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• W3023495288 abstract "An electromagnetic wave propagating through a material medium produces an electrical response in it in the form of an oscillating dipole moment in every small volume element, while the magnetic response is usually small in the visible part of the spectrum. For a wave of a sufficiently large amplitude, the polarization density depends nonlinearly on the electric field amplitude and can be expressed by means of a series of terms of successively higher degrees in the field strength, involving the frequency-dependent susceptibilities of various orders as coefficients, where the susceptibility tensors satisfy a number of symmetry requirements. The polarization density, in turn, acts as the source of the electric field, and the two are then determined by a set of nonlinear wave equations in the medium under consideration. Under appropriate conditions, including those relating to phase matching, the nonlinear wave equation possesses a solution in the form of a superposition of plane waves with a number of different frequencies and with slowly varying amplitudes. A set of ‘input’ waves of specified frequencies results in a set of ‘output’ waves, where the latter include a set of newly generated waves in the medium, depending on the dominant degree of nonlinearity.The medium is commonly a crystalline one whose symmetry class and geometrical orientation determine the amplitude distribution of the waves propagating in the medium, and also the amplitudes of the output waves.The nonlinear susceptibilities can be determined in a theoretical scheme where the quantum mechanical master equation of the atom-field system is set up and its dissipative interaction with a background reservoir is taken into account. The susceptibilities of successively higher orders are then determined in a step-by-step process, where the susceptibility of a given order is determined in terms of the susceptibility of a lower order. These results can then be compared with the susceptibilities calculated in the classical theory, where one finds that the latter theory enjoys a measure of relevance in sofar as the frequency dependence of the susceptibilities is concerned.Explaining all these basic ideas in the present chapter, we consider a number of nonlinear optical processes, setting up the relevant nonlinear wave equations and making a number of simplifying assumptions and approximations. A number of salient features of the second-order nonlinear processes of sum-frequency generation, difference-frequency generation, optical parametric amplification, second-harmonic generation, and parametric down conversion are explained. The working principle of the optical parametric oscillator, a device of great practical importance, is outlined. Several aspects of the third-order process of the optical Kerr effect are explained with reference to the nonlinear wave equation.A number of quantum mechanical aspects of second-harmonic generation and parametric down conversion that are not explained in the classical theory are illustrated by reference to phenomenological Hamiltonians and by working out approximate solutions to the Heisenberg equations for a set of slowly varying annihilation and creation operators. A feature of crucial relevance in the quantum theory of nonlinear processes relates to the role of field fluctuations, including the vacuum fluctuations." @default.
• W3023495288 created "2020-05-13" @default.
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• W3023495288 date "2016-01-01" @default.
• W3023495288 modified "2023-09-27" @default.
• W3023495288 title "Nonlinear Optics" @default.
• W3023495288 doi "https://doi.org/10.1016/b978-0-12-805357-7.00009-5" @default.
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