401 research outputs found

    Optical Transmission Systems based on the Nonlinear Fourier Transformation

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    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

    Nonlinear Fourier transform for optical data processing and transmission:advances and perspectives

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    Fiber-optic communication systems are nowadays facing serious challenges due to the fast growing demand on capacity from various new applications and services. It is now well recognized that nonlinear effects limit the spectral efficiency and transmission reach of modern fiber-optic communications. Nonlinearity compensation is therefore widely believed to be of paramount importance for increasing the capacity of future optical networks. Recently, there has been steadily growing interest in the application of a powerful mathematical tool-the nonlinear Fourier transform (NFT)-in the development of fundamentally novel nonlinearity mitigation tools for fiber-optic channels. It has been recognized that, within this paradigm, the nonlinear crosstalk due to the Kerr effect is effectively absent, and fiber nonlinearity due to the Kerr effect can enter as a constructive element rather than a degrading factor. The novelty and the mathematical complexity of the NFT, the versatility of the proposed system designs, and the lack of a unified vision of an optimal NFT-type communication system, however, constitute significant difficulties for communication researchers. In this paper, we therefore survey the existing approaches in a common framework and review the progress in this area with a focus on practical implementation aspects. First, an overview of existing key algorithms for the efficacious computation of the direct and inverse NFT is given, and the issues of accuracy and numerical complexity are elucidated. We then describe different approaches for the utilization of the NFT in practical transmission schemes. After that we discuss the differences, advantages, and challenges of various recently emerged system designs employing the NFT, as well as the spectral efficiency estimates available up-to-date. With many practical implementation aspects still being open, our mini-review is aimed at helping researchers assess the perspectives, understand the bottlenecks, and envision the development paths in the upcoming NFT-based transmission technologies

    Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

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    In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption

    Experiments on synthetic dimensions in photonics

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    The first and introductory section of the dissertation presents the working principle of a one- and two-dimensional photonic mesh lattice based on the time-multiplexing technique. The basis of a random walk interrelated to the corresponding light and quantum walk is comprehensively discussed as well. The second part of the dissertation consists of three experiments on a one-dimensional photonic mesh lattice. Firstly, the Kapitza-based guiding light project models the Kapitza potential as a continuous Pauli-Schrödinger-like equation and presents an experimental observation of light localization when the transverse modulation is bell-shaped but with a vanishing average along the propagation direction. Secondly, the optical thermodynamics project experimentally demonstrates for the first time that any given initial modal occupancy reaches thermal equilibrium by following a Rayleigh-Jeans distribution when propagates through a multimodal photonic mesh lattice with weak nonlinearity. Remarkably, the final modal occupancy possesses a unique temperature and chemical potential that have nothing to do with the actual thermal environment. Finally, the quantum interference project discusses an experimental all-optical architecture based on a coupled-fiber loop for generating and processing time-bin entangled single-photon pairs. Besides, it shows coincidence-to-accidental ratio and quantum interference measurements relying on the phase modulation of those time bins. The third part of the dissertation comprises two experiments on a two-dimensional photonic mesh lattice. The first project discusses the experimental realization of a two-dimensional mesh lattice employing short- and long-range interaction. To some extent, the second project presents a nonconservative system based on a two-dimensional photonic mesh lattice exploiting parity-time (PT) symmetry

    Source Modulated Multiplexed Hyperspectral Imaging: Theory, Hardware and Application

