# Coupling of Modes in Step-Index Plastic Optical Fibers by Using D-Shape Technique
## 2 Modes and Coupling  
Mode coupling determines the energy between the modal contents in the POF. This phenomenon gradually changes the distribution of the input energy along the length of the fiber and consequently significantly impacts the transmission characteristics of the fiber [1; 16]. Mode coupling in optical fibers is primarily induced by various imperfections and inconsistencies arising during fiber manufacturing. These include microscopic bends and variations in the diameter of the fiber, irregularities at the core-cladding boundary, and fluctuations in the refractive index distribution. In mode coupling, there is a transfer from low-order to high-order modes. Low-order modes correspond to the light propagation paths that pass through the center of the fiber core. They have smaller angles of incidence relative to the fiber axis and therefore suffer fewer reflections at the interface between the core and cladding, resulting in straighter and more direct paths along the fiber. They are more likely to be guided at the core for longer distances than higher-order modes [17]. The energy transfer to the higher-order modes is continuous and co-occurs with mode coupling [1] up to the SSD at the Zs point. When the light power distribution in the POF reaches an SSD, it maintains a constant angular distribution of the output light power, regardless of the angular distribution of the fiber entering it. Figure 1 shows the POF angular light power distribution output when the light emitted by a laser is introduced into the fiber coupled to the manual rotation system (MRS) goniometer. Figure 1a illustrates that, for z < Zs, the distribution of angular light power in the POF changes depending on the angle at which light enters the POF (\(0^{\circ}\), \(\pm 5^{\circ}\), \(\pm 10^{\circ}\), \(\pm 15^{\circ}\), and \(\pm 20^{\circ}\)). In this figure, each curve is for an input angle. Figure 1b, when z > Zs, shows that the angular light power distribution of the POF is independent of the angle at which the light enters the fiber. This behavior indicates that for lengths z greater than Zs, the light of the POF reaches a state of mode stabilization, where the output light power distribution becomes the same for different injection angles. Using the D-shape promotes the condition shown in Figure 1b, with shorter POF sections compared to without the D shape. For applications such as those mentioned in Section 1, using POFs (plastic optical fibers) of shorter lengths offers significant advantages. These advantages are clearly represented in Figure 1b, which shows that shorter POFs are easier to use and consume less space, thereby providing an efficient solution for embedded systems. To solve the problem of modal dispersion, researchers have developed various techniques, which are listed in Table 1: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & **Method** & **Reference** \\ \hline Mode Conditioning & \
\begin{tabular}{c} To eliminate high-order modes, an element such as a lens or \\ a specialized diffuser is used at the beginning of the fiber to \\ control the way the light enters. \\ \end{tabular} & [18] \\ Offset Launch Technique & It involves coupling light off-center relative to the fiber’s \\  &
\begin{tabular}{c} Axis, helping to reduce modal dispersion. \\ These filters, attached to the fiber’s leading edge, allow \\ low-order modes to pass while blocking high-order ones. \\ Light sources with narrow spectra and high power can \\ minimize power transfer between modes. \\ This method modulates modal energy distribution, \\ Twist Processing for Mode Control & encouraging energy transfer from lower to higher-order \\ modes by twisting the fibers. \\ Refractive Index Profiling & Adjusting the fiber core’s refractive index during \\ production can reduce high-order mode excitation. \\ \end{tabular} & [19] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Techniques and methods used to manage and control modal dispersion in optical fibers. Figure 1: Output POF stretch for different conditions.