Berenger and leaky modes in optical fibers terminated with a perfectly matched layer

Recently, it has been demonstrated that some field problems involving optical fibers can be solved more easily by enclosing the fiber with a perfectly matched layer (PML). In this paper, we investigate the dispersion relation for the transverse electric (TE), transverse magnetic (TM), and hybrid modes of such a fiber-PML combination. Within a good approximation, two types of modes can be distinguished: the leaky type, only depending on the fiber characteristics, and the so-called Berenger type, mainly depending on the PML characteristics. Analytical expressions for the propagation constants of the higher order modes are derived and compared with the exact values for two relevant examples: a vertical cavity surface emitting laser (VCSEL) cavity and a monomode fiber.