Performance comparison among three different Stokes vector direct-detection receivers

Data center interconnect has stimulated the research on the short-reach communications with data rate beyond 100G per wavelength and transmission distance of hundreds of kilometers. Aiming at the high-speed short-reach communications, we recently proposed the Stokes vector direct detection (SV-DD) that realizes a linear complex optical channel similar to the coherent detection. In SV-DD, the transmitter places the signal and the carrier onto the orthogonal polarizations, while the receiver achieves the polarization insensitive 3-D detection in the Stokes space with the digital signal processing enabled polarization acquisition. SV-DD achieves 100% spectral efficiency with reference to the single-polarization coherent detection, and simultaneously attains the receiver phase diversity and the cancellation of photo-detection nonlinearity. We experimentally demonstrate the SV-DD signal transmission over 160-km standard single-mode fiber at data rates of both 80 and 160-Gb/s. SV-DD significantly decreases both the system hardware and DSP complexity compared with the polarization multiplexed coherent detection, while increases the system spectrum efficiency compared with the conventional intensity modulation direct detection. Therefore, SV-DD offers a cost-effective solution for the 100G per wavelength and beyond metropolitan area network (MAN). It also owns the potentials to be deployed in the future high-speed passive optical network (PON).

We propose a novel detection scheme called Stokes vector direct detection (SV-DD) to realize high electrical spectral efficiency and cost-effective optical communication for short and medium reach. With SV-DD, the signal is modulated in only one polarization and combined with the carrier in the orthogonal polarization for fiber transmission. At reception, the combined signal is detected in Stokes space by three or four photo-detectors. Compared with conventional DD technique, SV-DD is resilient to both chromatic dispersion and signal-to-signal beat noise. Furthermore, SV-DD does not require polarization tracking or narrow band optical filtering for carrier extraction. In this paper, we present for the first time the numerical analysis and experimental demonstration of single-carrier SV-DD. We report 62.5-Gb/s data rate single-carrier SV-DD transmission over 160-km SSMF using 12.5-Gbaud 32-QAM modulation.

We introduce a three-dimensional modulation format using a Stokes-vector direct-detection system, where a pulse amplitude modulation (PAM) signal is polarization multiplexed with a quadrature amplitude modulation (QAM) signal. The phase reference of the PAM signal enables the retrieval of the phase information of the QAM signal using a Stokes vector receiver (SVR). A dual-polarization in-phase–quadrature modulator is employed to generate QAM-PAM optical signals with chromatic dispersion precompensation. We show direct detection of dual-polarization 16QAM-PAM2 and 16QAM-PAM4 signals delivering 280 and 336 Gb/s (net bit rate 233 and 280 Gb/s) below the soft-decision forward error correction threshold of 2 $\times$ 10 $^{-2}$ at 320 and 80 km, respectively. In addition, we study system performance at different modulation formats and symbol rates. Our findings indicate that increasing the order of modulation formats of the QAM signal is better than increasing that of the PAM signal to achieve the same bit rate. Finally, the performance of a 56 Gbaud 16QAM signal with PAM2 modulation on one polarization and a 56 Gbaud 16QAM signal with a pilot carrier on the orthogonal polarization detected with an SVR is experimentally investigated.

We review the optical direct detection subsystems based on the Stokes vector receiver (SV-R), which is fit for a variety of modulation formats in Stokes space. SV-R accommodates 2-dimension (2-D) or 3-D detection, greatly increasing the spectrum efficiency.

We propose a hybrid optical Hilbert receiver and Stokes vector receiver (OH-SVR) capable of phase and polarization diversity. We experimentally demonstrate single-wavelength direct detection at 1.6-Tb/s and 1.56-Tb/s line rates at BTB and after 10-km standard single-mode fiber transmission for data-center interconnects.

The state of polarization (SOP) is the key characteristic of light; its evaluation is typically based on measurements of the Stokes parameters. However, conventional approaches often have bulky and complex optical systems with long acquisition times. In this Letter, an ultracompact polarimeter based on dielectric metasurfaces is proposed. The pixel of the proposed metasuface has four areas; each area acts not only as a polarization separator, but also a flat focusing lens. It can acquire a certain polarization component of the incident light and focus the component on the receiver. Therefore, the Stokes parameters of the incident light can be immediately determined through the data from the receiver, fully describing its SOP. The incident waves with different SOPs are simulated to demonstrate that the reconstructed Stokes parameters are in good agreement with the original ones.

The detection technology of infrared polarization has gained significant attention due to its ability to provide better identification and obtain more information about the target. In this paper, based on the expression of the full polarization state in Stokes space, we designed micro-nano metasurface functional arrays to calculate the polarization state of the incident light by reading the Stokes parameters (a set of parameters that describe the polarization state). Metalens with linear and circular polarization-dependent functions are designed based on the propagation and geometric phases of the dielectric Si meta-atoms in the infrared band, respectively. The device exhibits a high polarization extinction ratio. The influence of incident angle on polarization-dependent metalens is discussed, and the analysis of incident angle is of great significance for the practical application. An infrared six-foci metalens is proposed, each corresponding to the Poincaré sphere's coordinate component (a graphical polarization state method). By matching the six polarization components of the incident light and the Stokes parameters, the polarization detection function can be realized by calculating the polarization state of the incident light. There is a slight error between the theoretical value and the calculated value of the unit coordinate component of the Stokes parameters. At the same time, the intensity distribution of different incident light polarization azimuth angles and ellipticity angles on the focal plane agrees with the theory. The advantage of the device is that the polarization state of the incident light can be directly calculated without passing through other components. The six-foci metalens have potential applications in polarization detection and imaging, space remote sensing, etc.

