In this dissertation, various analytical models to characterize fiber nonlinearities have been applied, and the ranges of validity of the models are determined by comparing with numerical results. First, the perturbation approach is used to solve the nonlinear Schrödinger equation, and its range of validity is determined by comparing to the split-step Fourier method. In addition, it is shown mathematically that the perturbation approach is equivalent to the Volterra series approach. Secondly, root-mean-square (RMS) widths both in the time domain and in the frequency domain are modeled. It is shown that there exists an optimal input pulse width to minimize output pulse width based on the derived RMS models, and the functional form of the minimum output pulse width is derived. The response of a fiber to a sinusoidally modulated input which models an alternating bit sequence is studied to see its utility in measuring system performance in the presence of the fiber nonlinearities. In a single channel system, the sinusoidal response shows a strong correlation with eye-opening penalty in the normal dispersion region over a wide range of parameters, but over a more limited range in the anomalous dispersion region. The cross-phase modulation (CPM) penalty in a multi-channel system is also studied using the sinusoidally modulated input signal. The derived expression shows good agreement with numerical results in conventional fiber systems over a wide range of channel spacing, ∆<i>f</i>, and in dispersion-shifted fiber systems when ∆<i>f</i> > 100GHz. It is also shown that the effect of fiber nonlinearities may be characterized with stochastic input signals using noise-loading analysis. In a dense wavelength division multiplexed (DWDM) system where channels are spaced very closely, the broadened spectrum due to various nonlinear effects like SPM (self-phase modulation), CPM, and FWM (four-wave mixing) is in practice indistinguishable. In such a system, the noise-loading analysis could be useful in assessing the effects of broadened spectrum due to fiber nonlinearities on system performance. Finally, it is shown numerically how fiber nonlinearities can be utilized to improve system performance of a spectrum-sliced WDM system. The major limiting factors of utilizing fiber nonlinearities are also discussed. / Ph. D.

Nonlinear fiber devices have been attracting considerable attention in recent years, due to their inherent ultrafast response time and potential applications in optical communication systems. They usually require long fibers to generate sufficient nonlinear phase shifts, since nonlinearities of conventional silica-core silica-clad fibers are too low. These long devices, however, cause the serious problems of pulse walk-off, pulse broadening, and polarization fluctuation which are major limiting factors for response time, switching bandwidth, and maximum transmittable bit-rate. Therefore, short device length is indispensable for achieving ultrafast switching and higher bit-rate data transmission. To shorten the required device length, fiber nonlinearities should be increased. In this dissertation, as a way of increasing fiber nonlinearities, high-nonlinearity materials of Litharge, Bismite, Tellurite, and Chalcogenide glasses have been considered. Although they have high nonlinearities, they also have high group-velocity dispersion and high losses deteriorating the performance of nonlinear fiber devices seriously. The aim of this work is to investigate how these high-nonlinearity glasses affect the performance of nonlinear fiber devices, taking into consideration both the advantages and disadvantages. To achieve it, the critical properties of various nonlinear fiber devices constructed with the different types of high-nonlinearity glasses and different types of fibers have been evaluated. It turned out that the required device lengths of nonlinear fiber devices constructed with the high-nonlinearity glasses were significantly reduced and high group-velocity dispersions and losses could not be major problems due to the extremely short device length. As a result, it would be possible to suppress the problems of pulse walk-off, pulse broadening, and polarization fluctuation in nonlinear fiber devices by introducing high-nonlinearity glasses, thus enabling ultrafast switching and higher bit-rate data transmission. Furthermore, in this dissertation, a new scheme of wavelength-division demultiplexing based on the optical Kerr effect has been proposed for the first time. The new scheme can turn the disadvantage of the extremely high group-velocity dispersion of high-nonlinearity glasses into an advantage of wavelength-division demultiplexing. Finally, it now would be possible to greatly increase maximum transmittable bit-rate in optical communication systems by simultaneously demultiplexing optical time-division-multiplexed signals and wavelength-division-multiplexed signals with an optical Kerr effect-based demultiplexer. / Ph. D.

The Internet has fundamentally changed the way of modern communication. Current trends indicate that high-capacity demands are not going to be saturated anytime soon. From Shannon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio (SNR), but a linear function of the number of dimensions. Ideally, we can increase the capacity by increasing the launch power, however, due to the nonlinear characteristics of silica optical fibers that imposes a constraint on the maximum achievable optical-signal-to-noise ratio (OSNR). So there exists a nonlinear capacity limit on the standard single mode fiber (SSMF). In order to satisfy never ending capacity demands, there are several attempts to employ additional degrees of freedom in transmission system, such as few-mode fibers (FMFs), which can dramatically improve the spectral efficiency. On the other hand, for the given physical links and network equipment, an effective solution to relax the OSNR requirement is based on forward error correction (FEC), as the response to the demands of high speed reliable transmission. In this dissertation, we first discuss the model of FMF with nonlinear effects considered. Secondly, we simulate the FMF based OFDM system with various compensation and modulation schemes. Thirdly, we propose tandem-turbo-product nonbinary byte-interleaved coded modulation (BICM) for next-generation high-speed optical transmission systems. Fourthly, we study the Q factor and mutual information as threshold in BICM scheme. Lastly, an experimental study of the limits of nonlinearity compensation with digital signal processing has been conducted.

