Applications
The most practical application of theory of quantum billiards is related with double-clad fibers. In such a fiber laser, the small core with low numerical aperture confines the signal, and the wide cladding confines the multi-mode pump. In the paraxial approximation, the complex field of pump in the cladding behaves like a wave function in the quantum billiard. The modes of the cladding with scarring may avoid the core, and symmetrical configurations enhance this effect. The chaotic fibers provide good coupling; in the first approximation, such a fiber can be described with the same equations as an idealized billiard. The coupling is especially poor in fibers with circular symmetry while the spiral-shaped fiber—with the core close to the chunk of the spiral—shows good coupling properties. The small spiral deformation forces all the scars to be coupled with the core.
Read more about this topic: Dynamical Billiards