Mathematical analysis of bent optical waveguide eigenvalue problem

This work investigates a mathematical model of the propagation of lightwaves in bent optical waveguides. This modeling leads to a non-self-adjoint eigenvalue problem for differential operator defined on the unbounded domain. Through detailed analysis, a relationship between the real and imaginary parts of the complex-valued propagation constants was constructed. Using this relation, it is found that the real and imaginary parts of the propagation constants are bounded, meaning they are limited within certain region in the complex plane. The orthogonality of these bent modes is also proved. By the asymptotic analysis of these modes, it is proved that as r ->infinity the behavior of the eigenfunctions is proportional to 1/r.