Announcements I should have exams back to you on Fri.

Reading Quiz The element that should be used to change linearly polarized light into circularly polarized light is the quarter waveplate half waveplate full waveplate

Reading Quiz When multiple elements are in a beam path, the Jones matrices multiplied to find the final optical polarization are written with the first element’s matrix on the right with the first element’s matrix on the left in any order

Silicon chip birefringence

Jones Matrix JM for linear polarizer Horizontal transmission (trans. axis along x) Vertical transmission (trans. axis along y)

Arbitrary angles for polarizers Rotation of coordinates transforms a vector from the original basis to the vector in the rotated basis. transforms a vector from the rotated basis to the vector in the original basis.

Linear polarizer at arbitrary angles Polarizer looks like in “rotated” coordinates if x’ is aligned with the transmission axis. Let’s get it in the x, y system: transforms a matrix operator from the original basis to the matrix in the rotated basis. JM for linear polarizer Transmission axis at q from x axos

Waveplates (optical retarders) Uniaxial crystals cut so optic axis is in the plane of the plate. Light comes in perpendicular to the plate. Light travels fastest if E is aligned with the fast axis (bold blue line). The optic axis is the fast axis if ____ no > ne. no < ne. fast To analyze, we break light into components along and perp to the fast axis. Phase difference between the fast and slow light after the WP in terms of thickness: slow

Quarter-wave plates fast slow Choose thickness so phase difference between fast and slow light is ____ If we start with linear polarization at 45o from the fast axis, we will end up with ________ polarized light linearly circularly elliptically Hint, figure out the components (Jones vector) in the “fast-slow” coordinate system, and then do the phase shift. fast slow

Quarter-wave plates If we start with linear polarization at 90o from the fast axis, we will end up with ________ polarized light linearly circularly elliptically

Quarter-wave plates If we start with linear polarization at general angle q from the fast axis, we will end up with ________ polarized light Summary: QWP’s usual purpose is to change between linear and circular pol, which means the linear light needs to be at 45 deg to the fast/slow axes. Other orientations give elliptical.

Half-wave plates fast slow Choose thickness so phase difference between fast and slow light is ____ If we start with linear polarization at 45o from the fast axis, we will end up with ________ polarized light linearly circularly elliptically Hint, figure out the components (Jones vector) in the “fast-slow” coordinate system, and then do the phase shift. fast slow

Half-wave plates If we start with linear polarization at a general angle q from the fast axis, we will end up with ________ polarized light linearly circularly elliptically Hint: figure out the components (Jones vector) in the x’, y’ coordinate system, and then do the phase shift. Summary: HWP’s usual purpose is to rotate linear polarization to a new line, by 2q.

JM for Waveplates fast slow For waveplates, q is orientation of fast axis vs the x (H) axis. What does the l/4 plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by p/2. fast What does the l/2 plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by p. slow

JM for Waveplates JM for quarter-wave plate JM for half-wave-plate

Polarization demos again Does our transparency sheet act more like QWP or HWP? http://optics.byu.edu/animation/polarwav.mov

Wood fibers between crossed polarizers

JM for Reflection (vertical mirrors) If a circularly polarized beam in the horizontal plane strikes a vertical mirror at say 45%, what will the final state be? JM for Reflection (vertical mirrors)

Why sunlight (scattered light) is partially polarized To get the most polarization difference, look at the molecules that have to scatter light 90 degrees to get to you Why: dipole radiation’s angular dependence!

Boomerang Nebula coldest known region: 1K Color indicates angle of polarization line. This shows that the light comes from the center. (Polarization caused by scattering light off tiny dust particles)

Sunset carousel demo and polarization LCD screen teardown

Notes Order of matrices matters! Fraction of intensity transmitted: compare initial and final vector squared magnitudes Choose x to stay on your right hand as you follow the beam around reflections.

If a R-cir beam strikes a mirror at normal incidence, what will the resulting beam be? L-cir linearly polarized