Four-Wave-Mixing (FWM)
Four-Wave-Mixing (FWM), or sometimes four-photon-mixing (FPM), describes a nonlinear optical effect at which four waves or photons interact with each other due to the third order nonlinearity of the material. As a result, new waves with sum and difference
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Four-wave-mixing (FWM), or sometimes four-photon-mixing (FPM), describes a nonlinear optical effect at which four waves or photons interact with each other due to the third order nonlinearity of the material. As a result, new waves with sum and difference frequencies are generated during the propagation in the waveguide. FWM is comparable to the so called intermodulation in electrical communication systems. This effect was already mentioned in the introduction of this book. The intermodulation, as weIl as the FWM, leads to noise in the neighboring channels which degrades the system performance. For WDM systems in dispersion-shifted fibers, FWM is the most important nonlinear effect. On the other hand, FWM can be used for a number of applications in optical telecommunications, such as wavelength conversion and optical switching. Of particular interest is the generation of a phase-conjugated wave due to the FWM effect which can be used to cancel any kind of signal distortions in the system. The applications of FWM and other nonlinear effects are treated in the third part of this book in detail. In the quantum mechanical model, two photons are annihilated by the atom as it generates two new photons simultaneously (see Fig. 4.12). Only virtual states of the atom are involved and hence, the rules of conservation of energy and moment um have to be fulfilled during the process. The conservation of momentum leads to the phase matching condition. The efficiency of FWM depends very strongly on this matching of the phases of the waves involved. Therefore, the FWM efficiency is a function of the fiber dispersion. In transmission systems using the zero dispersion of the material FWM is a severe problem. On the other hand, if the transmission system shows a high local dispersion, which is the case in dispersion-managed systems, the FWM can be effectively suppressed. In this chapter, FWM is described mathematically with the help of the NSE. The significance of the effect to WDM systems as weIl as possibilities for an effective suppression are discussed in detail.
T. Schneider, Nonlinear Optics in Telecommunications © Springer-Verlag Berlin Heidelberg 2004
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7. Four-Wave-Mixing (FWM)
7.1 Mixing between WDM Channels If three optical waves with frequencies fi, fj and fk are propagating in the fiber, they can interact via the third order susceptibility of the material and new waves with the frequencies fi,j,k
= 1; + fj
-
h
(7.1)
can be generated by the FWM process, where i, j and k can have the values 1, 2, and 3. Three elements arranged in three classes can lead to 27 possible variations. Eut if the third frequency (fk) in (7.1) equals the first, or second (fi, fj) frequency no new frequency is generated, resulting in fi or fj, respectively (fi + iJ - fi = iJ)· Furthermore, if the first two frequencies in (7.1) are changing their places as wen, no new frequencies are generated (fi + fj - h = iJ + fi - fk)' Therefore, a side condition for (7.1) is k -=1= i,j. If the side condition is introduced, 9 residual combinations ar
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