In this PhD thesis, we investigate the effect of optical Kerr non-linearity on light propagation through different dispersive media. Our main focus is to study the behavior of Goos–Hänchen shift in the reflected and transmitted light under the influence of Kerr non-linearity during its propagation through dispersive media. Goos–Hänchen shift is a very tiny lateral displacement, i.e., of the order of optical wavelength. It has potential applications in, for example, measuring surface smoothness, plasmon sensors, guidance system design of the optical devices in sensors, and information processing. It is, therefore, instructive to suggest and design experimentally viable models which can enhance the amplitude of Goos–Hänchen shift and the goal can be obtained in the presence of Kerr non-linearity. In this regard, we consider models based on artificial atoms, i.e., Quantum Dots. Initially, we consider four-level atomic system as intra-cavity medium in N-type configuration which exhibits Raman gain process for the incident Gaussian beam propagating through the medium. We consider Kerr non-linearity in the system due to which the group index of Raman gain medium enhances which in turns increases the amplitude of the Goos–Hänchen shift. We notice relatively large positive as well negative Goos–Hänchen shift in the reflected light for the incident Gaussian beam. The incident Gaussian beam has certain finite width and it can be distorted during propagation through the dispersive medium. Therefore, we also measure the distortion in the reflected beam and observe that it decreases for normal dispersion and increases for anomalous dispersion with increase in Kerr non-linearity. Next, we consider double quantum dots system to investigate effect of Kerr nonlinearity on Goos–Hänchen shift in the reflected and transmitted light for the case when incident light is a partially coherent Gaussian Schell-model beam. For double quantum dot system Goos–Hänchen shift in the reflected and transmitted light are investigated for p-polarized partially coherent incident Gaussian Schell-model beam. The coherent coupling between the two quantum dots via a tunneling field again leads to tunneling induced transparency and giant Kerr non-linearity with vanishing absorption can be obtained. We observe that the amplitude of Goos–Hänchen shift in the reflected and transmitted light increases with Kerr non-linearity. We also study influence of the spatial coherence and the beam width of incident Gaussian Schellxi model beam on Goos–Hänchen shift in the reflected and transmitted beams. It is reported that large Goos–Hänchen shift can be obtained for the small range of the spatial coherence and the beam width of the incident beam. For triple quantum dot system, double tunneling-induced transparency windows appear and giant Kerr non-linearity with vanishing absorption is noticed. This creates the possibility to achieve self-phase modulation in semiconductor nanostructures via controllable tunneling under the conditions of low light levels. As a result, a considerably high refractive index can be obtained. We suggest an intra-cavity medium which consists of triple quantum dot molecules to control the Goos–Hänchen shift in the reflected light. For a suitable design of a triple quantum dot system, our results show that relatively large positive and negative Goos–Hänchen shift are achievable, without significant distortion, using partially coherent incident light fields. Finally the idea of all-optical photonic crystal, which is generated using two counterpropagating fields, is revisited to study gain-assisted all-optical switch and all-optical diode using Kerr field. Two counter propagating fields with relative detuning Dn can generate standing-wave field pattern which interacts with a four-level atomic system. The standing wave field pattern acts like a static photonic crystal for Dn = 0, however, it behaves as a moving photonic crystal for Dn ¹ 0. The reflection and transmission coefficients are calculated for the case when a weak incident probe pulse propagates through the system. For static photonic crystal, the system acts like an all optical transistor as a switch via control of the external Kerr field, such that, when the Kerr field is off (on) the switch is ON (OFF). However, for a moving photonic crystal, the system acts as an all-optical diode via control of the external Kerr field. The advantage of using the gain-assisted model is the fact that the transmission efficiency is high, i.e. almost 100%.