elliptical polarization

4

Jus whipped up this lil ditty of elliptically polarized light as the second iteration of an earlier version of right circular polarized light, modeled after an illustration in the always inspiring “Optics” by Hecht. The blue n green plastic lanyard stuff is the paths traced out by the electric and magnetic field vectors respectively.

Also!! These things are so quick n easy to make once u got the cut template that I figured I’d make print n cut templates of em to share n so I made a point to only make em out of stuff I could find at Michaels (minus the mylar, acetate should work fine too). gotta putta few more tweaks em tho so im off to buy better markers for take 3 n gettin to it ok buh bye :o

Light becomes polarized because of its wave nature.

As electromagnetic radiation (in the visible spectrum), a light wave is composed of both electric and magnetic field components, and is usually represented by a phase vector that encodes information about just the electric field. The phase vector points in the direction of the electric field, and its magnitude denotes the electric field strength. Because the phase vector can be decomposed into orthogonal components that oscillate sinusoidally, light is called a wave, and the phase of the wave at a certain place and time refers to its place along the sine curve.

Examine a planar wave, which travels along the z axis with electric and magnetic fields in the x-y plane. Let E(t,z) be the phase vector with orthogonal components x(t,z) and y(t,z) that are time- and space-dependent. If the x and y field components oscillate with amplitudes Ex and Ey, then

Ex2 + Ey2 = ||E||2 for all t, z
x(z,t) = Excos(kz-ωt1)
y(z,t) = Eycos(kz-ωt2)

where the following are constants:

ω  is the frequency, in units of Hertz (Hz) or radians/second,
k  is the (angular) wavenumber, in units of radians/meter, and
φ1, φ2 are the phases, in units of radians.

Polarization is the phenomenon of light waves having the same spatial orientation of their phase vectors (if it happens in nature), or the restriction of the phase vectors to certain orientations (by experiment). Ordinary sunlight is generally unpolarized because the direction of the individual phase vectors are aligned randomly with each other as they oscillate. By passing unpolarized light through a linear polarizing filter, waves result whose phase vectors only oscillate along a particular axis, say the horizontal (x) axis. One has “filtered out” the vertical (y) electric field components from every wave that passed through the linear polarizer. Thus Ex = E is the amplitude for the whole wave, and

x(t,z) = E cos(kz-ωt)
y(t,z) = 0

If you projected the endpoint of the phase vector onto a cross-section of the travelling wave (a picture called a Lissajous curve), you would see a line - hence the name, linear polarization.

Other polarizations are possible where the direction rather than the magnitude of the phase vector changes. If one takes the horizontally polarized light, tilts it 45 degrees to halfway between horizontal and vertical (like the animation), and then passes it through a quarter wave plate that slows down electric field along the horizontal axis by a quarter phase, one obtains circularly polarized light. The horizontal component of the phase vector now oscillates a quarter phase (2π/4 = π/2) behind the vertical components, resulting in the parametric equations

x(t,z) = (1/√2) E cos(kz-ω(t-π/2))
y(t,z) = (1/√2) E cos(kz-ωt)

which, keeping z constant, represent a circle (the 1/√2 comes from sin 45 deg and cos 45 deg). You can calculate that the phase φ1 is

φ1 = ωπ/2

If the polarizing plate inserts a different phase in the x field component, then you’ll get elliptically polarized light.

How can you tell what polarization light has, or if it’s polarized at all? Unless you have a sensory organ that detects the direction of the electric or magnetic fields around you, the only way change you can see after polarizing a light source is a reduction (usually) in the intensity of the light, which is proportional to the square of the electric field amplitude. For example, the intensity of ordinary sunlight is approximately halved when you put on Polaroid sunglasses.

What happens when you pass light through two linear polarizers? Three linear polarizers?

Launching from Earth in 2011, the Juno spacecraft will arrive at Jupiter in 2016 to study the giant planet from an elliptical, polar orbit. Juno will repeatedly dive between the planet and its intense belts of charged particle radiation, coming only 5,000 kilometers (about 3,000 miles) from the cloud tops at closest approach.

Juno’s primary goal is to improve our understanding of Jupiter’s formation and evolution. The spacecraft will spend a year investigating the planet’s origins, interior structure, deep atmosphere and magnetosphere. Juno’s study of Jupiter will help us to understand the history of our own solar system and provide new insight into how planetary systems form and develop in our galaxy and beyond.

Juno’s principal investigator is Scott Bolton of Southwest Research Institute in San Antonio, Texas. NASA’s Jet Propulsion Laboratory in Pasadena, Calif., manages the mission. Lockheed Martin Space Systems of Denver, Colo., is building the spacecraft. The Italian Space Agency, Rome, is contributing an infrared spectrometer instrument and a portion of the radio science experiment