Quadratic Solitons: Theory
In the present paper the fundamental theory of parametric solitons, trapping and interacting in bulk media, cavities and gratings with quadratic nonlinearity are considered. We discuss the mechanism of parametric self-action due to which quadratic solitons are formed. Nonlinear dispersion of both plane waves and solitons is investigated. Change of quadratic soliton properties in the process of narrowing of its width is traced with the help of numerical and analytical solutions of Maxwell equations. The criteria of soliton stability and nature of modulation instability are analyzed. The dynamics of soliton trapping is demonstrated. Advantages and disadvantages of effective particle model of quadratic solitons are presented. The main features of soliton generation in resonators are discussed as well.
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