Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers. Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first used to generate the second-harmonic radiation inside a crystal [1], the use ofoptical fibers as a nonlinear medium became feasible only after 1970 when fiber losses were reduced to below 20 dB/km [2]. Stimulated Raman and Brillouin scatterings in single-mode fibers were studied as early as 1972 [3] and were soon followed by the study of other nonlinear effects such as self- and crossphase modulation and four-wave mixing [4]. By 1989, the field ofnonlinear fiber optics has advanced enough that a whole book was devoted to it [5]. This book or its second edition has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field of nonlinear fiber optics.

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Nonlinear Fiber Optics

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond optical pulses without distortion in dielectric fiber waveguides with group velocity dispersion. In the case of anomalous dispersion (∂2ω/∂k2>0) discussed here [the case of normal dispersion (∂2ω/∂k2<0) will be discussed in a succeeding letter], the stationary pulse is a ``bright'' pulse, or envelope soliton. For a typical glass fiber guide, the balancing power required to produce a stationary 1‐ps pulse is approximately 1 W. Numerical simulations show that above a certain threshold power level such pulses are stable under the influence of small perturbations, large perturbations, white noise, or absorption.

Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion

We demonstrate experimentally for what is to our knowledge the first time that air–silica microstructure optical fibers can exhibit anomalous dispersion at visible wavelengths. We exploit this feature to generate an optical continuum 550 THz in width, extending from the violet to the infrared, by propagating pulses of 100-fs duration and kilowatt peak powers through a microstructure fiber near the zero-dispersion wavelength.

Visible continuum generation in air–silica microstructure optical fibers with anomalous dispersion at 800 nm

This paper reports narrowing and splitting of 7-ps-duration pulses from a mode-locked color-center laser by a 700-m-long, single-mode silica-glass fiber, at a wavelength (1.55 \ensuremath{\mu}m) of loss and large but negative group-velocity dispersion. At certain critical power levels, the observed behavior is characteristic of solitons.

Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers

We report measurements of frequency broadening due to self-phase-modulation (SPM) in optical fibers. The use of single-mode silica-core fibers and mode-locked argon-laser pulses leads to the simplest and cleanest measurements yet made of SPM. The qualitative features of the frequency spectrum are in good agreement with theoretical expectations. The experiment provides an independent measurement of ${n}_{2}$, the self-focusing coefficient. The results also point to some simple and useful techniques based on fibers for the measurement and analysis of mode-locked laser pulses.

Self-phase-modulation in silica optical fibers

Observations of backward stimulated Brillouin scattering (SBS) in glass optical fibers are reported. Threshold for SBS has been achieved with less than 1 W of input power at 5355 A. Relaxation behavior in the SBS signal has also been observed and is attributed to finite‐cell‐length oscillation. Experimental results are compared with theory, and the implied limitation to optical fiber transmission is discussed.

Stimulated Brillouin scattering in optical fibers

The small signal Raman gain in a single‐mode glass waveguide amplifier has been measured directly. The measured gain is in good agreement with that calculated from the Raman cross section. The cross section was determined by a comparison of the spontaneous Raman scattering of fused quartz and benzene.

Raman gain in glass optical waveguides

The use of self-phase modulation in a single-mode fiber to chirp an optical pulse, which is then compressed with a grating-pair compressor, has been shown to be a practical technique for the production of optical pulses at least as short as 30 fsec. We report the results of a theoretical analysis of this process. Numerical results are presented for the achievable compression and compressed pulse quality as functions of fiber length and input pulse intensity. These results are given in normalized units such that they can be scaled to describe a wide variety of experimental situations and can be used to determine the optimum fiber length and compressor parameters for any given input pulse. Specific numerical examples are presented that suggest that the technique will generally be useful for input pulses shorter than about 100 psec. For energies of a few nanojoules per pulse, the compressed pulse widths will typically be in the femtosecond regime.

Roger H. Stolen

Papers

Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers

Self-phase-modulation in silica optical fibers

Stimulated Brillouin scattering in optical fibers

Raman gain in glass optical waveguides

Compression of optical pulses chirped by self-phase modulation in fibers