Nonlinear dispersive media

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). 

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

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... 

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. 

In most cases, the propagation equations discussed in this chapter do not require a specific form of material response. However, for the sake of concreteness, as well as for discussion of numerical methods, we want to describe a generic model of nonlinear material response. We consider a nonmagnetic, dispersive medium with relative permittivity e that is a function of the transverse coordinates x, y and of the angular frequency u>... 

Such a pulse propagation is illustrated in Fig. 6.40, which shows the spectral and time profiles of a pulse propagating through a medium in a linear dispersive medium without self-phase modulation (Fig. 6.40a) and in a nonlinear medium (Fig. 6.40b) with negative dispersion and positive SPM. 

The H NMR spectra of HjO/HPA/SiOj have significant distinctions in comparison with those for the parent nanosilica, and these differences depend not only on the adsorbed water content but also on reaction temperature, dispersion medium (Figure 1.131 and Table 1.24), and other parameters. Notice that the 5e(/t) function becomes more nonlinear with increasing temperature and this is accompanied by diminution of the 8e values (Figure 1.130b). 

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... 

Microemulsions also feature a convenient dispersed medium in this context because they have been widely studied in combination with chemical reactions. This paves the avenue to new chemo-hydrodynamic pattern formation and to unravel how cross-diffusion-driven convection interacts with linear and nonlinear chemical kinetics. 

Solitons A mathematically appealing model of real particles is that of solitons. It is known that in a dispersive linear medium, a general wave form changes its shape as it moves. In a nonlinear system, however, shape-preserving solitary solutions exist. 

Propagation of non-stationary light beam in a nonlinear medium with material dispersion is described by the scalar wave equation for the linearly-polarized y-component of electrical field E x,z,t) ... 

An illustration of this fact comes from the nonlinear Schrodinger equation. This equation describes an electromagnetic wave in a nonlinear medium, where the dispersive effects of the wave in that medium are compensated for by a refocusing property of that nonlinear medium. The result is that this electromagnetic wave is a soliton. Suppose that we have a Fabry-Perot cavity of infinite extend in the x direction that is pumped with a laser [6,7]. The modes allowed in that cavity can be expanded in a Fourier series as follows ... 

Maxwell theory, soliton flows are Hamiltonian flows. Such Hamiltonian functions define symplectic structures6 for which there is an absence of local invariants but an infinite-dimensional group of diffeomorphisms which preserve global properties. In the case of solitons, the global properties are those permitting the matching of the nonlinear and dispersive characteristics of the medium through which the wave moves. 

A simple thin film technique has been developed to measure the electrical properties of polyelectrolyte solutions under sinusoidal electric fields of 100-500 v/cm at frequencies of. 10-10 KHz. Ohmic heating is largely avoided by the rapid transfer of heat to the electrodes and by the high surface to volume ratios. The resulting temperature is not sufficient to damage the medium. Current and voltage wave forms are monitored directly so that dispersion and nonlinear phenomena of the medium can be viewed directly as functions of frequency, voltage, and concentration of the solution. Possible mechanisms for the observed phenomena are discussed. 

Neutral molecules, dissolved, dispersed or suspended in a liquid medium, are in continuous random motion (Brownian motion) with a mean free path (x) and collision diameter (xe), depending on c and vex effects. At a far separation distance, is negative, increasing to 0 at xe, where repulsion counterbalances attraction and the amphiphiles are at dynamic equilibrium in a primary minimum energy state. At x High concentrations shorten x and make the collision rate nonlinear with c, (Hammett, 1952). A separation distance of x < xe is sterically forbidden without fusion. 

D. L. Hovhannisyan, Analytic solution of the wave equation describing dispersion-free propagation of a femtosecond laser pulse in a medium with cubic and fifth-order nonlinearity, Optics Commun. 196, 103 (2001)... 

Stability of common polymers, and consequently, thermal degradation of mercaptide molecules ean be also carried out with the mercaptide dissolved into a polymeric medium. In this case, a finely dispersed inorganic solid phase, embedded in polymer, is generated. Materials based on clusters confined in polymeric matrices are called nanocomposites [Mayer, 1998 Caseri, 2000]. Both semiconductor-polymer and metal-polymer nanocomposites have unique functional properties that can be exploited for applications in several advanced technological fields (e.g., optics, nonlinear optics, magnetooptics, photonics, optoelectronics) [Caseri, 2000]. 

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