Description of partially coherent light beams using thermodynamic principles

While a thermodynamic description of light has been very useful in discussing light propagation in multimode nonlinear waveguides, it is often stated that such a description is not simple for free-space beams due to the onset of an ultraviolet catastrophe. Herein it is proposed that the beam width and divergence angle are natural cutoffs that remove the singular behavior. Also, the beam propagation (or quality) factor can be associated with a statistically defined temperaturelike parameter. In the high-temperature limit, the beam wavefront is described by a Gaussian Schell-model source, being strongly multimode with a specklelike intensity pattern. In the low-temperature limit the beam has a wandering Gaussian profile, showing strong correlations and anticorrelations for the intensity's Pearson correlation coefficient, with good agreement between numerical simulations and experimental data. Hence, the present results may subsidize the emerging discussions of thermodynamical descriptions in a wider range of optical systems, such as propagation in turbulent media or biological tissues. Moreover, this work's description is not limited to optical systems, since it is founded on a simple unbounded scalar linear system described using a complete orthonormal basis. Therefore, our findings may also provide further conceptual connections with properties of other systems, such as acoustic waves and quantum particles.