# Coupling of Modes in Step-Index Plastic Optical Fibers by Using D-Shape Technique
## 5 Discussion and Bit Error Rate (BER) Test  
As mentioned in Section 1, tests were carried out on POF optical links to assess the effects of inserting or not inserting the D shape. The bit error rate (BER) values were obtained using the BER analyzer model BA 1500 Synthesis and the Firecomm's evaluation boards, specifically the FB2M5 KRR, with transmission rates of up to 250 Mbps. A 95% confidence level was chosen as the threshold for a specified bit error rate (BER) of 1.10\({}^{-9}\). This same confidence level is used to estimate the BER through statistical methods [34]. Thus, for a bit rate of 250 Mbps, the accumulation time was 12 s. Figure 11 shows the setup for the measurements.  
The BA 1500 BER analyzer has its clock connections, clock output, and clock input; the test data generated according to the chosen configuration (PRBS-7, Burst minimum length 32, and integration period 1 \(\times\) 10\({}^{9}\) bits) are sent through the outputs (Data Output) to the Firecomm's FB2M5 KRR evaluation board, where the data are converted from the electrical to the optical domain, passing through the POF and returning to the Data Input inputs.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **POF SI TORAY:** & **POF SI ESKA SK40** & **POF SI ESKA CK30** \\  & **PFU-CD1001-22E (REF [23])** & **MITSUBISHI RAYON** & **MITSUBISHI RAYON** \\ \hline The refractive index of the & 1.492 & 1.49 & 1.49 \\ core (n0) & & & \\ \hline Numerical aperture (NA) & 0.46 & 0.5 & 0.5 \\ \hline Transmission loss & 150 dB/Km @ 650 nm & 150 dB/Km @ 650 nm & 200 dB/Km @ 650 nm \\ \hline Mode coupling coefficient, D & Unstrained 7.3 \(\times\) 10\({}^{-4}\) & Without D shape 8.6794 \(\times\) 10\({}^{-4}\) & Without D shape 1.191 \(\times\) 10\({}^{-3}\) \\ (rad\({}^{2}\)/m) & & & With D shape 2.151 \(\times\) 10\({}^{-3}\) & With D shape 2.976 \(\times\) 10\({}^{-3}\) \\ \hline Mode Stabilization Length, & Unstrained 49 (experimental) & Without D shape—27 & Without D shape 20 \\  & 26 (calculated) & (experimental) & (experimental) \\  & & 25.94 (calculated) & 19.3 (calculated) \\ Zs (m) & & & With D shape 10 m & With D shape 5\({}^{-}\)10 \\  & 1.46 (calculated) & (experimental) & (experimental) \\  & 10.4 (calculated) & 7.57 (calculated) \\ \hline Core diameter (mm) & 1000 \(\mu\)m & 980 \(\mu\)m & 735 \(\mu\)m \\ \hline \end{tabular}
\end{table}
Table 8: Comparative analysis of Zs reduction utilizing D shape and Strained techniques.  
Figure 11: (**a**) Image of setup for BER evaluation. (**b**) Ber analyzer and Firecomms evaluation connection diagram.  
From Table 9, one can see the mode equilibrium effect on light POF propagation. The BER values, without a D shape, increase as the optical fiber length increases, decrease as the length approaches Zs, and begin to increase again after Zs. For the CK-30 POF, the Zs equals 19.3 m, as shown in Table 7.  
With a D shape, the BER values reveal the effects of shortening the Zs length due to the D shape introduction. First, all of the BER values are smaller than the values obtained without a D shape. Second, the BER values increase as the optical fiber length increases and decrease around the new Zs values as before. The BER increases as expected after the new Zs value of 10 m, since the effects of the dispersion mode arise with the optical fiber length.  
For the shortest length in Table 8, despite a low value of the BER, resulting in reduced mode dispersion effects and attenuation, the D shape reduces it to a lower value.  
Figure 12 shows the screen of the BER BA 1500 analyzer when evaluating the POF CK30 at 10 m with and without the D format. We observed the following values: 9.38 \(\times\) 10\({}^{-6}\) without the D format in Figure 12a and 2.05 \(\times\) 10\({}^{-8}\) with the D shape in Figure 12b.  
If we consider the lengths of the POF to be beyond the Zs length, we note in our experiments that the D shape still improves the bit error rate (BER). In a 30 m segment, we observed an improvement in the BER from 1.03 \(\times\) 10\({}^{-6}\) to 4.83 \(\times\) 10\({}^{-7}\).