# Coupling of Modes in Step-Index Plastic Optical Fibers by Using D-Shape Technique
## 4 Experimental Results  
Determining the mode coupling coefficient, D, was the starting point for comparing the simulations and measurements. The variance in the CCD-detected optical signal beam distribution for various POF lengths was obtained to ascertain D. Utilizing the POF sections accessible in the laboratory, z-values of 5, 10, and 22 m were employed. The variance values were obtained with and without the D shape. Table 4 shows the variance values. After determining the variances, the values were subsequently inserted into Equation (2) to derive the modal coupling coefficient, as shown in Table 5.  
The values obtained for the D parameters are compatible with those of previous authors [7; 25; 28]. Figure 6a-g shows the experimental results of the output light power distribution of the POF ESKA SK40 without using the D shape for various input angles. The measurements were taken with 1, 15, 3, 5, 10, 22, and 27 m of POF stretches. Figure 6g shows the establishment of the SSD. This finding aligns with the simulations conducted through the tool developed and other previously published studies [25; 28]. The angular distribution of light power is a function of the POF input angle for all stretches considered [28]. The occurrence of SSD, as depicted in Figure 6g, in which the angular light power distribution of the POF output remains constant, materializes exclusively when the fiber length (z) exceeds the threshold length (Zs) [30]. The series of figures from 6a to 6g clearly demonstrate how the angular light power distribution changes with the extension of the POF's length (z), distinctly showing that the SSD is achieved at a length of 27 m, as specifically highlighted in Figure 6g. After taking the first measurements at the specified lengths, the D shape, always positioned at the same distance, x, from where the light is injected into the POF, was incorporated into the ESKA SK40 POF, as shown in Figure 5a. A 10 m section was applied using the device shown in Figure 4(b1) to insert the D shape into the POF. Figure 7 shows a change in the angular light power distribution compared to Figure 6e by inserting the D shape. The convergence of the angular light power distribution becomes visible, \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Stretch of the POF** & **The Variance in the Launch** \\  & **under Investigation** & **Beam Distribution \(\sigma^{2}\)** \\ \hline \multirow{2}{*}{POF without D-shape} & Z1 = 5 m & \(\sigma^{2}_{1}\) = 0.11328 \\ \cline{2-3}  & Z2 = 22 m & \(\sigma^{2}_{2}\) = 0.14279 \\ \hline \multirow{2}{*}{POF with D-Shape} & Z1 = 5 m & \(\sigma^{2}_{1}\) = 0.15354 \\ \cline{2-3}  & Z2 = 10 m & \(\sigma^{2}_{2}\) = 0.13203 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The variance in the launch beam distribution \(\sigma\)2 for POF ESKA SK40, with and without the D shape. \begin{table}
\begin{tabular}{c c} \hline \hline Mode coupling coefficient without the use of a D shape & 8.6794 \(\times\) 10\({}^{-4}\) (rad\({}^{2}\)/m) \\ \hline Mode coupling coefficient with the use of a D shape & 2.151 \(\times\) 10\({}^{-3}\) (rad\({}^{2}\)/m) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mode coupling coefficient, D, values with and without D-shaped applications in POF ESKA SK40. characterizing the SSD. The 10 m length obtained by the SSD when using the D shape aligns with the simulations and calculations of 10.4 m.  
Figure 6: Output light power distribution for the ESKA SK40 POP for various input angles without using D-shape (\(\lx@sectionsign\)\(=+-20\lx@math@degree\), \(\lozenge=+-15\lx@math@degree\), \(\Delta=+-10\lx@math@degree\), \(\Circle\)\(\equiv+-5\lx@math@degree\), and \(*=0\lx@math@degree\)). In the second part of the experiment, the ESKA CK30 POF, featuring the characteristics detailed in Table 3, was employed to implement the procedure on an alternative fiber. Stretches of 1, 3, 5, 10, 15, 20, and 30 m without a D shape were employed.