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Unformatted text preview: The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research in both experimental and theoretical physics after the invention of LASER. Nonlinear nature is very important for optical data processing applications and all physics of nonlinear optics can be ex- tracted by studying the behavior of applied optical field-induced polarization of the medium. In this article very basic properties of nonlinear electric susceptibilities are discussed qualitatively. 1 1 Introduction In linear optics it is assumed that an optical disturbance propagating through an optical medium can be described by a linear wave equation. As a consequence of that assumption regardless of the intensity of light, the principle of superposition is valid in the regime of linear optics. When the intensity of light becomes great enough, linear optics is no longer enough to describe the situation observed experimentally . It seems that light waves interact with one another and optical medium. These nonlinear phenomena require an extension of the linear theory, that allows for a nonlinear response of optical materials to the electromagnetic radiation. It was realized that the electric polarization induced in the medium is the key to study physics of nonlinear optics and so in general the polarization of the medium should be expressed as a power series of applied electric field E . P = [ (1) E + (2) EE + (3) EEE + ...... ] . (1) Where P is the polarization, is the free space permitivity and ( i ) is the i th order susceptibility tensor(material coefficient) of a given medium. First approximation of this equation gives linear optics and higher order terms contribute for nonlinear optics. 2 Theoretical framework of Nonlinear optics . Two major theoretical approaches can be employed in nonlinear optics as well as laser optics. They are semi-classical theory and quantum electrodynamical theory. In the semi- classical theory the media composed of molecules and atoms are described by quantum mechanics and light radiation is described by Maxwells theory. The key issue of semi-classical theory is to give the expressions of macroscopic nonlinear electric polarization for optical media. The density matrix method is used to derive the expressions for various orders of susceptibilities and the expressions for various orders of polarization components. Substituting the appropriate nonlinear polarization components into the generalized wave equation, in principle ,it is possible to predict many possible nonlinear optical responses of the medium for a given condition of the input intense optical fields....
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