# Overcoming Challenges in Large-Core SI-POF-Based System-Level Modeling and Simulation
## 4 System Level Modeling: Two-Step and One-Step Approaches  
Having provided an overview of the fundamental building blocks needed to model and simulate a large-core POF system, we will now turn our attention to the utilization of the models in POF-based system-level simulations. Conceptually, the modeling approach is the standard hierarchical method in which the building blocks are at the lowest level and the system is at a level above. This allows us to assess the impact of the individual building blocks on the overall system performance. Moreover, the cumulative impact on performance due to propagation through the connected components comprising the system can be quickly evaluated. Until recently, commercial software packages did not include the capability to model and simulate large-core POFs at the system-level. This led us to develop a two-step simulation approach to meet our immediate need for system-level simulations [34; 56]. The first step uses the matrix representation of the components to calculate the output intensity distribution and frequency response of the system being studied. In the second step, system-level simulations are performed by introducing, in any system-level simulation environment, a black box with this frequency response. For example, let us imagine that we have a system consisting of a source, four fiber segments connected by ST connectors, followed by a detector. This scenario is depicted in Figure 6 for the more general case of \(k\) fiber segments, where \(k\) is a positive integer. As the scheme shows, both the spatial characteristics of the optical source and the photodetector are modeled as was described above and introduced into the POF system (first step). On the other hand, their temporal (frequency) characteristics are introduced in the system-level simulation (second step). Our implementation utilized the frequency-domain approach for the first step where all the components, including the fiber, are modeled with matrices. However, the equivalent time-domain approach would yield the same results. The system has an optical source in the transceiver that is modeled by its angular intensity in vector form, \(\mathbf{P_{s}}(\omega)\). The frequency dependence in this vector is flat, as the temporal characteristics of the transmitter are introduced in the second step. As for the fiber segments, they can be modeled with the corresponding propagation matrices \(\mathbf{M_{Li}}(\omega)\), \(i\) = 1,..., 4, while ST connectors can be modeled by characteristic matrices \(\mathbf{M_{ST}}\). Finally, matrix \(\mathbf{M_{det}}\) is the diagonal matrix to account for angles that are not captured in the detector area, as discussed above. As in the case of the transmitter, the frequency response of the receiver and amplifier electronics is introduced in the second step. The optical intensityat the output of the whole POF layout, \(\mathbf{P_{out}(\omega)}\), can then be calculated as the product of the matrices of every component of the POF link:  
\[ \begin{array}{ll}\mathbf{P_{out}(\omega)}&=\mathbf{M_{det}}\cdot\mathbf{M_{L4} }(\omega)\cdot\mathbf{M_{ST}}(\omega)\cdot\mathbf{M_{L3}}(\omega)\cdot\mathbf{M _{ST}}(\omega)\cdot\mathbf{M_{L2}}(\omega)\cdot\mathbf{M_{ST}}(\omega)\cdot \mathbf{M_{L1}}(\omega)\cdot\mathbf{P_{s}}(\omega)\\ &=\mathbf{M_{det}}\cdot\mathbf{F}(\omega)\cdot\mathbf{P_{s}}(\omega)\,\end{array}  \tag{27}\]  
where \(\mathbf{F}(\omega)\) is a single matrix that models the fiber link without the active components and all the individual matrices for each component can be derived as described in the previous sections. Additionally, connector misalignment, fiber bend and injection aspects can be easily accommodated by inserting their corresponding matrices at the appropriate points in Equation (27).