Silicon chip birefringence

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

Rotation of coordinates Arbitrary angles for polarizers 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 transforms a matrix (operator) from the original basis to the matrix in the rotated basis. Polarizer looks like in “rotated” coordinates if x’ is aligned with the transmission axis. Let’s get it in the x, y system: JM for linear polarizer

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

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

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

Quarter-wave plates If we start with linear polarization at general angle  from the fast axis, we will end up with ________ polarized light a)linearly b)circularly c)elliptically

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

Half-wave plates If we start with linear polarization along the x axis, and the fast axis is rotated a general angle , we will end up with ________ polarized light a)linearly b)circularly c)elliptically

JM for Waveplates What does the  plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by ______. For waveplates,  is orientation of fast axis vs the x (H) axis. What does the  plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by ______.

JM for Waveplates JM for quarter-wave plate JM for half-wave-plate Main use of a QWP: Main use of a HWP:

Polarization demos again Does our transparency sheet act more like QWP or HWP? mov

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 metal mirror at normal incidence, what will the resulting beam be? a.R-cir b.L-cir c.linearly polarized