Nonlinear tunnel oscillations of light in spherical Bragg resonators
A weakly nonlinear regime of radial tunneling is theoretically considered for a light wave in a spherical dielectric Bragg resonator containing a set of ``shell'' eigenmodes (both TE and TM) with different azimuthal numbers $l\geq 1$, which are concentrated near a defect of the Bragg structure, several layers away from the origin. A single radial mode with $l=1$ is present at the resonator center, either TM or TE. Nonlinearity of the Kerr type in the main approximation is actual for the central mode only, while all the shell modes remain in the linear regime. The tunneling occurs between the central mode and the shell $l=1$ mode of the same symmetry. Nontrivial part of the dynamics of optical field is described by a Hamiltonian system of ordinary differential equations for complex vectors ${\bf C}_{1}(t)$ and ${\bf C}_{2}(t)$, which determine the magnitude and spatial orientation of the wave structures at the center and at the shell, respectively. Depending on ``asymmetry parameter'' of tunnel coupling, the system demonstrates different variants of nonlinear behavior.