Microdisk lasers have been invented and developed at Bell Labs over the past decade and the billiard model has been successfully used in designing the "optimal" cavity shape. We will show that a new class of billiard tables possessing an isolated caustic, which carries only periodic orbits, can be constructed using the methods of subriemannian geometry. We will also describe some important implications of this construction for the microdisk lasers, including the results of the wave equation simulations.