# POL-MUX System for Noncoherent Optical Networks
## 4 Proposal of a Wide-Band Passive Optical Network (WDM-PDM-PON)
### Design of the Dynamic Polarization Controller-DPC  
Due to the constantly changing angle of polarization in an optical transmission line, it is essential for the practical implementation of the POL-MUX to demultiplex signals in  
Figure 8: Block scheme of WDM-PDM-PON. a suitable way. As mentioned before, a dynamic polarization controller is able to quickly control changes in the polarization angle of the optical fiber and keep demultiplexed outputs automatically with minimal polarization crosstalk. Based on these requirements, a dynamic polarization controller was designed based on the patent in [3]. The block diagram of this controller is shown in Figure 9.  
The input polarization multiplexed signal goes through the DPC to the PBS. The demultiplexed signal goes through the coupler with a division ratio of 99:1, where 99 % of the signal goes to receivers RX1 and RX2 and 1 % goes to monitoring photodiodes PD1 and PD2. The optical signal is converted to an electrical signal and amplified. The electronic comparator compares the voltage levels of both photodiodes PD1 and PD2 and regulates the DPC via servo-engines that rotate polarization by wave plates. The control signal from the comparator provides feedback that maintains the polarization in an ideal setup. The described system is independent of the bit rate and the modulated formats utilized. The next advantage is that the system does not need to interrupt the distribution network, transmitters, receivers and many other components used on optical links [3]. Optical signals with orthogonal polarization TX1 and TX2 could be generated by one laser diode or by two different diodes that transmit on the same wavelength. Both signals are multiplexed by a polarization multiplex. During the transmission of the multiplexed signal in the optical fiber, the state of polarization is changed from linear to elliptical. Importantly, both signals are orthogonal to each other. Let us choose polarization planes on the input of the polarization beam splitter as \(x\) and \(y\). [PERSON]'s matrix of the polarization splitters is [6]:  
\[M_{x}=\frac{1}{2}\left[ \begin{array}{cccc}1&1&0&0\\ 1&1&0&0\\ 0&0&0&0\\ 0&0&0&0\\ \end{array} \right], \tag{3}\]  
\[M_{y}=\frac{1}{2}\left[ \begin{array}{cccc}1&-1&0&0\\ -1&1&0&0\\ 0&0&0&0\\ 0&0&0&0\\ \end{array} \right]. \tag{4}\]  
An optical signal \(i\) with an arbitrary state of polarization (SOP) can be expressed in [PERSON]'s space as [6]:  
\[\overset{\rightarrow}{S}_{i}=\left[ \begin{array}{c}S_{i0}\\ S_{i1}\\ S_{i2}\\ S_{i3}\end{array} \right]=\left[ \begin{array}{c}P_{i}cos2\chi_{i}cos2\varphi_ {i}\\ P_{i}cos2\chi_{i}sin2\varphi_{i}\\ P_{i}sin2\chi_{i}\end{array} \right], \tag{5}\]  
Figure 9: Block scheme of the dynamic polarization controller. where \(P_{i}\) is the optical power, \(\varphi_{i}\) is the angle of ellipticity (polarization) and \(\chi_{i}\) is the orientation angle of the \(i\)-th optical signal (see Figure 10). Behind the polarization beam splitter, the Stokes vectors along axes \(x\) and \(y\) are \(M_{x}\overset{\rightarrow}{S_{i}}\) and \(M_{y}\overset{\rightarrow}{S_{i}}\), respectively.