# Integrated Components and Solutions for High-Speed Short-Reach Data Transmission
## 3 Receiver for Short-Reach Transmission Systems
### Stokes Vector Direct Detection  
Another advanced direct detection scheme, Stokes vector direct detection, has recently gained much attraction in beyond 100-Gbit/s short-reach and metro transmission systems. It has been proposed to realize linear complex optical channels as well as enhance transmission reach and system capacity. As depicted in Figure 6a, the structure I of Stokes vector direct detection applied one polarization beam splitter (PBS), one optical 90\({}^{\circ}\) hybrid and three balance photodetectors (BPDs) to obtain three important Stokes vectors (e.g., \(S_{1}\), \(S_{2}\), \(S_{3}\)). In fact, Stokes vector direct detection can be generalized by any three or four detections of polarization states as long as they were nonsingular superpositions of Stokes vector components. Here, Figure 6b showed a structure that consisted of one optical 90\({}^{\circ}\) hybrid and four single-ended PDs. The structure can provide four outputs obtaining \(|\)X\(|\)\({}^{2}\), \(|\)Y\(|\)\({}^{2}\), \(|\)X\(+\) Y\(|\)\({}^{2}\), and \(|\)X\(+\) iY\(|\)\({}^{2}\), and then these components can be linearly converted to the three components \(S_{1}\), \(S_{2}\), and \(S_{3}\) of Stokes vector. Another structure using four single-ended PDs and three polarizers is shown in Figure 6c, where the signal intensity of different polarization states are detected, and then the four outputs can be linearly converted to Stokes vector. The applications of these structures have been proposed and verified in various high-speed transmission systems. For example, [PERSON] et al. proposed  
Figure 5: Kramers-Kronig direct detection scheme; PD: photodetector; ADC: analog to digital converter; DSP: digital signal processing module.  
a three BPDs-based structure (structure I) for Stokes vector direct detection for the first time, and experimentally verified in a 224-Gbit/s PDM-PAM-4 transmission system over 10-km SMF assisted by a single 1310-nm laser and a silicon photonic intensity modulator [19]. Furthermore, this group proposed a novel reduced-complexity single-stage SSBI cancellation algorithm to enhance the transmission rate to 480-Gbit/s and transmission distance to 80-km SMF [101]. On the other hand, [PERSON] et al. further proposed another Stokes vector direct detection solution (structure II) based on four PDs and one optical hybrid [20], which was then verified in a 1T-Gbit/s PS-64 QAM 100-km transmission system assisted by three-dimensional signal field recovery [102]. Furthermore, [PERSON] et al. proposed a novel Stokes vector receiver configuration (structure III) with four PDs and three polarizers. Based on the configuration, the polarization tracking and demultiplexing operations had been successfully verified in polarization multiplexing IM/DD transmission systems [21]. Moreover, based on the receiver configuration, [PERSON] et al. proposed an efficient and low-cost simplified detection solution, which was demonstrated in 160-Gbit/s 2 \(\times\) PDM-PAM-4 transmission system over 25-km NZDSF [103]. Generally, the Stokes vector direct detection, which can realize two-dimensional even three-dimensional detection, provides a compromise between one-dimensional direct detection and four-dimensional coherent detection.