Electric field of light emitted by atom, given the intensity

[bunchedupwalrus]

Homework Statement

Explain why the time-dependent electric field of an atom emitting a burst of light can be zero, or contain a cosine.

Relevant Equations

I(t)=I(0)exp (-t /tau) for t>=0
E(t) = 0 for t >= 0
E(t)=E_0 cos(w_0 *t)e^(t/2tau) for t < 0
I proportional to E^2 via poynting vector

For t < 0 , all I can think of is a qualatative " the field is zero because the intensitity is 0 when the burst of light hasn't been emitted yet "

For t >= 0 , I've tried squaring the given E and that let's me say the amplitudes are proportional (with a cos^2 term in the mix)

But I feel like I'm missing something. Is this the right idea? Thanks

(From quantum optics, fox)

 

[mfb]

The image has a different question than the title.

A linearly polarized electromagnetic wave will have an electric field of zero twice per period at a given place. Usually only the average energy density over one period is relevant. You don't consider things like the angular dependence of the emission here anyway.