Polarization of Light

Transcription

1 Polarization of Light A light beam which has all of the wave oscillations in a single plane of space is said to have total plane polarization. Light with an equal amount of oscillations in all directions is unpolarized. The in-between case is one where there is partially polarized light. Most sources of light in nature to not emit polarized light. To do so would require the oscillating electric charges that produce it to move in unison in the same direction. For a plane polarized beam. We can always subdivide the amplitude as the vector sum of two perpendicular components. We will see that this is useful, because we can usually choose how to do the subdivision to solve a particular problem. If we could see the amplitudes for a beam coming directly toward us, it might look like this. Similarly, an unpolarized beam could be represented this way.

2 Note that the unpolarized beam can be thought of as a large number of plane polarized beams, each of which can be decomposed into xy components. Now, any such beam can be decomposed into a net oscillation in the x and y directions. This in turn can be thought of as the sum of a completely (100%) polarized beam and an unpolarized beam! Mathematically, they are equivalent. Now, for some more fun, it should be stated that this sort of decomposition into two orthogonal (perpendicular) waves works if the waves have the same wavelength and phase. That is, the crests are lined up so that they hit a target together. It is also possible to have light where the two components are 1/4 wave out of phase, so the electric field traces out a helix in space! Such a beam, shown here, would not be plane polarized, but circularly polarized. An observer would see the tip of the net electric vector trace out a circle instead of a line as it arrived. And of course, light can even be a mixture of circular and plane polarized elliptically polarized (totally or partially). For now we will stick to linearly polarized light.

3 We can produce and alter the polarization of a beam in many ways. We will deal with 4 methods: transmission, reflection, refraction, and scattering. Transmission Polarizing filters, such as those in Polaroid sunglasses, are designed to allow only one plane of light through (although they are not 100% effective, they can be pretty close to that value).

4 If we then put another polarizing filter in the beam, we can get some interesting results! In each case shown, the second filter allows only that component that lies in the transmission direction though. In (a), all of the amplitude is in the transmission direction, so it all gets through. In (b), none of the amplitude is in the transmission direction, so none gets through. In (c), the transmission direction is rotated 45 to the direction of the amplitude, so some of the light gets through.

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6 amplitude transmitted through first filter K J H Component after the first filter that is on the transmission direction of the second filter Mathematically, J is the component of K in the transmission direction. By definition, J/K is the cosine of the angle between the two, so J = K cos (angle JK). For a 45 o angle, we get: J = K cos 45! 2 J 2 = K ( ) = K 1 2 = K 2 2 = K Plane of transmission of second filter Because the intensity is proportional to the square of the amplitude, the second filter transmits 1/2 of the light reaching it. If you would like to see this in action see the following 2-filter polarization and 3-filter polarization: Sorry! This page seems to have vanished.

7 Reflection Light striking a surface, such as a piece of glass, the surface of water, etc., can be both transmitted through the surface and reflected from it. The amount that is transmitted or reflected, and its polarization, depends on the angle of incidence and the material it is hitting. The important angle here is the angle of incidence, in the figure. If we decompose the incident beam into two perpendicular (sometimes called orthogonal ) components, we can follow each individually. And they behave differently! We will call the two components by the following terms: Perpendicular component: the amplitude is in the plane of incidence (strictly speaking, it is the plane of incidence and reflection) Parallel component: the amplitude runs along the plane of the surface as it hits For the parallel component, there is always some reflection, even when the angle of incidence is 0 (hitting normal to the surface). At higher angles of incidence, the reflectance increases until it reaches 100% at grazing incidence. The perpendicular component has a more complex behavior. It begins at the same reflectance as the parallel beam for angle of incidence of 0, slowly decreases to 0 reflectance at some specific angle, then increases. The angle where the reflection goes to 0% (and the transmission to 100%) is called Brewster s Angle. and it depends on the index of refraction of the material.

8 Seeing the effects of reflection using polarizing filters

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10 Polarized Light in the Environment Due to the optical properties of various natural and artificial materials, the effects of polarized light are all around us. In addition to Haidinger s Brush, we often use polarized filters in the form of sunglasses to cut glare due to reflected sunlight. It is also used to darken the sky in photography, remove glare from subjects behind windows, etc. Note that this implies that properties of the atmospheres and surfaces of planets and other astronomical objects may be derived from measurements of polarized light.

11 Refraction Some materials, such as the mineral calcite, have the interesting property of refracting the two planes of polarized light at slightly different angles! This birefringence is useful in the design of optical devices that need to measure both components simultaneously (such as optical polarimeters used in astronomy and other fields). Many plastic materials become birefringent when physically stressed. Likewise, safety glass in cars has built-in stress that is visible when viewed through a Polaroid filter (see later in these notes) Scattering and Haidinger's Brush Sunlight scattering off molecules in the air produces polarized light. The degree of polarization depends on the scattering angle, becoming a maximum near 90 degrees. This phenomenon seems to be utilized by animals whose eyes are sensitive to the polarization direction. The human eye has its own weak sensitivity to polarized light that give rise to Haidinger s Brush, a yellowish patch that can actually become annoying once you become aware of it!

