In this paper we present a general approach to determine the stability of a laser cavity which can include non-conventional phase transformation elements. We consider two pertinent examples of the detailed investigation of the stability of a laser cavity firstly with a lens with spherical aberration and thereafter a lens axicon doublet to illustrate the implementation of the given approach. In ...

We investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium-u...

Line-tension-induced scenario of heterogeneous nucleation is studied for a lens-shaped nucleus with a finite contact angle nucleated on a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the free energy of a critical nucleus can be separated from the usual volume term. By comparing the free energy of a lens-shaped critical nucleus of a finit...

We consider the free energy of confinement for a flexible self-avoiding polymer inside a spherical cavity. Accurate numerical calculations allow us to arbitrate between competing scaling predictions. We find that, for moderate confinement, the free energy exhibits a power-law dependence on cavity size that is different from what is observed for planar and cylindrical confinement. At high monome...

In this paper, the problem involving a half-space or an infinite space with a cylindrical or spherical cavity have been subjected to certain boundary conditions. The material is elastic and has an inhomogeneity in the direction perpendicular to the boundary surface for the halfspace problem with a cylindrical or spherical cavity. The system of fundamental equations have been solved by using an ...