## 3 Influence of Dispersion on an OFDM-OCDMA System  
Dispersion is a type of physical effect caused by different group velocities that generate different time delays when optical carrier waves with different wavelengths are transmitted through an optic fiber. Three main types of dispersion exist, namely modal dispersion, CD, and polarization dispersion. CD can further be divided into material dispersion and waveguide dispersion. In multimode fibers (MMFs), modal dispersion is greater than are material dispersion and waveguide dispersion, making modal dispersion the principal type of dispersion in MMFs. Regarding SMFs, modal dispersion does not exist because only one mode is being transmitted in the optic fiber; only CD and polarization dispersion exist. This study adopts SMF as the transmission medium. Furthermore, the influence of CD in a multi-wavelength system is severer than that of polarization dispersion; therefore, simulation analysis is performed in this section after introducing the dispersion parameters. The CD is caused by different time delays produced when light with different wavelengths are transmitted in an optic fiber at different velocities. CD can also be divided into material dispersion and waveguide dispersion, and is generally referred to as dispersion. Because actual light sources are not made up of pure monochromatic light and the SMF refraction index varies among light of different wavelengths, the time delay is dissimilar for light of different wavelengths, causing a broadening of the output light pulse. The output pulse expansion is also greater when the optic fiber is longer, which not only causes interference among the data and increases the BER, but also limits the system's transmission rate and bandwidth. The material dispersion-induced broadening per unit length can be expressed as in Equation (5). \[\frac{\Delta\tau_{m}}{L}=\left|D_{m}(\lambda)\right|\Delta\lambda, \tag{5}\]  
where the suffix \(m\) specifies material dispersion, \(L\) is the optic fiber length, \(\Delta\tau_{m}\) is the pulse expansion time caused by material dispersion, as all light emission sources emit nonmonochromatic light within a specific wavelength range, and \(D_{m}(\lambda)\) is the material dispersion coefficient. Waveguide dispersion is related to the fundamental mode group velocity and the parameter \(V\), and \(V\) is also related to the light source and wavelength. Because light sources have specific frequency spectra, the value of \(V\) is different when light of different wavelengths is transmitted in the optic fiber, causing the group velocity to differ as well. This further causes the time delay with which each wavelength reaches the end of the optic fiber to differ, inducing a broadening phenomenon of the output signal. Waveguide dispersion differs from material dispersion, in which waveguide dispersion is related to the group velocity and \(V\), but the group velocity of material dispersion is related to the refraction index. The pulse broadening per unit length caused by waveguide dispersion is expressed in Equation (6), which is similar to Equation (5). \[\frac{\Delta\tau_{w}}{L}=\left|D_{w}(\lambda)\right|\Delta\lambda, \tag{6}\]  
where the suffix \(w\) specifies material dispersion, \(\Delta\tau_{w}\) is the pulse expansion time caused by material dispersion and \(D_{w}(\lambda)\) is the waveguide dispersion coefficient, which is related to the characteristics of the optic fiber. The general literature collectively refers to the effects caused by material and waveguide dispersion as dispersion; thus, the total dispersion per unit length can be written as Equation (7). \[\frac{\Delta\tau_{CD}}{L}=\left|D_{m}(\lambda)+D_{w}(\lambda)\right|\Delta\lambda, \tag{7}\]  
where \(\Delta\tau_{CD}\) is the output pulse expansion time caused by dispersion. As previously described, different wavelengths of light reach the receiver at distinct times.