Chaotic microlasers

Since the mid 1990s, Chaotic microlasers have been established as an alternative to the conventional and well-known Fabry-Perot lasers in the course of the ongoing miniaturization of devices. Those microdisk lasers (see for example McCall et al.(1992) or Vahala (2003)) allow one to keep high quality (or Q) factors which is important, e.g., in micro- and nanophotonic applications. Chaotic microlasers are typically realized as so-called microcavity lasers, i.e., essentially planar systems (the third dimension can be neglected) of slightly deformed disk shape, as shown in the lowest panel of Figure 1. They have to be distinguished (at least for the purpose of this article) from other microlasers such as VCSELs (vertical cavity surface emitting lasers, truly three-dimensional structures similar to a vertical Fabry-Perot set-up, with typically mid-range Q factors). Besides the quest for developing high Q microcavity lasers driven from the experimental and application-oriented point of view, microcavity lasers open actually a new venue for the established fields of chaos and quantum chaos: They represent open two-dimensional billiards systems. Therefore, the theoretical description of chaotic microlasers turns out to be very closely related to the fields of dynamical systems, chaos and quantum chaos where hard wall, closed billiards have been used as model systems for a long time. We shall see below how close the relation is - and one important difference: As light may escape by diffraction, microcavity lasers are intrinsically open systems. The hard-wall case, i.e., the closed billiards typically studied in the field of quantum chaos, is only reached in the limit of a (infinitely) large refractive index when the condition of total internal reflection is always fulfilled, and when evanescent leakage of light can be neglected