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1. I am studying dynamic light scattering in which one experimentally measures intensity correlation i.e., <I(t)I(t+tau)>. Therefore, if the detector looks at a scattering signal from a solution of particles undergoing Brownian motion, under right experimental conditions one can detect the above correlation signal which looks like a reversed S shaped curve when plotted as correlation on Y axis and tau on X axis. Therefore one can obtain a sizable correlation all the way up to microseconds to milliseconds and then it decays.

2. I am told that more fundamental than intensity correlation is field correlation <E(t)E(t+tau)> and intensity correlation can be derived from field correlation. Great books such as "dynamic light scattering" by Carole and Pecora do begin with field correlation and then discuss intensity correlation.

3. This is my question: All the books assume a plane wave E0 exp(ik.r-wt). But in reality one should actually consider E0 exp(ikr-wt+theta(t)), where theta is the phase of the wave and will be a function of time, because each wave train emitted by a laser will have a different phase and there will be many such wave trains between t and t+tau. Therefore, shouldn't the term <E(t)E(t+tau)> average out to 0? why should there be any coherence between a wave at time t=0 and time t= tau which is as long as microseconds to milliseconds. Even the best lasers have a coherence length of few meters i.e., few nanoseconds. Milliseconds? - no way.

Appreciate any clue to my confusion.

Thanks in advance.

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# Dynamic light scattering and coherence of light

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