Dispersion nonlinear

Agrawal G P 1989 Ultrashort pulse propagation in nonlinear dispersive fibers The Supercontinuum... 

Nonlinear dispersion becomes relevant at sufficient pulse powers. In some fibre stmctures tire interiDlay between tire nonlinear dispersion and tire group velocity dispersion can be used to produce non-dispersive waves called solitons. Solitons, altliough beyond tire scope of tliis treatment, may revolutionize tire communication systems of tire future. A full treatment of soliton tlieory can be found in [4, 261. 

Van Wijingaarden, L., 1966, Linear and Nonlinear Dispersion of Pressure Pulses in Liquid Bubble Mixtures, 6th Symp. on Naval Hydrodynamics, Washington, DC. (3)... 

P. M. Goorjian, and A. Taflove, "Direct time integration of Maxwells equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons," Opt. Lett 17, 180-182 (1992). 

Here Uq is the linear refractive index and An is the nonlinear part of the refractive index. Linear dispersion of the refractive index is accounted for in (2.2), (2.3). In general, nonlinear dispersion has to be taken into consideration, too. However, due to non-resonant character of the electronic nonlinearity in fused silica it is possible, as a first approximation, to neglect the nonlinear dispersion. 

J. K. Ranka, R. W. Schirmer, A. L. Gaeta, Observation of pulse splitting in nonlinear dispersive media, Physical Review Letters 77, 3783 (1996)... 

Figure 8.1. Schematic of wavelength dispersion by a diffraction grating. Wavelength and Raman shift scales illustrate the nonlinear dispersion of Raman shift for diffraction of scattering from a 785 nm laser. Scales shown are linear in wavelength but nonlinear in Raman shift.

As stated above, their shape, their velocity, and their collisions characterize soliton-like waves. In the present state of knowledge, comparison between theoretical analysis and experimental data can be obtained in two basic situations when there is predominance of the nonlinearity dispersion balance, as in BKdV solitons (case A) and when the (free)-energy production dissipation terms dominate (case B). ... 

Such interactions include all active processes and all nonresonant nonlinear dispersions. Thus, in such spectroscopies, the signal field must always remain in-phase with the induced polarization and y(r) is determined from Eq. (2.15a) with Ay(r) = 0. 

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media, IEEEJ. Quantum Electron., vol. 40, no. 2, pp. 175-182, Feb. 2004.doi 10.1109/JQE.2003.821881... 

M. Fujii, M. M. Tentzeris, and P. Russer, Performance of nonlinear dispersive APML in high-order FDTD schemes, in Proc. IEEE Microw. Theory Tech. Int. Symp., Philadelphia, PA, June 2003, vol. 2, pp. 1129-1132. 

Nayfeh, A. H. Hassan, S.D. The method of multiple scales and nonlinear dispersive waves. J. Fluid Mech. 48,463 75 (1971). 

A soliton is a localized collective excited state likely to arise in nonlinear dispersive media. The soliton is capable of migrating over relatively long distances with very little energy dissipation. It may be electrically charged or may be neutral such as a kink in a polymeric chain, or a domain wall. 

The Chapter is organized as follows. First the theoretical calculations with A -type three-level atoms in the optical ring cavity are described. The EIT-enhanced linear and nonlinear dispersions are calculated, and their effects to the cavity linewidth are discussed in different parametric regions. Second, various experimental observations are presented to demonstrate those interesting effects on cavity linewidth narrowing and broadening, as well as WLC. The last part serves as the summary with some discussions. 

EIT resonance both the linear and nonlinear refractive indices have very sharp slopes but with opposite signs. Figure 4 shows the derivatives of the linear and nonlinear refractive indices as a function of the probe frequency detuning [16], At small probe frequency detuing, the linear dispersion is normal and positive while the nonlinear dispersion is anomalous and negative. This sensitive dependence on probe frequency detuning can be used to obtain the desired dispersion... 

Wg 1 and the group velocity of the light pulses can be slowed down as the intensity of the input light increases, the nonlinear dispersion term becomes... 

Sinee the linear and Kerr nonlinear dispersions in such EIT medium change dramatically as fimctions of various parameters, such as the coupling beam Rabi frequency and its frequency detuning, the probe beam frequency detuning, and the cavity frequency detuning, the WLC condition can be easily satisfied by choosing the appropriate and different sets of parameters. To... 

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