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    The design, analysis and application of a multiplexing hyperspectral imager is presented. The hyperspectral imager consists of a broadband digital light projector that uses a digital micromirror array as the optical engine to project light patterns onto a sample object. A single point spectrometer measures light that is reflected from the sample. Multiplexing patterns encode the spectral response from the sample, where each spectrum taken is the sum of a set of spectral responses from a number of pixels. Decoding in software recovers the spectral response of each pixel. A technique, which we call complement encoding, is introduced for the removal of background light effects. Complement encoding requires the use of multiplexing matrices with positive and negative entries. The theory of multiplexing using the Hadamard matrices is developed. Results from prior art are incorporated into a singular notational system under which the different Hadamard matrices are compared with each other and with acquisition of data without multiplexing (pointwise acquisition). The link between Hadamard matrices with strongly regular graphs is extended to incorporate all three types of Hadamard matrices. The effect of the number of measurements used in compressed sensing on measurement precision is derived by inference using results concerning the eigenvalues of large random matrices. The literature shows that more measurements increases accuracy of reconstruction. In contrast we find that more measurement reduces precision, so there is a tradeoff between precision and accuracy. The effect of error in the reference on the Wilcoxon statistic is derived. Reference error reduces the estimate of the Wilcoxon, however given an estimate of theWilcoxon and the proportion of error in the reference, we show thatWilcoxon without error can be estimated. Imaging of simple objects and signal to noise ratio (SNR) experiments are used to test the hyperspectral imager. The simple objects allow us to see that the imager produces sensible spectra. The experiments involve looking at the SNR itself and the SNR boost, that is ratio of the SNR from multiplexing to the SNR from pointwise acquisition. The SNR boost varies dramatically across the spectral domain from 3 to the theoretical maximum of 16. The range of boost values is due to the relative Poisson to additive noise variance changing over the spectral domain, an effect that is due to the light bulb output and detector sensitivity not being flat over the spectral domain. It is shown that the SNR boost is least where the SNR is high and is greatest where the SNR is least, so the boost is provided where it is needed most. The varying SNR boost is interpreted as a preferential boost, that is useful when the dominant noise source is indeterminate or varying. Compressed sensing precision is compared with the accuracy in reconstruction and with the precision in Hadamard multiplexing. A tradeoff is observed between accuracy and precision as the number of measurements increases. Generally Hadamard multiplexing is found to be superior to compressed sensing, but compressed sensing is considered suitable when shortened data acquisition time is important and poorer data quality is acceptable. To further show the use of the hyperspectral imager, volumetric mapping and analysis of beef m. longissimus dorsi are performed. Hyperspectral images are taken of successive slices down the length of the muscle. Classification of the spectra according to visible content as lean or nonlean is trialled, resulting in a Wilcoxon value greater than 0.95, indicating very strong classification power. Analysis of the variation in the spectra down the length of the muscles is performed using variography. The variation in spectra of a muscle is small but increases with distance, and there is a periodic effect possibly due to water seepage from where connective tissue is removed from the meat while cutting from the carcass. The spectra are compared to parameters concerning the rate and value of meat bloom (change of colour post slicing), pH and tenderometry reading (shear force). Mixed results for prediction of blooming parameters are obtained, pH shows strong correlation (R² = 0.797) with the spectral band 598-949 nm despite the narrow range of pH readings obtained. A likewise narrow range of tenderometry readings resulted in no useful correlation with the spectra. Overall the spatial multiplexed imaging with a DMA based light modulation is successful. The theoretical analysis of multiplexing gives a general description of the system performance, particularly for multiplexing with the Hadamard matrices. Experiments show that the Hadamard multiplexing technique improves the SNR of spectra taken over pointwise imaging. Aspects of the theoretical analysis are demonstrated. Hyperspectral images are acquired and analysed that demonstrate that the spectra acquired are sensible and useful

    Hybrid Strategies for Link Adaptation Exploiting Several Degrees of Freedom in WiMAX Systems

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    Enabling Technologies for Cognitive Optical Networks

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    MIMO Systems

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    In recent years, it was realized that the MIMO communication systems seems to be inevitable in accelerated evolution of high data rates applications due to their potential to dramatically increase the spectral efficiency and simultaneously sending individual information to the corresponding users in wireless systems. This book, intends to provide highlights of the current research topics in the field of MIMO system, to offer a snapshot of the recent advances and major issues faced today by the researchers in the MIMO related areas. The book is written by specialists working in universities and research centers all over the world to cover the fundamental principles and main advanced topics on high data rates wireless communications systems over MIMO channels. Moreover, the book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

    High-multiplicity space-division multiplexed transmission systems

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