Modelling and analysis of fibre microlenses with ray-tracing and finite-difference methods

Fibre optic microlenses are small optical elements formed on the end-faces of optical fibres. Their dimensions range from a few tens to hundreds of micrometres. In the article, four optical fibre microlenses are modelled and analysed. Microlenses are used for light beam manipulation and quantitative metrics are needed to evaluate the results, for example, the size of focusing spot or intensity distribution. All four lenses tested are made of rods of the same refractive index; they were welded to a single-mode fibre. Two modelling methods were used to analyse the lenses: ray-tracing and finite-difference time-domain. The ray-tracing algorithm moves rays from one plane to another and refracts them on the surfaces. Finite-difference time-domain consists of calculating Maxwell’s equations by replacing spatial and temporal derivatives by quotients of finite differences. In this paper, the results of the microlenses analyses obtained from ray-tracing and finite-difference timedomain methods were compared. Both mets of analysis showed the presence of undesirable side lobes related to lens design, namely rods too long for lens fabrication. The test results were compared with the measurements made with the knife-edge method. The use of a single tool to determine parameters of an optical fibre lens does not allow for precise determination of its properties. It is necessary to use different tools and programs. This allows a complete analysis of the beam parameters, letting us find the causes of technical issues that limit the performance of the lenses.