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Sunday, May 20, 2007

polarized light------- part 1

read between the lines:- "this guy is so lazy that he posts on what he has been doing for his summer project."


the first part calls for a recapitulation of sorts----I've been reading a really lovely book on optics by hecht---i don't know who he is guys......but i am a fan!


so , we can start with the polarization states of light---
(i) natural / randomly polarized light(never unpolarized,no!)
(ii) plane polarized light (P - state)
(iii) circularly polarized light----divided further into right handed(clockwise)--R-state
left handed (anti-clockwise)--L-state
(iv)elliptically polarised light --can be right/left handed or horizontal/vertically polarized-depends which way it has a larger amplitude.


essentially every state can be generalised into the elliptical light category-- i mean plane polarised and circularly polarised light are but special cases of the elliptical category.

the mathematical treatment too is very general - assuming the polarized (or randomly so) radiation to consist of the orthogonal components -- horizontally and vertically polarized light respectively.

assumption: propagation of the ray is along z axis.

in the x-y plane, A(x)= acos(wt - kx)
A(y)= bcoswt(wt - kx+ 0) "sorry 0 for theta



adding up amplitudes , A(tot)= acos (wt - kx) + b cos(wt - kx + 0)
= a' cos(wt - kx + 0') where a'= ........ you know the drill


now,
apparently this represents the general elliptic equation, you know where the pricipal axes dont constitute the major and minor axes.
(my knowledge of gemetry and maths is seriously limited)

so when the phase difference in the orthogonal polarized states of light(0)is zero-
we get plane polarization
when 0= 45*(degrees) ,and the two impinging amplitudes are different the elliptic phase takes over,
while for 0=45* and equal amplitudes, circular polarization takes up.

i dont why i explained all this, but this is only the beginning............ most of you should know this but i started dutifully.

in the next part i will take in something that we dont know till now and expand on it.
this article actually deals wth mathematical methods of denoing polarized light.
but what makes it interesting is that we can treat polarization optics entirely through matrix algebra. i mean denote the incident light with a matrix, multiply it with a square matrix that is specific to the optical element to which the incident ray is subjected, and you obtain the emerging ray.
the simplicity of the whole process drew me in, and i perfomed my project on the same thing.

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