# POL-MUX System for Noncoherent Optical Networks
## 1 Introduction
A POL-MUX can thus be used not only for doubling the bandwidth but also for reducing the influence of PMD, which has a negative effect in the form of polarization crosstalk [7]. POL-MUX system was the subject of research mostly in the 1990s and plenty of research groups were interested in this topic. Although it allows doubling of bandwidth and brings many advantages in comparison with other known multiplexing techniques, due to difficult demultiplexing, it was no longer prospective for further development, and WDM systems played the main role in the field of optical networks for many years [8; 9; 10; 11; 12; 13]. The renaissance came after 2000, when the group of [PERSON] et al. [5; 6] engaged in research of POL-MUX systems using an all-optic scheme for polarization demultiplexing. Nevertheless, it was not employed in optical data networks and real a comeback occurred with the development of coherent high-speed networks with direct detection system, digital signal processing and multistate modulation formats. Many groups were interested in this topic [14; 15; 16; 17; 18], e.g., [PERSON] et al. studied synchronous demodulation of coherent 16-QAM with feedforward carrier recovery [19], [PERSON] et al. described coherent 16 quadrature amplitude modulation (16 QAM) Optical Communication Systems [20], [PERSON] et al. examined spectrally-efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM [21]. Finally, direct detection systems with digital signal processing and X-QAM modulations were deployed into real high-speed transport optical networks, with high tolerance to negative dispersions effects [22]. On the other hand, there is also a disadvantage: difficult demultiplexing caused by changing the polarization angle and state of polarization. The principle of the POL-MUX system, shown in Figure 1 works only in laboratory environments. Under real conditions, the system must react to real-time polarization changes, such as those regarding the angle of polarization. For this purpose, a dynamic polarization controller could be used. In  
Figure 1: Principle of the polarization multiplex. coherent high-speed networks, a direct detection system is used, and demultiplexing is performed directly in the receiver via digital signal processing (DSP). Currently, 100 G transmission systems use POL-MUXs with coherent detection and multistate modulation formats [23]. The important parameters of the polarization multiplex are as follows [24]:  
* Degree of polarization (DOP): The degree of polarization is given by: \[DOP=I_{pol}/\left(I_{pol}+I_{unp}\right)\qquad[-],\] (1) where \(I_{pol}\) and \(I_{unp}\) are intensities of polarized and nonpolarized light, respectively. If \(DOP=0\), we can say that the light is nonpolarized; if \(DOP=1\), the light is fully polarized. If the light is between 0-1, it is partially polarized. * Polarization extinction (PER): The polarization extinction ratio is an important parameter given by the ratio between the optical powers in both polarization planes. It is defined by the ratio of the power in the principal polarization mode to the power in the orthogonal polarization mode after propagation through an optical system, expressed in dB [24]. \[PER=10 log_{10}\frac{P_{principal}}{P_{orthogonal}}.\qquad[dB],\] (2)
* Polarization dependent loss (PDL): The polarization-dependent loss is a parameter that specifies the maximal change in attenuation caused by polarization changes in optical fibers; this parameter is given also in dB.