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Light transport in disordered systems can be described as a multiple scattering process in which light waves are multiply scattered by random variations of the refractive index of the material. This has close analogies with other transport phenomena, such as electrons in a conducting material, sounds waves in random structures, and even matter waves. A particularly interesting situation in light transport arises when optical amplification is included in the multiple scattering process. In this case, the intensity of the light waves increases during the multiple scattering. This can lead to an unstable situation wherein the overall gain exceeds the total losses. Multiple scattering and amplification form the two main ingredients to create what is called a random laser. This is a system in which a threshold exists above which gain becomes larger than the losses due to the multiple scattering process.
One can wonder how it is possible to speak of laser action in a material that is random and therefore, obviously has no structure that resembles a laser cavity. To that end, one has to keep in mind two important points. The first point is that light waves that propagate in a dielectric material, even if that material has a disordered structure, will not lose memory of their phase. The disorder will scatter the light in a complicated way, thereby creating very complex amplitude and phase fields. However, this process is well defined, and a specific configuration of the disorder will lead to a unique phase and intensity distribution that can be predicted and measured. One can even define optical modes of such random structures as the (complex) field patterns that are formed when the samples are illuminated with monochromatic light.
The second point to keep in mind is that a laser cavity, as such, is not essential to obtain coherent emission. The fundamental property of a laser that leads to coherent emission is not the cavity itself, but the gain saturation that it creates. The cavity creates a situation in which gain is larger than loss, which leads to a rapid growth of the intensity until the gain medium is depleted. It is this saturation that leads to second-order coherence by suppressing fluctuations of the intensity. [In terms of photon statistics, second-order coherence reflects a certain level of "antibunchingâ" of the photons induced by the gain saturation. The photons from a chaotic source are "bunched," meaning that they arrive in clusters. In a coherent beam, the photons are more smeared-out (antibunched) in time, meaning that the intensity fluctuations are reduced.]
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