1. Mar 28, 2017

### davon806

1. The problem statement, all variables and given/known data
Please see the attached,this was extracted from my notes.(Left side is the 1st page).I was trying to prove the sentence underlined (on the right page). Given ε(r,t) , how can I prove that the cross-terms average to 0? Actually I don't really understand why there are cross-terms. Would be much appreciated if someone can elaborate the paragraph on right page in detail !

2. Relevant equations

3. The attempt at a solution
To calculate the intensity and energy density, using the formula on left page, I suppose we need to find ε(r,t) ^2 by taking its dot product. However,this would give me a double integral which I don't know how to proceed...

2. Mar 28, 2017

If you sum up and have a bunch of different frequencies (or take an F.T. and get a sum of $E(\omega)exp^{i \omega t}$ over all frequencies), when you square the expression, the terms involving two frequencies (the cross terms) each time average to zero.