Grid Job Routing Algorithms - Phosphorus

Grid Job Routing Algorithmswhere f is a fraction of the bit duration (typically 0.1) and B denotes the bit rate.4.1.2 Nonlinear ImpairmentsIn WDM systems there are, in general, two ways to increase the system channel capacity. One is to increasethe number of WDM channels, and the other is to increase the channel bit rate for each wavelength. Bothattempts are associated with higher total injected power into the fiber, leading to the intensification in the fibernonlinearities which fall into two categories. One is stimulated scattering (Raman and Brillouin), and the other isthe optical Kerr effect due to an harmonic motion of bound electrons in the material resulting in an intensitydependent refractive index with optical power [Agrawal95]. While stimulated scatterings are responsible forintensity dependent gain or loss, the nonlinear refractive index is responsible for intensity dependent phaseshift of the optical signal.In the simulations we consider only nonlinearities stemming from the Kerr effect which occur due to thenonlinear relationship between the induced polarization P and the applied electric field E when higher powersand/or bit rates are applied as shown in (Eq.13)(1) (3) 3( )P = ε χ E + χ E + ...(13)0where ε 0 is the permittivity of vacuum and χ (j) the j-th order susceptibility. The linear susceptibility χ (1) is thedominant contribution to the polarization P and its effects are included through the refractive index n[Agrawal95]. The cubic term χ (3) is responsible for phenomena like third-harmonic generation, four wave mixingand nonlinear refraction. The first two processes (processes that generate new frequencies) are usually notimportant unless phase matching conditions are satisfied. Nonlinear refraction instead is always present anddeeply affects the propagation of intense light in an optical fiber. The electromagnetic wave passing along theoptical fiber induces a cubic polarization which is proportional to the third power of the electric field (13). This isequivalent to a change in the effective value of χ (1) to χ (1) + χ (3) E 2 . In other words the refractive index is changedby an amount proportional to the optical intensity%( )2n Ι = n + n I(14)where n is the linear part , I is the optical intensity and n 2 is the nonlinear-index coefficient related to χ (3) byn22 3ε cn 8n χ(3)= (15)0This intensity dependence of the refractive index (optical Kerr effect) is responsible for numerous nonlineareffects. Note that even if the value of the nonlinear coefficient n 2 is quite small, nonlinear effects in optical fibersassume a relevant importance due to the fact that the magnitudes of these effects depend on the length of thefiber along which the wave travels and on the ratio n 2 /A eff , where A eff is the effective area of the lightmode.Despite the intrinsically small values of the nonlinear coefficient for silica, the nonlinear effects in optical fibersProject:PHOSPHORUSDeliverable Number: D.5.3Date of Issue: 31/06/07EC Contract No.: 034115Document Code: Phosphorus-WP5-D5.334