<p>Fiber-optic communication systems have revolutionized the telecommunications industry and have played a major role in the advent of the Information Age. Thousands of kilometers of optical fiber are used by telecommunications companies to transmit telephone signals, Internet communication, and cable television signals throughout the world. So, working in this area has always been interesting. This thesis analyzes the nonlinearity of fiber-optic systems and proposes a system to mitigate fiber nonlinear e®ects. The topics of this thesis can be categorized into two parts. In the first part of thesis (Chapters 2, 3, and 4), analytical models are developed for fiber-optic nonlinear effects. It is important to have an accurate analytical model so that the impact of a specific system/signal parameter on the performance can be assessed quickly without doing time-consuming Monte-Carlo simulations. In the second part (Chapters 5, and 6), a multi-core/fiber architecture is proposed to reduce the nonlinear effects.</p> <p>In Chapter 2, intrachannel nonlinear impairments are studied and an analytical model for the calculation of power spectral density (PSD) and variance of the non- linear distortion is obtained based on quadrature phase-shift keying (QPSK) signal. For QPSK signals, intrachannel four-wave mixing (IFWM) is the only stochastic non- linear distortion. To develop the analytical model, a first order perturbation theory is used. For a Gaussian pulse shape, a closed form formula is obtained for the PSD of IFWM. For non-Gaussian pulses, it is not possible to find the PSD analytically. However, using stationary phase approximation approach, convolutions become multiplications and a simple analytical expression for the PSD of the nonlinear distortion can be found. The total PSD is obtained by adding the PSD of amplified spontaneous emission (ASE) PSD to that of the nonlinear distortion. Using the total PSD, bit error ratio (BER) can be obtained analytically for a QPSK system. The analytically estimated BER is found to be in good agreement with numerical simulations. Significant computational effort can be saved using the analytical model as compared to numerical simulations, without sacrificing much accuracy.</p> <p>In Chapter 3, the same approach as that in Chapter 2 is used to find an analytical expression for the PSD of the intrachannel nonlinear distortion of a fiber-optic system based on quadrature amplitude modulation (QAM) signal. Unlike the QPSK signal, intrachannel cross-phase modulation (IXPM) is a stochastic process for the QAM signal which leads to the increase of the nonlinear distortion variance. In this chapter, analytical expressions for the PSDs of self-phase modulation (SPM), IXPM, IFWM, and their correlations are obtained for the QAM signal. Simulation results show good agreement between the analytical model and numerical simulation.</p> <p>In Chapter 4, inter-channel nonlinear impairment is studied. This time, a first order perturbation technique is used to develop an analytical model for SPM and cross-phase modulation (XPM) distortions in a wavelength division multiplexing (WDM) system based on QAM. In this case, SPM distortion is deterministic and does not contribute to the nonlinear noise variance. On the other hand, XPM is stochastic and contributes to the noise variance. In this chapter, effects of input launch power, fiber dispersion, system reach, and channel spacing on the nonlinear noise variance are investigated as well.</p> <p>In Chapter 5, a single-channel multi-core/fiber architecture is proposed to reduce intrachannel fiber nonlinear effects. Based on the analytical model obtained in the first part of thesis, the nonlinear distortion variance scales as P³, where P is the fiber input launch power, which suggests that decreasing the fiber input power can reduce the nonlinear distortion significantly. In this system, the input power is divided between multiple cores/fibers by a power splitter at the input of each span and a power combiner adds the output fields of multiple cores/fibers so that one amplifier can be used for each span. In this case, each core/fiber receives less power and hence adds less nonlinear distortion to the signal. In a practical system, individual fiber parameters are not identical; so the optical pulses propagating in the fibers undergo different amounts of phase shifts and timing delays due to the fluctuations of fibers' propagation constants and fibers' inverse group speeds. Optical and electrical equalizers are proposed to compensate for these inter-core/fiber dispersions. In the case of an optical equalizer, adaptive time shifters and phase shifters are adjusted such that the maximum power is obtained at the output of power combiner. Our numerical simulation results show that for unrepeatered systems, the performance (Q factor) is improved by 6.2 dB using 8-core/fiber configuration as compared to single- core fiber system. In addition, for multi-span system, the transmission reach at BER of 2.1*10^-3 is quadrupled in 8-core/fiber configuration.</p> <p>In Chapter 6, a multi-channel multi-core/fiber architecture is proposed to reduce the inter-channel nonlinear distortions. In this architecture, different channels of a WDM system are interleaved between multiple cores/fibers which increases the channel spacing in each core/fiber. Higher channel spacing decreases the inter-channel nonlinear impairments in each core/fiber which leads to system performance improvement. At the end of each span, a multiplexer adds the channels from different cores/fibers so that one amplifier can be used for all of the channels. Unlike the single-channel multi-core/fiber system, the WDM multi-core/fiber system does not require equalizers since different cores/fibers carry channels with different frequencies. Simulation results show that for a 39-span system, the 4-core/fiber system with negligible crosstalk outperforms the single-core system by 2.2 dBQ₂₀. The impact of crosstalk between cores of a multi-core fiber (MCF) on the system performance is studied. The simulation results show that the performance of the multi-core WDM system is less sensitive to the crosstalk effect compared to conventional multi-core systems since the propagating channels in the cores are not correlated in frequency domain.</p> / Doctor of Philosophy (PhD)