations of different polarizers on Stokes vectors can be described by Mueller matrices.

What in the universe creates polarized light?

Polarization can be affected by dichroism, reflection, scattering, or birefringence (more on dichroism and birefringence in the next section!), as well as other electromagnetic effects. Some radiation processes, such as synchrotron radiation, also naturally produce polarized light.

Light can be polarized by scattering due to interactions with electrons. For unpolarized incident light, light scattered along the axis of incidence remains unchanged, and light scattered at orthogonal (90 degree) angles becomes linearly polarized. Scattering can be more complicated depending on the size of the particles relative to the wavelength of the light: Rayleigh scattering describes what happens when the particles are much smaller than the wavelength, and Mie scattering describes scattering more generally.

Light can also be polarized by reflection off a dielectric medium, reflecting only one component of the incident polarization and refracting the other. Brewster’s law describes the angle at which the reflected beam becomes fully polarized and deviations from this angle become partially polarized.

Some examples of situations that produce polarized light in astronomy are:

How do you measure polarization?

To find out how much of the incoming light is polarized, we need to use some kind of polarizer — a filter that breaks light down into its component parts, or lets only a specific polarization of light through. As Pike says in his optics Textbook for polarizers to work, “there must be some kind of asymmetry involved in the process”.

Some polarizers use dichroism, in which only one polarization state is selectively absorbed and the other orthogonal polarization state easily passes through. Some crystals are inherently dichroic, as are Polaroid filters. Another commonly used effect is birefringence, which means that a substance has different refractive indices due to the arrangement of the atoms it contains. Certain birefringent crystals can split light into orthogonal states of polarization. A useful example in astronomy is the Wollaston prism, which serves as a polarizing beam splitter in many instruments.

Another important type of optic is known as a waveplate, something that changes the polarization of the light in your incoming beam. A full-wave plate produces a phase difference of 360 degrees (2π radians), while a half-wave plate induces a phase difference of 180 degrees (π radians), and a quarter-wave plate shifts the phase by 90 degrees (π/2 radians). There are also polarizers that induce circular polarization, such as B. the combination of a linear polarizer and a waveplate.

So what makes an astronomical polarimeter? At least in the optical/infrared there is usually some sort of beam splitter like a Wollaston prism that splits the light into two orthogonal polarizations, plus a half-wave plate that allows the observer to modulate the polarization to calibrate instrumental effects. (As an example, you can read in detail about the Gemini Planet Imager polarimeter here!)

Besides optical and IR, there are other ways to measure polarimetry. Radio telescopes can detect polarization because they essentially record the state of the electric field, and other types of detectors for high-energy light such as X-rays (e.g. gas pixel detectors) have also been developed to measure polarization.

Some recent observatories with polarimetry capabilities and their cool science results (plus relevant astrobites!)

IXPE [The Imaging X-Ray Polarimetry Explorer] — NASA’s recently launched IXPE mission will look for polarization from some extreme sources like supernovae, AGN and pulsars! Stay tuned for the first results, which will appear very soon.

VLT/SPHERE — SPHERE is focused on exoplanet characterization and discovery, including the wildly cool discovery of PDS 70b, a very young forming planet still embedded in its disk.

Gemini Planet Imager — As briefly mentioned before, the Gemini Planet Imager not only imaged planets, but also debris disks! And it did so in polarized light, using differential polarimetric imaging, a technique that separates starlight from disk light. You’ve got a whole survey sample of polarized debris disks, plus some decent in-depth studies of individual disks!

Subaru/SCExAO/CHARIS — The CHARIS instrument on the Subaru telescope can perform spectropolarimetry [looking at polarization in multiple wavelengths] in the infrared, including differential polarimetric imaging (CHARIS-PDI), useful for finding exoplanets and disks. You’ve got some cool shots of jets from young T Tauri stars and debris disks!

ALMA — Polarimetry works a little differently with radio telescope arrays like ALMA, but they make it possible. ALMA was key to understanding the magnetic fields of objects throughout the universe, such as B. the interesting and extreme supernova AT2018cow!

Event Horizon Telescope — Similar to ALMA in that it is somewhat different from a “normal” single telescope, the EHT array managed to measure one of the most extreme examples of polarization to date – the polarized light from the dusty region around M87’s supermassive black hole!

HARPS — HARPS, ESO’s famous spectrograph, now has polarimetric capabilities! It is capable of performing spectropolarimetry, which can help in understanding the magnetic fields of stars.

SOFIA HAWC+ — The SOFIA airborne observatory has a unique far-infrared imaging polarimeter called HAWC+, which has been used to study star-forming regions and emissions in a dusty torus around an active galactic core.

There are definitely more polarimeters and scientific cases out there than mentioned here, but hopefully this is a useful start if you’re considering polarimetry in your research or just trying to learn more!

Astrobite edited by: Jessie Thwaites and Sabina Sagynbayeva

Credit for selected images: Encyclopedia Britannica

Resources:

ESO polarimetry

Polarimetry: A powerful diagnostic tool in astronomy

Astronomical polarimetry (diploma thesis)

[Book] Kolokolova, L., Hough, J., & Levasseur-Regourd, A. (eds.). (2015). Polarimetry of stars and planetary systems. Cambridge: Cambridge University Press. doi:10.1017/CBO9781107358249

[Textbook] Hecht, Eugene. optics. Pearson Education, 2012.