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

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

/pdf/coherent-detection-in-optical-fiber-systems-26jfovi6pk.pdf

Coherent detection in optical fiber systems

Publisher Summary Polarization mode dispersion (PMD) is a linear effect that can be compensated in principle. In an ideal circularly symmetric fiber, the two orthogonally polarized modes have the same group delay. However, in reality, fibers exhibit a certain amount of birefringence because of imperfections in the manufacturing process or mechanical stress on the fiber after manufacture. It is noted that fluctuations in the polarization mode and fiber birefringence produced by the environment lead to dispersion that varies statistically with time and frequency. PMD causes different delays for different polarizations and when the difference in the delays approaches a significant fraction of the bit period, it leads to pulse distortion and system penalties. Environmental changes— including temperature and stress—cause the fiber PMD to vary stochastically in time. PMD, illustrating the basic concepts, the measurement techniques, the PMD measurement, the PMD statistics for first- and higher orders, the PMD simulation and emulation, the system impairments, and the mitigation methods has been summarized in the chapter. Both the optical and the electrical PMD compensations are considered.

Polarization-Mode Dispersion

We report the most detailed long-term measurement of polarization mode dispersion (PMD) made to date. We measured two separate fibers under the same time period, which makes it possible to compare the drift properties of two similar fibers in the same environment. The measured Jones matrices suffers from both random and systematic errors, a generic problem which we discuss in detail and solve. The results confirmed the well-known statistical properties of the PMD-vector. Furthermore, the drift averaged over wavelength is very well (96%) correlated between the two fibers. We finally quantified the temporal drift by computing the autocorrelation function of the PMD-vector analytically, both with respect to wavelength and to drift time. The analytical theory shows good agreement with the measurements.

Long-term measurement of PMD and polarization drift in installed fibers

In this paper, we conduct theoretical and experimental study on the PMD-supported transmission with coherent optical orthogonal frequency-division multiplexing (CO-OFDM). We first present the model for the optical fiber communication channel in the presence of the polarization effects. It shows that the optical fiber channel model can be treated as a special kind of multiple-input multiple-output (MIMO) model, namely, a two-input two-output (TITO) model which is intrinsically represented by a two-element Jones vector familiar to the optical communications community. The detailed discussions on various coherent optical MIMO-OFDM (CO-MIMO-OFDM) models are presented. Furthermore, we show the first experiment of polarization-diversity detection in CO-OFDM systems. In particular, a CO-OFDM signal at 10.7 Gb/s is successfully recovered after 900 ps differential-group-delay (DGD) and 1000-km transmission through SSMF fiber without optical dispersion compensation. The transmission experiment with higher-order PMD further confirms the immunity of the CO-OFDM signal to PMD in the transmission fiber. The nonlinearity performance of PMD-supported transmission is also reported. For the first time, nonlinear phase noise mitigation based on receiver digital signal processing is experimentally demonstrated for CO-OFDM transmission.

/pdf/theoretical-and-experimental-study-on-pmd-supported-1micirivp7.pdf

Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems.

A polarization-mode dispersion (PMD) transient recorder setup was realized enabling for the first time to our knowledge the monitoring of fast PMD fluctuation with a bandwidth of up to 1 MHz. Thirty-six hours of observation of an installed field fiber exhibits significant PMD variation within 10 ms.

Measurement of the maximum speed of PMD fluctuation in installed field fiber

Optical systems and technologies have been radically changing the telecommunication networks for past 15 years; today wavelength division multiplexing (WDM) technology, optical amplifiers, and simple optical switching elements like optical add-drop multiplexers (OADMs) are used in the backbone networks of all operators worldwide. Optical systems nowadays provide the basis for cost-effective transmission of large amounts of bandwidth over the Internet, and will enable its future growth and the spreading of new applications and services. This paper summarizes the main trends in optical networking and investigates potential future application areas. Optical system technology has become so pervasive in network design that it needs to be considered in the context of provisioning new applications and services. Therefore, the analysis is not limited to the aspects of physical transmission, but also takes into account recent developments in integrated network design as well as network control and management. The following sections describe the key functionalities of future optical network architectures, and the key findings of the theoretical analysis are supported by the results of a field trial of advanced transmission technology

Evolution of Terrestrial Optical System and Core Network Architecture

Optical systems and technologies have been radically changing the telecommunication networks for past 15 years; today wavelength division multiplexing (WDM) tech- nology, optical amplifiers, and simple optical switching elements like optical add-drop multiplexers (OADMs) are used in the backbone networks of all operators worldwide. Optical systems nowadays provide the basis for cost-effective transmission of large amounts of bandwidth over the Internet, and will enable its future growth and the spreading of new applications and services. This paper summarizes the main trends in optical networking and investigates potential future application areas. Optical system technology has become so pervasive in network design that it needs to be considered in the context of provisioning new applications and services. Therefore, the analysis is not limited to the aspects of physical transmission, but also takes into account recent developments in integrated network design as well as network control and management. The following sections describe the key func- tionalities of future optical network architectures, and the key findings of the theoretical analysis are supported by the results of a field trial of advanced transmission technology.

Evolution of Terrestrial Optical System and Core Network

A novel two-output PON amplifier is demonstrated to provide over 8-dB output power budget improvement over a conventional SOA, with negligible ASE noise. With an additional preamplifier it can accommodate up to 30 dB burst-to-burst power variation.

Dual output SOA based amplifier for PON extenders

A method for optical data transmission in a wavelength multiplexing system having at least two transmission channels of different wavelengths includes determining at least one value which is a measure of a physical property of an optical data transmission path of the wavelength multiplexing system; and automatically adjusting a transmission parameter of at least one of the transmission channels as a function of the determined at least one value.

Werner Weiershausen

Papers

Measurement of the maximum speed of PMD fluctuation in installed field fiber

Evolution of Terrestrial Optical System and Core Network Architecture

Evolution of Terrestrial Optical System and Core Network

Dual output SOA based amplifier for PON extenders

Method and device for channel-adapted signal transmission in optical networks