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Let's consider a situation: we have distant point source of unpolarized light in certain non-zero range of wavelengths (it's polychromatic). Let's divide this light into 2 beams depending on polarization direction with e.g. Wollaston prism. Then let's rotate the polarization plane of one of these beams by angle 90 degrees. Are resulting beams coherent (able to produce interference pattern)?

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No. Coherence means "fixed, definite phase relation", or in a polychromatic context it can mean "definite phase relation at any given frequency". What would be the phase relation of the horizontally- and vertically-polarized waves? $0^\circ$? $90^\circ$? There's no reason for any definite phase relation.

Here's a more specific way to think about it. Unpolarized light is exactly the same as light where 50% of the photons are clockwise-circularly-polarized and 50% are couterclockwise-circularly-polarized. For the former, the vertical polarization component is $+90^\circ$ out-of-phase with the horizontal component; for the latter it's $-90^\circ$. These two parts would lead to equal and opposite opposite interference fringes; altogether, there are no interference fringes.

If the light from the source is initially fully- or partially-polarized, then it is definitely possible to get interference fringes in the way you describe.

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Steve B already nailed it. The two polarization basis states of light -- usually either vertical/horizontal or clockwise/counter-clockwise, but infinitely many such pairs are possible -- are fully independent and can each carry an entirely separate signal. This is how two types of 3D movie theater glasses work, in fact. It's a fascinating effect, really a type of quantum orthogonality of states, though it's so commonplace (theaters!) that we seldom think of it that way. Notably, 3D theaters are not natural, so most ordinary light sources will have correlation between the selected basis states. –  Terry Bollinger Mar 31 '12 at 0:34
    
Thank you. You have helped me very much. –  Boris Mar 31 '12 at 11:55

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