Tapered- and straight-core fiber microlenses of hyperbolic shape are studied with the segmented beam propagation method (Se-BPM). This new formulation extends to a large scale the finite-difference time-domain method for calculating propagation of the wave field in guiding systems. It is based on partitioning an entire computational domain into subdomains along the direction of propagation. The Helmholtz equation can be solved directly for each subdomain, and an iterative procedure is used to propagate the field from one subdomain to another. The Se-BPM is compared with other approaches that are commonly used to analyze straight-core fiber microlen devices in the paraxial approximation. We deal mainly with small-spot-size fiber microlenses where this approximation does not apply. We show that the emergent beam is not Gaussian in the far field. Instead of the usual far-field characterization we propose a near-field characterization of the fiber microlens. This is possible with the near-field scanning optical microscopy technique.
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