M. 4.2.7.3 Kerr-Induced Four-Wave Mixing Besides XPM, when several signals at a different wavelength propagate through an optical fiber, another important nonlinear interaction is caused by the Kerr effect: the so-called Even if FWM is also generated by a couple of propagating waves, it is a four photons phenomenon, involving, in the case of two interacting wavelengths, two photons from one wavelength and one from the other, besides a photon at a different wavelength. This dif- ferent wavelength photon is generated via absorption of photons of the traveling radiation and reemission through the transition at an intermediate molecular vibration level. Thus, the nature of the FWM is more evident imagining three different radiations at angular wavelengths Wi 1, 2, 3) that travels through a fiber in the same direction. The third-order nonlinear polarization can be obtained by substituting the expression of the overall field into Equation 4.34 and grouping the terms with the same frequency to determine the frequency components of the output spectrum. Telecommunication Networks Besides three components at the input frequencies, the output spectrum is composed of the four frequency components at the angular frequencies (4.42) In spontaneous FWM, these new frequencies are created in a part of the spectrum that does not contain any radiation power at the fiber input, if on the other side a radiation is present at the FWM frequencies like in the case of WDM transmission, the FM component superimposes to the input field causing crosstalk. At each FWM frequency, there is a corresponding term of the nonlinear glass polariza- tion whose amplitude depends on the product of the amplitudes of the input fields and whose phase has the following expression (4.43) The term 0 is called phase matching of the jth FWM frequency and the power of the jth FWM frequency is maximum when 0 is equal to zero and minimum when 0 is equal to /2. During the propagation through a real fiber, the phase matching for a certain FWM fre- quency depends on 