Optical Transmission Systems based on the Nonlinear Fourier Transformation

Solitons are stable pulse shapes, which propagate linearly and maintain their shape despite the highly nonlinear fiber optical channel. A challenge in the use of these signal pulses in optical data transmission is to multiplex them with high efficiency. One way to multiplex many solitons is the nonlinear Fourier transform (NFT). With the help of the NFT, signal spectra can be calculated which propagate linearly through a nonlinear channel. Thus, in perspective, it is possible to perform linear transmissions even in highly nonlinear regions with high signal power levels. The NFT decomposes a signal into a dispersive and a solitonic part. The dispersive part is similar to spectra of the conventional linear Fourier transform and dominates especially at low signal powers. As soon as the total power of a signal exceeds a certain limit, solitons arise. A disadvantage of solitons generated digitally by the NFT is their complex shape due to, for example, high electrical bandwidths or a poor peak-to-average power ratio. In the course of this work, a scalable system architecture of a photonic integrated circuit based on a silicon chip was designed, which allows to multiplex several simple solitons tightly together to push the complex electrical generation of higher order solitons into the optical domain. This photonic integrated circuit was subsequently designed and fabricated by the Institute of Integrated Photonics at RWTH Aachen University. Using this novel system architecture and additional equalization concepts designed in this work, soliton transmissions with up to four channels could be successfully realized over more than 5000 km with a very high spectral efficiency of 0.5 b/s/Hz in the soliton range

Tackling Problems of Maintenance and Evolution in Industry 4.0 Scenarios Using a Distributed Architecture

Growing complexity in Industry 4.0 environments goes hand in hand with an increasing number of vulnerabilities. Due to internal and external influences, these vulnerabilities can cause a negative effect on the production process as well as the finished product. These influences include e. g., defective machine tools, deviations in quality or configuration changes of an assembly line, which in turn require to adjust the model and the workflow of the respective facility to prevent risks to human health or minimise costs due to production stops. To evaluate the necessity of a novel approach to handle these vulnerabilities and influences along with their subsequent system adaptation, three emerging problems are identified and provide the basis for the discussion of a distributed architecture that aims to facilitate the evolution of context models, workflows and configurations while allowing for reasonable involvement of human operators

Mitigation of Nonlinear Impairments by Using Support Vector Machine and Nonlinear Volterra Equalizer

A support vector machine (SVM) based detection is applied to different equalization schemes for a data center interconnect link using coherent 64 GBd 64-QAM over 100 km standard single mode fiber (SSMF). Without any prior knowledge or heuristic assumptions, the SVM is able to learn and capture the transmission characteristics from only a short training data set. We show that, with the use of suitable kernel functions, the SVM can create nonlinear decision thresholds and reduce the errors caused by nonlinear phase noise (NLPN), laser phase noise, I/Q imbalances and so forth. In order to apply the SVM to 64-QAM we introduce a binary coding SVM, which provides a binary multiclass classification with reduced complexity. We investigate the performance of this SVM and show how it can improve the bit-error rate (BER) of the entire system. After 100 km the fiber-induced nonlinear penalty is reduced by 2 dB at a BER of 3.7 × 10 −3 . Furthermore, we apply a nonlinear Volterra equalizer (NLVE), which is based on the nonlinear Volterra theory, as another method for mitigating nonlinear effects. The combination of SVM and NLVE reduces the large computational complexity of the NLVE and allows more accurate compensation of nonlinear transmission impairments

Additive manufacturing technologies for EUROFER97 components

By uncoupling the manufacturability from the design process, additive manufacturing of the baseline material EUROFER97 can open significant design freedom for divertor and breeding blankets in fusion technology. As additive manufactured components are known to possess unique microstructures compared to EUROFER97 from standard technologies, the aim of this paper is to investigate additive manufactured EUROFER97 components and the influence of post processing steps on their microstructure and mechanical properties from a materials science point of view. This paper covers the technological fabrication process of EUROFER97 by selective laser melting (SLM), including the production of pre-alloyed EUROFER97 powder, an SLM-parameter study and the design and production of custom-build thin walled test components by SLM. In the initial state after fabrication, SLM-EUROFER97 components exhibit a bimodal, anisotropic microstructure with large ferritic grains. The fraction of ferritic grains increases with decreasing wall thickness. A heat treatment including austenitization, quenching and tempering, allows to achieve a fully martensitic, uniform microstructure for all wall thicknesses. Therefore, there is no influence of wall thickness on mechanical properties of EUROFER97 produced by SLM to be expected, as long as the SLM-part is submitted to an appropriate heat treatment. Further, the comparison of the initial state after fabrication and after post processing reveals the necessity of both hot isostatic pressing and heat treatment to improve the performance. While all material conditions lead to sufficient tensile properties, the Charpy impact properties of SLM-EUROFER97 are inferior in comparison to conventionally produced EUROFER97. A heat treatment alone only improves the ductile-to-brittle transition temperature, whereas hot isostatic pressing reduced the residual porosity of the SLM parts and a subsequent heat treatment improved the ductile-to-brittle transition temperature as well as the upper shelf energy

Fundamental bounds on qubit reset

Qubit reset is a key task in the operation of quantum devices which, for many quantum hardware platforms, presently limits device clock speed. While it is known that coupling the qubit to an ancilla on demand allows for the fastest qubit reset, the limits on reset accuracy and speed due to the choice of ancilla have not yet been identified-despite the great flexibility in device design for most quantum hardware platforms. Here, we derive bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. For two-level ancillas, we find a provably time-optimal protocol which consists of purity exchange between qubit and ancilla brought into resonance. The globally minimal time can only be realized for specific choices of coupling and control which we identify. When increasing the size of the ancilla Hilbert space, the maximally achievable fidelity increases, whereas the reset time remains constant. Our results translate into device design principles for realizing, in a given quantum architecture, the fastest and most accurate protocol for qubit reset

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case