Propagation of short pulses in birefringent single-mode fibers is considered. Initial pulses are assumed to be linearly polarized at an arbitrary angle with respect to the polarization axes. The Kerr nonlinearity leads to a substantial interaction between the partial pulses in each of the two polarizations. When the amplitudes of the partial pulses are equal, it is found that above a certain amplitude threshold, whose size increases with birefringence, the two partial pulses lock together and travel as one unit. This unit can be a single soliton or, at higher amplitudes, a breather. At the same time, the central frequencies of both polarizations shift just far enough so that, if a rapid oscillation is ignored, their group velocities become identical. When the initial amplitudes are unequal, it is found as before that above a certain threshold one or more solitons emerge from the initial pulse. However, the breathers that appeared when the amplitudes were equal are unstable; they break up into two distinct solitons moving at different velocities when the amplitudes become slightly unequal. It is further shown that realistic fiber attenuation has little effect on these results. The numerical method used to obtain these results is described in detail.

Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes

The spectral development of stimulated Raman scattering in single-mode silica fibers was studied both experimentally and by computer modeling. The most striking feature that emerges is the rapid growth of a weak feature at 490 cm−1 at the expense of a broad band at 440 cm−1 as pump power increases. These experimental results are in good agreement with our numerical simulations, although neither experiments nor calculations show the spectral broadening of higher Stokes orders commonly observed with high pump powers and at infrared wavelengths. It is shown that, in general, spectral broadening from four-wave mixing should be important in the development of the stimulated Raman spectrum. However, the present experiments fall into a regime of relatively low pump powers at visible wavelengths in which four-wave mixing is negligible and the stimulated spectrum depends only on the shape of the Raman gain curve.

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Development of the stimulated Raman spectrum in single-mode silica fibers

Intense ultrashort waveforms of light that can be produced with an exactly predetermined electromagnetic field are essential in a number of applications of extreme nonlinear optics, most prominently in laser-driven sources of high-energy attosecond radiation. Field reproducibility in each laser shot requires stabilization of the carrier-envelope phase. The authors analyze different schemes of phase-stable pulse amplification and identify constraints limiting the precision with which the phase can be maintained. Next, they describe a phase-stabilized laser system based on a 20-fs multipass Ti:sapphire amplifier supplemented with a fiber compression stage for producing pulses in the few-cycle regime. It is shown that the amplifier introduces only a slow millihertz phase drift and, therefore, can be seeded by a standard phase-stabilized oscillator. This residual phase drift is assigned primarily to the beam pointing instability and can be precompensated in the phase-control loop of the seed oscillator using a feedback signal from a phase detector placed in the amplifier output. The phase stability of the resultant 5-fs 400-/spl mu/J pulses at a 1-kHz repetition rate is subsequently independently verified by higher order harmonic generation, in which different carrier-envelope phase settings are shown, both theoretically and experimentally, to produce distinctly different spectral shapes of the XUV radiation. From a series of such spectral patterns, the authors succeed in calibrating the value of the carrier envelope phase (with a /spl plusmn//spl pi/ ambiguity), which in turn allows them to fully characterize the temporal structure of the electric field of the laser pulses. The estimated precision of the phase control on the XUV target is better than /spl pi//5, which reduces the timing jitter between the driving laser pulse and the XUV bursts to /spl sim/ 250 as and opens the way to generate stable isolated attosecond pulses.

Phase-controlled amplification of few-cycle laser pulses

Chapter 8 – Fiber Nonlinearities and Their Impact on Transmission Systems

Aspects of the interaction of the Kerr nonlinearity and polarization mode dispersion (PMD) are reviewed. The basic equation that governs this interaction on the length scale of interest in optical fiber communications systems is the Manakov-PMD equation. This equation is derived using multiple-length-scale techniques. The focus of the derivation is the elucidation of common misunderstandings and pitfalls rather than mathematical rigor. It is shown that the scalar nonlinear Schro/spl uml/dinger equation is valid when PMD is absent and the signal is initially in a single polarization state. Two examples are then presented that illustrate the complexity of the interaction between nonlinearity and PMD. The first example considers the interaction of a nonlinearly induced chirp with PMD. As the power increases, one can obtain an improved eye opening relative to the case when PMD is absent. The second example considers the effect of nonlinear polarization rotation in a wavelength-division-multiplexed system. When nonlinear polarization rotation is important, the principal states of polarization become time dependent and PMD compensation becomes ineffective. This problem can be mitigated through the use of line codes.

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Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems

It is shown by theory and experiment that spectral self-broadening in optical fibers is enhanced in fibers that maintain linear polarization. Spectral self-broadening can be treated as self-phase modulation or three-wave mixing, and we show that these are simply different representations for the same process.

J. Botineau

Papers

Effect of polarization on spectral broadening in optical fibers