Optical fiber solitons, their properties and uses

The history and mathematical formulation of solutions are briefly reviewed. Solitons of the nonlinear Schrodinger equation are studied in greater detail because they describe nonlinear pulse propagation on dispersive optical fibers. The proposal by A. Hasegawa and the experiments of L.F. Mollenauer on long distance soliton propagation for use in repeaterless transoceanic fiber transmission cables are described. In 1986, limitations on the distance that can be spanned by a repeaterless link for a given bit rate were shown to exist. It has been shown recently that by proper design these limitations can be overcome, so that newer transoceanic cable designs are likely to utilize solitons. The special properties of solitons make them particularly suited for all optical switching and logic operations. Some recent experiments with such switches are described     

Interaction of soliton with sinusoidal wave packet

The interaction of a soliton of the Nonlinear Schrodinger Equation (NSE) with a weak sinusoidal wave packet is treated analytically. The second-order soliton solution containing the original soliton and a perturbing soliton is expanded to first order in the amplitude of the perturbating soliton. From this expansion, one obtains the associate function of Gordon (1992) and a continuous change of position and phase of the perturbed soliton. One finds that the soliton experiences a second-order change of velocity under the influence of the perturbation. This result is then used to derive the displacement due to a wave packet of general shape, which is also confirmed by computer simulation     

Air trenches for sharp silica waveguide bends

Air trench structures for reduced-size bends in low-index contrast waveguides are proposed. To minimize junction loss, the structures are designed to provide adiabatic mode shaping between low- and high-index contrast regions, which is achieved by the introduction of "cladding tapers." Drastic reduction in effective bend radius is predicted. We present two-dimensional (2-D) finite-difference time-domain/effective index method simulations of bends in representative silica index contrasts. We also argue that substrate loss, while present, can be controlled with such air trenches and reduced to arbitrarily low levels limited only by fabrication capabilities. The required trench depth, given an acceptable substrate loss, is calculated in three dimensions using an approximate equivalent current sheet method and also by a numerical solver for full-vector leaky modes. A simple, compact waveguide T-splitter using air trench bends is presented.     

Theory of soliton stability in asynchronous modelocking

A new type of fiber laser modelocking is examined where a phase modulator is driven asynchronously with respect to a harmonic of the roundtrip cavity frequency. An asynchronous drive is able to produce high repetition rate (>1 GHz) soliton pulses that are shorter than the classic, active modelocking pulse width limit. It is shown that with a proper choice of fiber parameters, noise cleanup and soliton pulse shaping can be obtained using filtering and asynchronous phase modulation. Limits of asynchronous detuning are derived and a comparison with the parameters ranges for synchronous phase modulation is also presented     

Microring resonator channel dropping filters

Microring resonators side coupled to signal waveguides provide compact, narrow band, and large free spectral range optical channel dropping filters. Higher order filters with improved passband characteristics and larger out-of-band signal rejection are realized through the coupling of multiple rings. The analysis of these devices is approached by the novel method of coupling of modes in time. The response of filters comprised of an arbitrarily large dumber of resonators may be written down by inspection, as a continued fraction. This approach simplifies both the analysis and filter synthesis aspects of these devices     

Self-stabilized passive, harmonically mode-locked stretched-pulse erbium fiber ring laser

We have studied a passive, harmonically mode-locked stretched-pulse erbium fiber ring laser with net positive dispersion that is self-stabilized by gain depletion and electrostriction. Periodic pulses with supermode suppression of >75 dB and picosecond jitter are achieved. The pulses are compressible to 125 fs by external chirp compensation. The repetition rate is 220 MHz, and the average power is as high as 80 mW.     

Kinetic and mechanistic study with optically active, four-coordinate nickel(II) complexes: stereoselectivity in ligand substitution

Conventional and rapid scan stopped-flow spectrophotometry as well as polarimetry was used to study the kinetics of ligand substitution in six chiral bis N-alkylsalicylaldiminato nickel(II) complexes NiA2 by different chiral salen-type ligands H2B, according to NiA2 + H2B --> NiB + 2HA, in acetone at 298 K and, partly, at variable temperature. In most cases ligand substitution was found to follow monophasic second-order kinetics, rate = k x [NiA2] x [H2B]. Second-order rate constant k, lying in the range 10(-2)-400 M(-1) s(-1) at 298 K, was determined for the various combinations of enantiomers in a given system NiA2/H2B, namely, R-NiA2/R-H2B, S-NiA2/R-H2B, R-NiA2/S-H2B, and S-NiA2/S-H2B. It was found that ligand substitution is subject to chiral discrimination. The ratio of second-order rate constants, kfast/kslow, with kfast being rate constant k for the faster reacting pair of enantiomers and vice versa, lies in the range 1.0-3.0, depending on the nature of the N-alkyl groups in NiA2 and organic groups attached to the ethylene bridge in the salen ligands H2B. The rate discrimination factor of 3.0, as obtained for NiA2 = bis[N-dehydroabietylsalicylaldiminato]nickel(II) reacting with the R- and with the S-enantiomer of H2B = N,N'-disalicylidene-1,2-diamino-4-methylpentane, appears to be the highest stereoselectivity reported so far for ligand substitution in nickel(II) complexes. With NiA2 = R- and S-bis[N-(1-phenylethyl)-5-nitrosalicylaldiminato]nickel(II) and H2B = R- and S-N,N-disalicylidene-1,2-diamino-4-methylpentane, the kinetics of ligand substitution are biphasic, describing initial adduct formation between NiA2 and H2B (equilibrium constant K) and stepwise loss of the two bidentate ligands HA (first-order rate constants k1 and k2). The data for K, k1, and k2 for one of the combinations of enantiomers were determined at variable temperature, and the corresponding activation parameters are presented.