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We talk about how coherent light has a $g^{(2)}(\tau)=1$ and thermal light has $g^{(2)}(0)=2$. However, we can talk about the coherence length of a thermal source if we put it through a very narrow filter and say it has some coherence length. I guess my question is: does this coherence length relate to $g^{(1)}$ rather than $g^{(2)}$? Maybe I'm getting mixed up with the definition of a coherent source.

Thanks

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To be correct, thermal light has a coherence length even if it's not spectrally narrow. The coherence length would just be very short.

In Loudon – The quantum theory of light (2000) chapter 3.1 the coherence time is defined by the spectral width of the light. Therefore, by the Wiener-Khinchin theorem it is related to $g^{(1)}$. But for thermal light the Siegert relation holds, which states $g^{(2)} (\tau) = 1 + \left( g^{(1)} (\tau) \right)^2$.

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  • $\begingroup$ Thank you, makes more sense now. $\endgroup$
    – rogerkoulitt
    Commented Mar 7, 2021 at 10:22

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