## 5 Coupling Efficiency Experiment and Discussion  
To measure the coupling efficiency of the GRIN fiber probe and HC-PCF, an experimental system was built to test the probes above. Both the GRIN fiber probe and HC-PCF are fixed in a V-type groove of micro-displacement platform. The coupling distance between two fibers can be adjusted by a micro-displacement platform. An amplified spontaneous emission (ASE) laser is used as the light source for the GRIN fiber probe and Beam Analyzer is used as a detector to measure the power of emitted light from HC-PCF. The schematic of the experimental system is shown in Figure 3.  
ASE-C-11-G of HOYATEK Company was adopted as the ASE light source, which has a central wavelength ranging from 1527 nm to 1565 nm. We selected HC19-1550-01 of NKT Photonics Company as HC-PCF. This fiber has a core radius of 10 \(\upmu\)m, outer cladding diameter of 115 \(\upmu\)m, and attenuation \(<\)0.03 dB/m. We cut 5 cm of this fiber for the experiment to reduce the effect of attenuation. XYZW76H-25-0.25 and MGA2 micro-displacement platforms of Shanghai Lianyi Company were used to adjusted the coupling distance between the two fibers, which can achieve a resolution of 1 \(\upmu\)m displacement within 25 mm in the direction of the measurement axis. The experimental system setup is shown in Figure 4a and the detail of the coupling part marked with a red frame is shown in Figure 4b. As shown in Figure 4a, the GRIN fiber probe connected to the ASE laser was mounted in the V-groove of the micro-displacement platform, and the emitted power \(p_{0}\) was detected by the Beam Analyzer. After that, the GRIN fiber probe and HC-PCF were installed according to the assembled method in Figure 4b. The micro-displacement platform was adjusted to align two fibers until the emitted power received by the Beam Analyzer was at the maximum. The micro-displacement platform fixed with HC-PCF was moved from the position where the distance between the GRIN fiber probe and HC-PCF was zero to 1 mm at intervals of 10 \(\upmu\)m. The emitted power \(p_{\text{t}}\) at each position was measured five times and the average value was used as the result. As a comparison, the coupling efficiency between SMF and HC-PCF was also measured following the same procedure as above by replacing the GRIN fiber probe with SMF. Figure 4: Coupling efficiency testing system: (**a**) Experimental system setup; (**b**) detail of coupling part. Figure 3: Schematic of the experimental system. In fact, the start position can only make two fibers as close to each other as possible, but the distance cannot be zero. It is difficult to tighten two fibers completely because it is likely to damage the porous structure of HC-PCF. Therefore, coupling distance correction of the result is necessary. We used a 40\(\times\) magnifying glass to take pictures at the start position and measured the initial distance by image processing. The image processing is shown in Figure 5.  
Figure 5a is an original image taken by means of a magnifying glass. We extracted the pixel value in a black channel and adopted binarization processing, and the result is showed in Figure 5b. The detail in pixels marked with the frame is shown in Figure 5c. The outer diameter of 125 \(\upmu\)m of the GRIN fiber probe that has a clear outline is used as the reference to calculate the initial distance. The initial distance between the two can be calculated as 125*14/21 \(\upmu\)m, which is about 80 \(\upmu\)m. The initial distance in a comparison experiment that used SMF is processed in the same way. To avoid accumulative error due to the fabrication errors in Table 1, the actual waist radius and working distance of GRIN fiber probes from No. 6-No. 10 were used as the input for calculation. The theoretical coupling efficiency of the GRIN fiber probe with a ratio \(\gamma\) of 0.95 according to Equation (5) and the experimental results that have been corrected are shown in Figure 6. The theoretical and experimental results of the SMF fiber are plotted in this figure as a comparison.