Loss of spatial coherence and limiting of focal plane intensity by small-scale laser-beam filamentation

We describe a nonlinear optical mechanism that leads to a decrease of the degree of (transverse) spatial coherence of a laser beam as a function of propagation distance. This prediction is in direct contrast with those of the van Cittert-Zernike theorem, which applies to propagation through a linear, homogeneous material. The mechanism by which coherence is lost is the growth of small phase irregularities initially present on the laser wave front. We develop a detailed theoretical model of this effect and present experimental results that validate this model. The practical importance of this result is that by being able to controllably decrease the spatial coherence of a laser beam, one can limit the maximum intensity that is produced in its focal region. By limiting the intensity, one can prevent laser damage to bulk optical components or to sensitive photodetectors. This mechanism thus provides an alternative to current approaches of sensor protection based on optical power limiting.

Figure 1

Demonstration of small-scale filamentation (beam breakup into multiple filaments) in carbon disulfide. Top row: Near-field distribution at the output of the interaction region. Bottom row: Far-field intensity distributions. Pulse energies increase left to right: 100 nJ, 0.69 $\mu$J, 2.2 $\mu$J, and 5.0 $\mu$J in a 25-ps pulse. The diameter of the lowest-energy, near-field spot is 80 $\mu$m, and the diameter of its far-field pattern is 0.5 degree. One sees that under these experimental conditions, the spatial-coherence properties of the laser light are strongly diminished by the filamentation process.

Figure 2

Schematic diagram of the optical configuration used to study the transmission of a 532-nm laser pulse through a 10-mm-long CS${}_2$ cell.

Figure 3

Measured far-field diffraction angle (circles) and the predictions of our theoretical model (solid line) as functions of the incident pulse energy. The square-root dependence on pulse energy predicted by Eq. (4) is evident.