Effect of absorption on the spatial coherence in scalar fields generated by statistically homogeneous and isotropic sources

We investigate the behavior of the spectral degree of coherence of fluctuating scalar wave fields generated by statistically homogeneous and isotropic sources within absorbing media. In the limit of negligible losses, the degree of coherence is shown to be of a known universal form (sinc function), whereas in the limit of infinite losses it is shown to asymptotically approach the degree of coherence of the source. The intermediate cases are studied for fields produced by sources with Gaussian and sinc-type coherence functions. These studies show that the concept of negligible losses is meaningful only when defined with respect to specific source distribution statistics, and that even for arbitrarily small nonzero losses, the coherence length of the field can be arbitrarily short.

Figure 1

Degree of coherence ${\mu }_U\left(\mathbf{r}\right)$ as given by Eq. (37), when (a) ${\kappa }^{\prime }\gamma ∕2=3$ and (b) ${\kappa }^{\prime }\gamma ∕2=1∕3$.

Figure 2

Degree of coherence ${\mu }_U\left(\mathbf{r}\right)$ as given by Eq. (41), when ${\chi }^{\prime }∕{\kappa }^{\prime }=3$ and ${\kappa }^{″}∕{\kappa }^{\prime }={10}^{-16}$.