Maxwell fields, nonlinear optical

The solution to this equation is A sech (kx)emt, which is a soliton solution. In the case where we have nonlinear optics and the occurrence of the cyclic electromagnetic fields, the Maxwell equations for the propagation of an electromagnetic wave are co variant and then give rise to soliton wave equations. 

The macroscopic optical responses of a medium are given by its linear and nonlinear susceptibilities, which are the expansion coefficients of the material polarization, P, in terms of the Maxwell fields, 1 3]. For a dielectric or ferroelectric medium under the influence of an applied electric field, the defining equation reads... 

The theory of nonlinear optical processes in crystals is based on the phenomenological Maxwell equations, supplemented by nonlinear material equations. The latter connect the electric induction vector D(r,t) with the electric field vector E(r, t). In general, the relations are both nonlocal and nonlinear. The property of nonlocality leads to the so-called spatial dispersion of the dielectric tensor. The presence of nonlinearity leads to the interaction between normal electromagnetic waves in crystals, i.e. makes conditions for the appearance of nonlinear optical effects. 

The contributions to the fifth-order nonlinear optical susceptibility of dense medium have been theoretically estimated by using both the local-field-corrected Maxwell-Bloch equations and Bloembergen s approach. In addition to the obvious fifth-order hyperpolarizability contribution, the fifth-order NLO susceptibility contains an extra term, which is proportional to the square of the third-order hyperpolarizability and which originates purely from local-field effects, as a cascaded contribution. Using as model the sodium 3s 3p transition system, it has been shown that the relative contribution of the cascaded term to the fifth-order NLO susceptibility grows with the increase of the atomic density and then saturates. 

Consider a one-dimensional optical structure that consists of nonlinear layers. The structure is illustrated in Fig. 1. Assuming no field variation in the X and z directions and the convention exp(icot) for the time dependence of the fields, Maxwell s equations take the form... 

Directly following the development of the optical laser, in 1961 Frankel et al. [10] reported the first observation of optical harmonics. In these experiments, the output from a pulsed ruby laser at 6943 A was passed through crystalline quartz and the second harmonic light at 3472 A was recorded on a spectrographic plate. Interest in surface SHG arose largely from the publication of Bloembergen and Pershan [11] which laid the theoretical foundation for this field. In this publication, Maxwell s equations for a nonlinear dielectric were solved given the boundary conditions of a plane interface between a linear and nonlinear medium. Implications of the nonlinear boundary theory for experimental systems and devices was noted. Ex-... 

The interaction of various optical fields inside a nonlinear medium are described by Maxwell equations. For n-wave mixing processes, there are n coupled Maxwell wave equations. 

Maxwell s equations are linear. However, the parameters that describe material properties may become nonlinear in exceptionally strong fields, such as in powerful lasers. In these cases nonlinear terms have to be included. The linear material equations, Eqs. (1.1.6) to (1.1.8), are not applicable to ferroelectric or ferromagnetic substances where the relationship between the electric field strength, E, and the electric displacement, D, or between the magnetic field strength, H, and the magnetic induction, B, are not only nonlinear, but show hysteresis effects as well. In any case. Maxwell s equations are the foundation of electromagnetism, which includes optics and infrared physics. 

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