Silicon chip birefringence

Waveplates (optical retarders) Asymmetric 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. 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:

Quarter-wave plates 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 x’, y’ coordinate system, and then do the phase shift.

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 lin-pol line has to be at 45 deg to the fast/slow axes. Other orientations give elliptical.

Half-wave plates 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 x’, y’ coordinate system, and then do the phase shift.

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.

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 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

JM for Waveplates 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. What does the l/2 plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by p.

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

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

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)

Notes Order of matrices matters! Fraction of intensity transmitted: compare initial and final vector squared magnitudes Convention: choose x always so it stays on either your left or right hand as you follow the beam around reflections in a plane.