# Coupling of Modes in Step-Index Plastic Optical Fibers by Using D-Shape Technique
## 3 Material and Methods, Components, and Experimental Setup
For the example in Figure 3a, this length is around 30 m. This length permits the investigation of light propagation at various light-entering angles in the POF. As one can see in Figure 3b,  
Figure 3: Screenshots of the application developed. (**a**) The simulation result with a single POF length and four different angles of light entering the POF; (**b**) simulation with a single angle of light entering the POF and four different POF lengths. the output power distribution is almost constant for POF lengths longer than 30 m for several entering angles. Figure 3a,b shows that the POF lengths determine the mode stabilization for all input angle conditions. This result was compared to experimental data, showing excellent concordance. A preliminary step in conducting simulations that elucidate the modal behavior within the POF involves determining the mode coupling coefficient, denoted as \"D\". This coefficient quantifies the rate of energy transfer between the various modes. The method described in the literature was employed to calculate D [28]. In order to measure the variance in the light intensity at the outputs of the POF with lengths z1 and z2 and accurately calculate the coupling factor D as established in Equation (3), we implemented the methodology described below:  
1. Collecting the light: The first step consists of collecting the light at the ends of the POFs with lengths z1 and z2, where z1 and z2 are lengths of the POF with z > 0 [25]. To capture the light at the exit of the POF, a CCD is positioned 2 mm from the end face of the POF. 2. Image processing: We then transferred the image obtained by the CCD to ImageJ 1.53r software. This platform allows for not only detailed visualization of the image but also precise extraction of the numerical data related to the angular light power distribution. 3. Statistical analysis in Origin: With the angular light power distribution curve data obtained by far-field imaging using ImageJ software, we proceeded to perform a statistical analysis using Origin 2019b software. This software was used to calculate the variance in the angular light power distribution for lengths z1 and z2 of the POF. This method ensures the accuracy of the variance data obtained, which is confirmed by the literature [29; 30; 31; 32]. These variance values are essential and are applied directly to Equation (3), providing a solid basis for determining the coupling factor. The integration of these advanced techniques and tools, from light collection to statistical analysis, establishes a reliable protocol for investigating the transmission characteristics of POFs. \[D=\frac{\sigma_{zz-}^{2}\,\sigma_{z_{1}}^{2}}{2(z_{2}-z_{1})} \tag{3}\]  
To corroborate the experimentally determined and simulated Zs values, Equation (4), as defined in previous studies [30; 31; 32; 33], was employed to ascertain the Zs length. \[Zs=\frac{0.2}{D}*\left(\frac{NA}{n_{1}}\right)^{2} \tag{4}\]  
where D is the mode coupling coefficient, NA is the numerical aperture, and n\({}_{1}\) is the refractive index of the core. This study adopted the D-shape to induce SSD in shorter POF segments instead of incorporating additional components into the fiber. The process involved the development of a specialized device, which served as the basis for grinding the fiber body to achieve the desired D-shaped effect. Two devices with depths of 0.5 mm and 0.75 mm were fabricated. Figure 4a shows a steel device specially developed for grinding the POF, equipped with two supports that ensure the POF is securely fixed during the process. Figure 4(b1,b2) show, in detail, the cavities of this device, designed to precisely fit POFs with diameters of 1 mm and 0.75 mm, respectively. During manual sanding, the POF is accommodated in these cavities, leaving only the area to be sanded exposed. Figure 4d shows how the POF is positioned in the cavity prepared for sanding, while Figure 4c highlights the result of the POF after receiving the D-shaped finish. POFs with 1 mm and 0.75 mm diameters were utilized in this study.