In order to optimize ultra-small gradient-index (GRIN) fiber probes and provide a theoretical prediction for the fabrication of such probes with high performance, focusing performance of the GRIN fiber probe is further analyzed based on the optical characteristic parameters. According to the optical model of the GRIN fiber probe and its mathematical expressions of characteristic parameters, the three-dimensional (3-D) function diagram is used for analyzing the impact of the lengths of probe components on the characteristic parameters. Partial derivatives of the mathematical expressions of characteristics are derived to analyze the mutation of focusing performance caused by the different lengths of probe components. According to the analytical results, our predictions suggest that focusing performance could be reflected through the 3-D function diagram between the characteristic parameters and the continuous change of the lengths of probe components. In addition, mutation occurs in the focusing performance of the GRIN fiber probe when the length of probe components changes. The research results are of practical guiding significance for the fabrication of GRIN fiber probes requiring specific optical focusing performance.
A numerical method is investigated to design gradient-index (GRIN) fiber probes. The GRIN fiber probe is composed of
a single mode fiber (SMF), a no-core fiber (NCF), and a GRIN fiber lens. The optical software GLAD is adopted to
simulate the optical performance of the probe. The simulation results show that, given the length of the GRIN fiber lens
0.1mm and the length of the NCF 0.36mm, the working distance is 0.73mm and the focus spot size 33μm, which are well
agreement with the experimental data. As a result, the proposed numerical method is validated to be effective to design
such GRIN fiber probes.