This study explores how impurity parameters influence the energy dispersion of electron-hole pairs in a doped quantum wire containing Gaussian impurities. The system is analysed under the effects of external electric and magnetic fields, along with Rashba spin-orbit interaction (SOI). Initially, we establish the system's Hamiltonian and determine the energy eigenvalues, which are then used to compute the partition function. Our numerical findings reveal that an applied electromagnetic field alters the energy dispersion, consequently shifting the peak positions of optical absorption coefficients and modifying the refractive index. Additionally, the results indicate that increasing both the magnetic field and impurity strength leads to higher energy eigenvalues.