Chromatic Dispersion Modeling in Optical Fiber Transmission Systems

The rapid increase in data transmission requirements in modern optical communication systems has made chromatic dispersion a major limiting factor in optical fiber links. At high bit rates, even moderate dispersion can cause significant temporal broadening of optical pulses, leading to intersymbol interference and degradation of system performance. Chromatic dispersion originates from the wavelength dependence of the refractive index of the fiber material and from the waveguiding properties of the fiber, causing different spectral components of an optical signal to propagate at different group velocities. In this study, chromatic dispersion in silica-based optical fibers is investigated through analytical modeling using realistic physical and system parameters suitable for numerical simulation. The analysis considers single-mode optical fibers operating in the second and third telecommunication windows, centered at wavelengths of 1.3 µm and 1.55 µm, respectively. Typical fiber lengths ranging from 10 km to 100 km are considered, along with optical sources having spectral widths between 0.1 nm and 2 nm, representative of laser diodes and light-emitting diodes used in practical systems. The refractive index dispersion of silica is modeled using the Sellmeier equation, allowing the calculation of the group refractive index and its wavelength derivatives. Based on these parameters, the group delay and temporal pulse broadening are analytically derived as functions of wavelength, fiber length, and source spectral width. For standard single-mode fibers, the chromatic dispersion coefficient is assumed to be approximately 0 ps/(nm·km) near 1.3 µm and about 17 ps/(nm·km) at 1.55 µm, in agreement with widely reported experimental data. Numerical simulations are performed by injecting Gaussian optical pulses with initial temporal widths on the order of 50 ps to 200 ps and peak powers normalized to unity. The temporal evolution of the pulses is analyzed after propagation over different fiber lengths. The results are expected to show minimal pulse broadening around 1.3 µm, while a noticeable temporal spreading is observed at 1.55 µm, increasing linearly with both fiber length and source spectral width. The quantitative analysis presented in this work provides a clear framework for simulating and evaluating chromatic dispersion effects in optical fiber transmission systems. The chosen numerical parameters enable direct implementation in simulation tools and offer practical insight into the trade-off between low attenuation and dispersion in high-capacity optical communication networks.