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Old Oct 20th 2009, 02:05 PM   #1
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Posts: 21
Equation for linearly polarized light

I need to write an equation for a beam of polarized light traveling alone in the xy-plane 45 degrees from the x-axis. The plane of vibration corresponds to the xy-plane and the angular frequency is $\displaystyle \omega$ .

Given the initial conditions: at t=0 the E-field at the origin is zero, normally, if the wave is propagating in the z-direction I would write:

$\displaystyle \overrightarrow{E}=E_0\left [ \hat{i}sin(kz-\omega t)+\hat{j}sin(kz-\omega t) \right ]$
\overrightarrow{E}=E_0\left [ \hat{i}sin(kz-\omega t)+\hat{j}sin(kz-\omega t) \right ]

But now the propagation direction has changed, how can I deal with that? Can I just change z to something else like:

$\displaystyle \overrightarrow{E}=E_0\left [ \hat{i}sin(k?-\omega t)+\hat{j}sin(k?-\omega t) \right ]$
\overrightarrow{E}=E_0\left [ \hat{i}sin(k?-\omega t)+\hat{j}sin(k?-\omega t) \right ]

Something is wrong with my latex, I've typed the codes below what I intended to display.

Last edited by synclastica_86; Oct 20th 2009 at 02:08 PM.
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