Time-Frequency (Wigner) Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers
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Time-Frequency (Wigner) Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers ˜ Jose´ Azana ´ Institut National de la Recherche Scientifique, Energie, Mat´eriaux et T´el´ecommunications, 800 de la Gaucheti`ere Ouest, bureau 6900, Montr´eal, QC, Canada H5A 1K6 Email: [email protected] Received 12 April 2004; Revised 7 June 2004 Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD) and self-phase modulation (SPM) are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking) are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers), providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems. Keywords and phrases: Wigner distributions, dispersive media, nonlinear fiber optics, optical pulse propagation and solitons.
1.
INTRODUCTION
The study of optical pulse propagation in optical fibers is interesting from both fundamental and applied perspectives. Understanding the physics behind the processes that determine the evolution of optical pulses in single-mode fibers is essential for the design and performance analysis of optical fiber communication systems. As an example, it is well known that in intensity-modulated direct-detection (IM/DD) systems, the combined effects of source chirping, group velocity dispersion (GVD) and, for long-haul or highpower systems, self-phase modulation (SPM) cause distortion of the propagating signals [1]. This distortion essentially limits the maximum achievable bit rates and transmission distances. The influence of fiber GVD and fiber nonlinearities (e.g., SPM) on the performance of communication systems is becoming more critical in view of the expected evolution of fiber optics communications systems [2], in particular, (i) the channel data rates are expected to continue increasing, with 40 and 80 Gbps rate systems now under development; and (ii) the communication strategies (e.g., densewavelength-division-multiplexing, DWDM, strategies) tend to increase the number of channels and information (i.e., the signal power) launched into a single fiber. For the study of the dynamics of pulse propagation in fibers, the involved signals (optical pulses) can be represented in either the temporal or the frequency domains. However, since these signals are intrinsically nonstationary (i.e., the spectrum content changes as a function of time), these conventional one-dimensional representations provide
only partial information about the analyzed signals and, consequently, about the system under study. In this paper, we analyze linear and nonlinear pulse propagation in optical fibers using joint time-frequency (T
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