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I have been given the following equation to show the difference between coherence and non-coherence in optics and how the third term represents the interference between two optical pulses. Can someone explain what the terms represents and how this equation changes when the two signals are the same continuous data signal but $\vec{Z}_2$ is now $\vec{Z}_1$ delayed by $\Delta t$?

\begin{equation} I(t) = \left| \mathbf{\vec{Z}}_1(t) + \mathbf{\vec{Z}}_2(t) \right|^2 = \left| \mathbf{\vec{Z}}_1(t) \right|^2 + \left| \mathbf{\vec{Z}}_2(t) \right|^2 + 2 \left| \mathbf{E}_1 \right| \left| \mathbf{E}_2 \right| \cos\phi \label{eqn:coherent} \end{equation}

prof123
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1 Answers1

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i'm an undergrad but it is to my understanding that the equation shows us that the optical signals are coherent if the phase difference is zero. Z is the vector equivelant of the signal. I is the intensity and E is the electric field. If you apply it to a delayed signal then since the phase difference changes they stop being coherent. Am i right?

kid22
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