12 Optical Activity Some crystals and organic materials have a twisted molecular structure that produces another interesting effect: optical activity. Here, the plane of polarization rotates as the beam passes through the material, and it can rotate different amounts for different wavelengths. This phenomenon is useful for analyzing mineral crystals and organic pharmaceuticals.

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14 A SIMPLE POLARIMETER DESIGN As we saw before, many materials (such as calcite) have an index of refraction that depends on the orientation of the polarization component. Effectively, they separate them. These can be combined in clever ways to make an effective polarimeter. One example uses a Wollaston prism: This can be combined with a rotating half-wave plate that has the effect of rotating the plane of polarization (it s optically active) by an amount that depends on the orientation of the plate to the plane of polarization. For every 1/2 turn of the plate, the plane of polarization rotates 360 o. Inserted in front of a Wollaston prism causes a polarized input beam to be redirected in one exit beam, and then the other. An example of a rotating half-wave plate: polarization/simulations/modulator1.html

15 U = +1 P = 1 The Sky Q = +1 N Q-U Plot Q = +1 E Q = 1 θ U = 1 2θ U = +1 U = 1 Q = 1 Note that two equally bright totally polarized beams with orthogonal planes should cancel out. The QU plot SHOWS this.

16 An example of a QU plot for an active galaxy 3C 345. Each circle is plotted at the location of the Stokes parameters Q and U. The radius of each is equal to the 1 uncertainty in the measurement. Each circle represents the QU value on a different date. The object is a strong source of synchrotron radiation, and it went into a polarization (and total brightness) outburst where the plane of polarization changes. Here I had U becoming more positive to the left, to preserve the direction of the plane of polarization more like that on the sky (increasing eastward is counter-clockwise here). From Sitko, Schmidt, and Stein, 1985, ApJS, 59, 323.

17 A measurement uncertainty also introduces a positive bias into the value of P Q U Because P can never be negative it cannot follow true Gaussian statistics!

18 Polarimetry in Astronomy Interstellar Polarization

19 The Planck spacecraft planck.caltech.edu recently made a map of the galactic magnetic field. Full Celestial Sphere 30 degree FOV closeup This work was the one responsible for casting doubt on the detection of B-wave polarization of the cosmic microwave background from the big bang!

20 The polarization reaches a maximum at visible wavelengths, suggesting that the grains responsible must be about 1 μm in size: It is thought that elongated or flattened spinning silicate grains, aligned by the galactic magnetic field, are responsible. Above: models of a spinning grain. Below: An interstellar-like grain.

21 Scattering Angles scattering angle phase angle scattering angle

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23 Circumstellar Dust observed model

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25 A polarized intensity ( PI ) image of the material inside the gap in the disk of SAO Because the light from a star is not ordinarily polarized, a polarized flux image automatically cancels out much of the light from the star, while allowing the disk, which polarized by scattering the light off of dust grains, to be seen more easily. The spiral pattern is thought to be produced by a pair of Jupiter-mass planets somewhere inside the orange circle (where the instrument cannot yet see well). From Muto et al, 2012, ApJ, 728, L22.

26 Jets in Active Galaxies: The jet in the elliptical galaxy M87, thought to be powered by a supermassive black hole. Polarization map of the jet. The polarization and spectrum indicates the jet emission is due to synchrotron emission electrons traveling close to the speed of light in a magnetic field.

27 Stellar (& Solar) Magnetic Fields

28 Planetary Surfaces

29 polarization versus phase angle effects of grain size Negative polarization branch is not truly negative, but indicates a 90 degree change in the plane of polarization

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31 Comets "zombie" Comet C/2012 S1 ISON

32 Images of Comet ISON obtained with the Hubble Space Telescope, using the F606W filter, and rotatable polarizer at angles of 0 (a), 60 (b), and 120 (c) degrees. Frame (d) is a stack of all three images. The brightness (gray scale) and polarization of ISON. The scale is in detector pixels. A 100% polarization signal would extend 500 pixels in this diagram. Both images are from Hines et al., ApJL, 780, L32, (2014).

33 Polarization Resources Classics W.A. Shurcliff Polarized Light D. Clarke & J.F. Granger Polarized Light and Optical Measurement Astronomy Tindbergen Astronomical Polarimetry J.-L. Leroy Polarization of Light and Astronomical Observation M. I. Mishchenko et al. Polarimetric Remote Sensing of Solar System Objects T. Gehrels (ed.) Planets, Stars, and Nebulae studied with Photopolarimetry Other Kliger, Lewis, and Randall Polarized Light in Optics and Spectroscopy Popular Können Polarized Light in Nature Pye Polarized Light in Science & Nature