# On the Capacity of Optical Backbone Networks
## 2 Basics on Optical Networks and Physical Impairments
### Major Physical Impairments  
Optical reach can be defined as the maximum distance over which an optical signal can be transmitted before its quality of service degrades below a certain metric (bit-error rate (BER), SNR, etc.) threshold. The reach in optical networks is limited by various physical  
Figure 2: Example of an optical backbone network architecture. phenomena related to both optical fiber transmission and optical nodes operation. For what concerns fiber transmission, the major impairments are attenuation, chromatic dispersion, and nonlinear effects. On the other hand, optical nodes are affected by impairments such as filter narrowing and crosstalk. Fiber optic attenuation measures the loss of power in an optical signal as it propagates along an optical fiber and is described by the fiber attenuation coefficient \(\alpha\) in dB/km. In the C-band, where it reaches its minimum value, \(\alpha\) is typically around 0.2 dB/km. Optical amplifiers are used to compensate for the optical fiber losses. To achieve this, optical amplifiers, typically EDFAs, are placed at discrete intervals along an optical link, with each amplifier exactly compensating the loss incurred by each fiber span. For a link with the length \(L\), made up of \(N_{s}\) identical spans, the span length is \(L_{s}=L/N_{s}\) and the span attenuation is \(A_{s}=\alpha L_{s}\). Optical amplifiers, besides amplifying the signal, also generate noise known as amplified spontaneous emission (ASE) noise. This noise accumulates as the signal propagates along the link and turns out to be one of the major sources of impairment, significantly affecting the optical reach. Chromatic dispersion is another limitation and is due to the fact that different wavelengths of a signal travel at different velocities, and therefore, they arrive at the end of the fiber at different times, leading to distortion in the original signal waveform. This occurs because the refractive index of the optical fiber, denoted as \(n(\lambda)\), is wavelength-dependent, and the transmission velocity is defined as \(c/n(\lambda)\). Chromatic dispersion can be characterized using the fiber dispersion coefficient \(\beta_{2}\), measured in ps\({}^{2}\)/km. Traditional direction-detection systems, which use simple photodetectors to detect optical signals, require the use of dispersion compensation. This operation is generally achieved by adding sections of a specific type of fiber known as dispersion compensating fiber (DCF) into the standard optical fiber spans. DCF is designed to have the opposite dispersion sign to standard fiber. In coherent detection systems, which employ relatively complex receiver structures, chromatic dispersion can be compensated in the electrical domain through digital signal processing. This solution, which is the one considered in this paper, avoids the use of dispersion compensation in optical domain, leading to the concept of dispersion uncompensated transmission [11]. Another significant impairment in optical fibers is nonlinear interference (NLI) resulting from the Kerr effect. The Kerr effect refers to the dependence of the refractive index of the fiber \(n(\lambda)\) on the transmitted signal power and is quantified by the non-linear fiber coefficient \(\gamma\) (measured in watt\({}^{-1}\)km\({}^{-1}\)). Unlike attenuation and chromatic dispersion, the Kerr effect is a non-linear phenomenon due to its dependence on optical power. This characteristic makes the optical fiber channel intrinsically non-linear and, in this sense, different from other transmission media used for information transmission that have a linear behavior. The filter-narrowing effect in optical nodes primarily results from the non-ideal filtering characteristics of WSSs within ROADMs. As a consequence, when an optical signal traverses multiple nodes, the resulting channel bandwidth can be significantly reduced, leading to signal distortion and performance degradation.