Astrobites Guide to Polarimetry

By Briley Lewis

A diagram showing the random electric field directions before a polarizer and then one electric field direction after
A diagram of unpolarized light, showing a lack of a uniformly oriented electric field, which is then polarized (e.g. one electric field orientation is chosen) by a polarizing filter. Image from Encyclopedia Britannica.

A brief intro to polarized light

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

We categorize polarization in three main ways: unpolarized light, linearly polarized light, and elliptically polarized light. Unpolarized light (a.k.a. natural light) is better described as randomly polarized light; that is, many light sources are a collection of emitters where the emitted light’s polarization is changing very frequently and randomly. This is one extreme, and often light is partially polarized in some way. Linearly polarized light has a constant orientation of the electric field (although the magnitude of the wave may vary still.) Elliptically polarized light has an electric field whose vector rotates, tracing out an ellipse. Circularly polarized light is one case of this, where both x and y directions have the same magnitude. Some of these cases are illustrated in the figure below.

Figure showing three types of polarization: linear, right-circular, and elliptical
Types of polarization, illustrating what’s happening with the orientation of the electric field. Image from Merve Karakaya via ResearchGate.

We can describe polarization mathematically using matrices. Stokes vectors (a.k.a. Stokes parameters) are a useful way to do so. There are four parameters: I, Q, U, and V. I is the total intensity, Q describes linear polarization (horizontal or vertical, depending on the sign), and U describes polarization at a 2nd 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 through a linear polarizer with a horizontal axis)
  • U = S3 = 2I2 – 2I0 (where I2 is the light through a linear polarizer with an axis at 45o)
  • V = S4 = 2I3 – 2I0 (where I3 is the light through a circular polarizer)
A diagram illustrating the Stokes vectors and their connection to polarization states
Diagram of the Stokes vectors and their meanings. Image from Wikipedia.

For completely polarized light, I2 = Q2 + U2 + V2. For a partially polarized system, the degree of polarization is given by P = (Q2 + U2 + V2)½ / I. See Table 8.5 from Hecht for an illustrative example of Stokes vectors for various polarization states. Similarly, the operations of different polarizers on Stokes vectors can be described by Mueller matrices.

A reference table showing the Stokes matrices for various polarization states
Table of Stokes vectors from Optics (Hecht) Chapter 8. In this notation, a P-state is linear polarization, whereas R- and L-states are different orientations of circular polarization.

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, like synchrotron radiation, naturally produce polarized light as well.

A diagram showing how light is polarized at different angles by scattering
Polarization by scattering. Image from Physics Stack Exchange.

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

A diagram showing polarization by reflection
Polarization by reflection. Image from Wikipedia.

Light can also be polarized by reflection off a dielectric medium, where only one component of the incoming polarization will be reflected and the other will be refracted. Brewster’s law describes the angle where the reflected ray will be fully polarized, and deviations from that angle will be partially polarized.

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

How do we measure polarization? 

To figure out how much of the incoming light is polarized, we need to use some sort of polarizer — a filter that separates light into its components, or only lets a certain polarization of light to pass through. As Hecht says in his Optics textbook, for polarizers to work “there must be some sort of asymmetry associated with the process.”

Some polarizers use dichroism, where only one polarization state is selectively absorbed, and the other orthogonal polarization state passes through just fine. Some crystals are naturally dichroic, as are Polaroid filters. Another commonly harnessed effect is birefringence, meaning that a substance has different indices of refraction due to the arrangement of atoms within it. Certain birefringent crystals can split light into orthogonal polarization states. A useful example in astronomy is the Wollaston prism, which serves as a polarizing beamsplitter in many instruments. 

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

So, what makes an astronomical polarimeter? At least in optical/infrared, there’s 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 in order to calibrate out instrumental effects. (You can read in detail about the Gemini Planet Imager polarimeter here as an example!)

Three real Wollaston prisms optics pieces, which look like black pucks with a clear cube in the center. Plus a diagram showing how the cube splits light into 2 polarization states
Images of real Wollaston prisms, with a diagram of how the prism splits light into two polarization states. Image from ThorLabs.

Beyond the optical and IR, there are other ways of measuring polarimetry, too. Radio telescopes can detect polarization since they are essentially recording the state of the electric field, and other types of detectors for high-energy light like X-rays (e.g. gas pixel detectors) have been devised to measure polarization as well.

Some current observatories with polarimetry capabilities and their cool science results (plus relevant Astrobites!)

IXPE [The Imaging X-Ray Polarimetry Explorer] — The recently launched NASA mission IXPE is going to be looking for polarization from some extreme sources, like supernovae, AGN, and pulsars! Be on the lookout for its first results coming very soon.

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

Gemini Planet Imager — Briefly mentioned earlier, the Gemini Planet Imager didn’t just image planets, it also imaged debris disks! And it did so in polarized light, using polarimetric differential imaging, a technique that separates the starlight from the disk’s light. They’ve got a whole survey sample of polarized debris disks, plus some neat in-depth studies of individual disks!

Subaru/SCExAO/CHARIS — The CHARIS instrument on the Subaru Telescope can do spectropolarimetry [looking at polarization in multiple wavelengths] in the infrared, including polarimetric differential imaging (CHARIS-PDI) which is useful for finding exoplanets and disks. They’ve done some cool imaging of jets off young T Tauri stars and debris disks!

ALMA — Polarimetry works a bit differently for radio telescope arrays like ALMA, but they make it happen. ALMA has been key for understanding magnetic fields of objects across the Universe, such as the interesting and extreme supernova AT2018cow

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

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

SOFIA HAWC+ — The airborne observatory SOFIA has a unique far-infrared imaging polarimeter called HAWC+ which has been used to look at star-forming regions and emission in a dusty torus around an active galactic nucleus

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

Astrobite edited by: Jessie Thwaites and Sabina Sagynbayeva

Featured image credit: Encyclopedia Britannica

Resources:

ESO Polarimetry

Polarimetry: A Powerful Diagnostic Tool in Astronomy

Astronomical Polarimetry (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.

About Briley Lewis

Briley Lewis is a PhD Candidate and NSF Fellow at the University of California, Los Angeles studying Astronomy & Astrophysics. Her research interests are primarily in planetary systems – both exoplanets and objects in our own solar system, how they form, and how we can create instruments to learn more about them. She has previously pursued her research at the American Museum of Natural History in NYC, and also at Space Telescope Science Institute in Baltimore, MD. Outside of research, she is passionate about teaching and public outreach, and spends her free time bringing together her love of science with her loves of crafting and writing, and playing with her rescue dog Rocky.

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