There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Lithium niobate on insulator (LNOI) technology is revolutionizing the lithium niobate industry, enabling higher performance, lower cost and entirely new devices and applications. The availability of LNOI wafers has sparked significant interest in the platform for integrated optical applications, as LNOI offers the attractive material properties of lithium niobate, while also offering the stronger optical confinement and a high optical element integration density that has driven the success of more mature silicon and silicon nitride (SiN) photonics platforms. Due to some similarities between LNOI and SiN, established techniques and standards can readily be adapted to the LNOI platform including a significant array of interface approaches, device designs and also heterogeneous integration techniques for laser sources and photodetectors. In this contribution, we review the latest developments in this platform, examine where further development is necessary to achieve more functionalities in LNOI integrated optical circuits and make a few suggestions of interesting applications that could be realized in this platform. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Status and Potential of Lithium Niobate on Insulator (LNOI) for Photonic Integrated Circuits

Data transmission rates in optical communication systems are approaching the limits of conventional multiplexing methods. Orbital angular momentum (OAM) in optical vortex beams offers a new degree of freedom and the potential to increase the capacity of free-space optical communication systems, with OAM beams acting as information carriers for OAM division multiplexing (OAM-DM). We demonstrate independent collinear OAM channel generation, transmission and simultaneous detection using Dammann optical vortex gratings (DOVGs). We achieve 80/160 Tbit s−1 capacity with uniform power distributions along all channels, with 1600 individually modulated quadrature phase-shift keying (QPSK)/16-QAM data channels multiplexed by 10 OAM states, 80 wavelengths and two polarizations. DOVG-enabled OAM multiplexing technology removes the bottleneck of massive OAM state parallel detection and offers an opportunity to raise optical communication systems capacity to Pbit s−1 level. Dammann gratings are used to realize multiplexing based on the generation, transmission and detection of optical angular momentum (OAM). The OAM of optical vortex beams offers a new degree of freedom for multiplexing and hence the promise of higher data communication rates, but massive parallel detection of OAM states has proved challenging. Now, researchers in China, Australia and Singapore have used Dammann optical vortex gratings (DOVGs) to realize multiplexing of massive OAM channels with individual modulation and simultaneous detection capabilities. They achieved a data capacity of 80 Tbit s−1 by multiplexing 1600 channels using ten OAM states, 80 wavelengths and two polarizations. This DOVG-enabled OAM multiplexing technology removes the bottleneck of massive parallel detection of OAM states and has the potential to increase optical communication capacities to the Pbit s−1 level.

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Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings

We report the first experimental demonstration of dispersion-enhanced phase noise (DEPN) in reduced-guard-interval (RGI) coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. It is first shown that channel estimation enhances DEPN. Then we experimentally demonstrate that for 28 Gbaud dual-polarization QPSK (112 Gb/s) RGI CO-OFDM systems with different inverse fast Fourier transform sizes, the transmission distance at a bit error rate = 3.8×10-3 is limited to 1830-2550 km by DEPN when a distributed feedback laser with a 2.6-MHz linewidth is employed as the local oscillator. We also, however, show that using DEPN compensation can increase the distance to 3320-4400 km.

Demonstration of Dispersion-Enhanced Phase Noise in RGI CO-OFDM Systems

We present both theoretically and experimentally a novel blind and fast method for estimating the State of Polarization (SOP) of a single carrier channel modulated in square Dual Polarization (DP) MQAM format for optical coherent receivers. The method can be used on system startup, for quick channel reconfiguration, or for burst mode receivers. It consists of converting the received waveform from Jones to Stokes space and looping over an algorithm until a unitary polarization derotation matrix is estimated. The matrix is then used to initialize the center taps of the subsequent classical decision-directed stochastic gradient algorithm (DD-LMS). We present experimental comparisons of the initial Bit Error Rate (BER) and the speed of convergence of this blind Stokes space polarization recovery (PR) technique against the common Constant Modulus Algorithm (CMA). We demonstrate that this technique works on any square DP-MQAM format by presenting experimental results for DP–4QAM, –16QAM and –64QAM at varying distances and baud rates. We additionally numerically assess the technique for varying differential group delays (DGD) and sampling offsets on 28 Gbaud DP–4QAM format and show fast polarization recovery for instantaneous DGD as high as 90% of symbol duration. We show that the convergence time of this blind PR technique does not depend on the initial SOP as CMA does and allows switching to DD–LMS faster by more than an order of magnitude. For DP–4QAM, it shows a convergence time of 5.9 ns, which is much smaller than the convergence time of recent techniques using modified CMA algorithms for quicker convergence. BER of the first 20 × 103 symbols is always smaller by several factors for DP–16QAM and –64QAM but not always for DP–4QAM.

Blind, fast and SOP independent polarization recovery for square dual polarization-MQAM formats and optical coherent receivers.

We experimentally demonstrate improved intra-channel nonlinearity tolerance of the root M-shaped pulse (RMP) with respect to the root raised cosine (RRC) pulse in spectrally efficient 128 Gbit/s PDM-16QAM coherent transmission systems. In addition we evaluate the impact of dispersion map and fiber dispersion parameter on the intra-channel nonlinearity tolerance of the RRC pulse and the RMP via both simulation and experimentation. The RMP is shown to have a better nonlinear tolerance than the RRC pulse for most investigated scenarios except for links with zero residual dispersion percentage per span or the zero dispersion region of a fiber. Therefore, the RMP is suitable for extending the maximum reach of spectrally efficient coherent transmission systems in legacy links in addition to currently intensively studied standard single mode fiber (SSMF) based dispersion unmanaged links.

Experimental investigation on the nonlinear tolerance of root M-shaped pulse in spectrally efficient coherent transmissions.

The time domain hybrid QAM enabled flexible transceiver is proposed to adaptively optimize the transmission performance in DWDM systems with cascaded ROADMs. Comprehensive performance investigations are conducted for both fixed and flexible grid systems.

Performance optimization in ROADM-enabled DWDM systems using flexible modulation formats

Multiple receivers are comprised in a flexible coherent transceiver of a multi-span optical fiber network. Each of the multiple receivers is operative to handle communications on a respective channel. The multiple receivers measure optical characteristics. For each of the multiple receivers, the optical characteristics include optical nonlinear interactions on the respective channel, the optical nonlinear interactions being at least partially dependent from one span to another span. An optical power of a signal on each of the multiple channels is adjusted as a function of the optical characteristics.

Qunbi Zhuge

Papers

Demonstration of Dispersion-Enhanced Phase Noise in RGI CO-OFDM Systems

Blind, fast and SOP independent polarization recovery for square dual polarization-MQAM formats and optical coherent receivers.

Experimental investigation on the nonlinear tolerance of root M-shaped pulse in spectrally efficient coherent transmissions.

Performance optimization in ROADM-enabled DWDM systems using flexible modulation formats

Power Control in an Optical Fiber Network