Nonlinear Effects
In the previous chapters it was assumed that the discrete oscillators, which compose the material, would react linearly on the external field. This simplification is only valid if the optical field strength is rather low. Hence, the intensity has to be sm
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In the previous chapters it was assumed that the discrete oscillators, which compose the material, would react linearly on the external field. This simplification is only valid if the optical field strength is rather low. Hence, the intensity has to be small. This is the case for noncoherent light sources such as lamps, light emitting diodes, and sunlight. Since the invention of the laser, a light source that deli vers coherent light with extremely high intensities is available. The field strength of this light source can be so large that it is in the range of the inner atomic field. In this case, the excursion of the valence electron is no longer linear and hence, the rules of nonlinear optics are valid. Compared to solid state lasers the semiconductor laser diodes, used in the field of telecommunications, deliver rather low powers in the m W range. Nevertheless, due to the small effective areas, as described in this chapter, the intensity in the core area is very high. Furthermore, the large effective length in optical fibers can lead to very strong nonlinear effects. In principle two possibilities are feasible for the mathematical description of nonlinear optics. One is the so called semi-classical theory, the other is the theory of quantum-electrodynamics. In the semi-classical theory the external field is described with the Maxwell equations. But the medium by itself is considered as consisting of atoms and moleeules and is hence described with the rules of quantum mechanics. In the theory of pure quantum-electrodynamics the external field as weIl as the medium are described with the equations of quantum mechanics. Both approaches have particular advantages and disadvantages, but in most cases they deliver the same results and predictions for the nonlinear optical response of the medium. In the following the semi-classical theory is used almost exclusively. Nevertheless, for the phenomenological description of harmonie generation and wave mixing, the quantum-electrodynamical description is preferred here. This chapter describes the fundament als of some optical effects whose origin is the nonlinear response of the dipole system to the external optical field. The interaction between light and matter will be restricted to nonresonant effects, which is valid in optical fibers, for example, but not in resonant nonlinear optical devices like semiconductor optical amplifiers. We first start with an extension of the linear oscillator, introduced in Sect. 2.3. From the T. Schneider, Nonlinear Optics in Telecommunications © Springer-Verlag Berlin Heidelberg 2004
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4. Nonlinear Effects
model the nonlinear suseeptibility tensor elements will be derived. As will be seen in Sect. 4.3, a large number of these elements ean be responsible far the generation of nonlinear effeets. But due to symmetry arguments, only one residual element, eonsidered a eonstant, is used to deseribe the nonlinear effeets in optieal fibers. The nonlinear suseeptibility is used to expand the wave eqllation derived in Sect. 2.2 tü a nonlinear wa
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