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What are coherent and incoherent radiation?

I am a mathematician who is self-learning physics. In reading Jackson's electrodynamics and other books, I often hear that radiation is incoherent or coherent. What does this mean? Does it just mean that the phases are the same in coherent radiation and are different in incoherent radiation?

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Related: – Qmechanic Apr 16 '13 at 16:51
up vote 1 down vote accepted

Yes, coherent radiation means that the phases of two ( or more ) waves representing the radiation differ by a known constant.

Incoherence means that the phase differences are unknown/random.

Laser radiation is coherent because stimulated emission assures phase differences are constant . Radiation from an incandescent lamp is incoherent because the electromagnetic waves are generated in a statistically random manner depending on which atoms are excited and de-excited.

To develop intuition think of the classical example of soldiers marching in step. Their motion is coherent and so are the vibrations they set up. They break step over ancient bridges so as to become incoherent, there were cases where ancient bridges resonated to the step and were damaged.

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So an LED producing the same frequency of light but with random phases isn't coherent? – Brandon Enright Apr 16 '13 at 17:48
I would think in general the light would be incoherent unless there is a special design of the diodes to control the phases. There is a reference to a coherent junction in the wiki LED article. – anna v Apr 16 '13 at 17:52

Radiation is temporally coherent, if its coherence time is greater than some agreed value, incoherent otherwise (the value is chosen depending on the context). Coherence time is characteristic time of decay of the temporal auto-covariance function of the electric field $$ \langle E (x,t) E(x,t+\tau)\rangle $$ as $\tau$ increases.

Analogously, radiation is spatially coherent, if its coherence length is greater than some agreed value. Coherence length is characteristic length of decay of spatial auto-covariance function $$ \langle E (x,t) E(x+\xi,t)\rangle $$ as $\xi$ increases.

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