Polarizati

onEyes!

Nose!

http://www.mbari.org/news/news_releases/2009/barreleye/barreleye.html!

7.1 !

Lecture 14: Polarization of Light!

Waves and Optics !

[Extra notes available on wattle]!

7.2 !

Contents!

•  This lecture contains the following slides:! –  Title! –  Contents! –  Polarization! –  Example of polarization mathematics 1! –  Example of polarization mathematics 2! –  Example of polarization mathematics 3! –  Jones vectors! –  Jones vector examples 1 & 2! –  Jones vector example 3! –  A few polarization terms! –  Poincaré basis! –  Poincaré sphere! –  Summary! –  Octopus Vision! –  Exercise 1: standard form Jones vector!

7.3 !

Polarization!

ˆ ˆ E ( z,t ) = H E 0 H exp(i( kz " #t + $ H )) + V E 0V exp(i( kz " #t + $V ))

•  Assume k is in the z direction (i.e. choose z axis well!).! –  V is the unit vector in the y direction (Vertical)! –  H is the unit vector in the x direction (Horizontal)! –  Taking out the phase of H as a common factor:!

!

ˆ ˆ E ( z,t ) = ( H E 0 H + V E 0V e i("V #" H ) ) e i(kz#$t +" H )

!The phase on the outside won’t change the polarisation state, it all depends on !" = ("V - "H). !

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7.4 !

Example of polarization mathematics 1!

•  Example 1: When !" = 0.!

ˆ ˆ E ( z,t ) = ( H E 0 H + V E 0V ) e i(kz"#t +$ H )

–  In this case, we get linearly polarized light, with the angle = arctan(E0V/E0H)!

!

–  –  –  –  – 

E0V = 0, then Horizontally polarized! E0H = 0, then Vertically polarized! E0V= E0H, then Diagonally polarized! E0V= -E0H, then anti-Diagonally polarized! NB: !" = #, is same as having a negative sign in one of the coefficients.!

7.5 !

Example of polarization mathematics 2!

ˆ ˆ ˆ ˆ E ( z,t ) = ( H E 0 H + V E 0V e"i# / 2 ) e i(kz"$t +% H ) = ( H E 0 H " iV E 0V ) e i(kz"$t +% H ) ˆ ˆ & Re[E ( z,t )] = H E cos(kz " $t + % ) + V E sin(kz " $t + % )

0H H 0V H

•  Example 2: When !" = #/2.!

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–  E0V is 90º out-of-phase (in quadrature) with the phasor of E0H.! –  The direction...