Stokes parameters (S) on the Poincaré sphere are very useful values to describe the polarisation state of photons. However, the fundamental principle on the nature of polarisation is not completely understood, yet, because we have no concrete consensus on how to describe spin of photons, quantum-mechanically. Here, we have considered a monochromatic coherent ray of photons, described by a many-body coherent state, and established a fundamental basis to describe the spin state of photons, in connection with a classical description based on Stokes parameters. We show that a spinor description of the coherent state is equivalent to Jones vector for polarisation states, and obtain the spin operators (Ŝ) of all components based on rotators in an SU(2) group theory. Polarisation controllers such as phase-shifters and rotators are also obtained as quantum-mechanical field operators to change the phase of the wavefunction for polarisation states. We show that the Stokes parameters are quantum-mechanical average of the spin operators, S=⟨Ŝ⟩.

We propose the Stokes vector direct detection (SV-DD) algorithm to achieve photo-detection nonlinearity cancellation and phase diversity. A 160-Gb/s single-polarization modulated SV-DD signal is successfully received after 160-km SSMF transmission with 7.76-bit/s/Hz electrical spectrum efficiency.

Demodulation of polarization-modulated signals can be done via Stokes-vector direct detection. We analyze the receiver sensitivity for the multi-level polarization-modulation format having the cubic-lattice constellation in the three-dimensional Stokes space.

Split ratio is an important parameter for permanent magnet brushless motors (PMBLM) since it have significant influence on torque and loss. The split ratio of low-speed PMBLM has been optimized analytically in existing papers, while the iron loss is neglected. However, the iron loss in high-speed PMBLM can not be neglected. The split ratio and the maximum flux density in the stator iron is relate to both the copper loss and the iron loss closely. The split ratio, togerther with the maximum flux density in the stator iron, is optimized for maximum torque. An analytical model to determine the optimal combination of the split ratio and the maximum flux density in the stator iron for high-speed PMBLM is proposed in this paper. The analytical results are verified by finite element analysis.

According to different transmission distances, application scenarios of a data center mainly include intra- and inter-data center optical interconnects. The intra-data center optical interconnect is considered as a few kilometers optical interconnect between servers and racks inside a data center, which accounts for nearly 80% of data traffic of a data center. The other one, inter-data center optical interconnect, is mainly applied in tens of kilometers data transmission among different data centers. Since data exchange in data centers generally occurs between many servers and racks, and a lot of transmitter and receiver components are required, optical interconnects become highly sensitive to component costs. In this paper, we firstly review the development and applications of mainstream transmitter components (e.g., VCSEL, DML, EML, MZM, and monolithic integrated transmitter) and receiver components (e.g., single-end photodetector, Kramers-Kronig receiver, Stokes vector receiver, and monolithic integrated receiver), which have been widely applied in short-reach transmission systems. Then, two types of integrated solutions including simplified detection scheme and transceiver integration scheme are presented in detail. Finally, we summarize and discuss the technological and component options for different transmission distances. We believe that monolithic integrated components, especially transceiver integration, will become a powerful solution for next-generation high-speed short-reach transmission systems.

Split ratio optimization of high torque density PM BLDC machines considering copper loss density limitation and stator slot leakage

To describe the state of polarization (SOP) of light, the Stokes parameters are obtained using intensity measurements made at different component polarization states. Using these Stokes parameters, complex field distributions called Stokes fields can be synthesized, and the phase singularities present in these Stokes fields are called Stokes vortices. The SOP of a Stokes vortex can be either linear or circular at the singular point. Of the three types of Stokes vortices, only one of them has handedness associated with it. We show here that changing the handedness of this Stokes vortex results in index sign inversion for the other two types of Stokes vortices. To accomplish handedness inversion without Stokes index sign inversion, a new phase engineering method is introduced here. The current study may unfold applications in the optical chirality measurement and structured illumination microscopy.

In the fall of 1989 a series of flights were made to compare backscatter measurements performed by different lidars and a second flight may be made in the spring of 1990. The lidars to be compared may be monostatic and bistatic systems and will transmit light of one state of polarization and analyze received light in a different state of polarization. In this paper the nature of the signals will be analyzed by a vector-matrix theory where the light is represented by (4x1) Stokes vectors and the interaction with the atmosphere is represented by a (4x4) Mueller matrix. In each apparatus a value for β, the volume backscatter coefficient, is measured and it will be sums of differences of certain components of the β^ matrix which will depend upon the polarization properties of the laser. Pritchard and Elliott1 have performed a similar analysis for an atmospheric polarimeter but they studied a fixed target of magnesium oxide. This discussion will assume a pulsed lidar (rectangular pulse of width τ) so a thin slab of the atmosphere of thickness cτ/2 centered about Rs=c(t/2−τ/2) is examined.