Coherent Control of the Goos-Hänchen Shift

Abstract

Coherent Control of the Goos-Hänchen Shift The coherent control of the Goos-Hänchen (GH) shift has been investigated when a probe light is incident on a cavity which contains dispersive atomic medium. We consider different atom-field configurations for the intracavity atomic medium, i.e., electromagnetically induced transparency (EIT), Raman gain process and double  (duplicated two-level). The sub- and super-luminal pulse propagations which correspond to normal and anomalous dispersion, respectively, through a dispersive atomic medium can be coherently controlled without changing the structure. This is due to the manipulation of group index of the dispersive atomic medium via different parameters associated with the driving fields, i.e., intensity, detuning and phase shift. In this research thesis, we use these facts and report coherent control of the GH shift in the reflected and transmitted light when the light is incident on a cavity containing dispersive atomic medium. The positive and negative GH shifts in the reflected and transmitted light corresponding to the sub- and super-luminal propagation of the pulse, respectively, could be observed. We consider a cavity which is consisted of an intracavity medium and two dielectric slabs being the walls of the cavity. The thickness of each dielectric slab is d 1 and length of the intracavity medium is d 2 , i.e., the total length of the cavity is L = 2d 1 + d 2 . A TE-plane polarized probe light is incident on the cavity. We consider two types of intracavity media, i.e., three- and four-level EIT atomic configuration. Following the EIT configuration of the atom-field system inside the cavity, we observe a coherent control of the GH shifts via the intensity and detuning of the driving fields. We observe negative and positive GH shift in the reflected beam via intensity of the driving fields, however, only positive GH shift is observed in the transmitted light. This is due to the fact that the group index of the cavity which includes the dielectric slabs and intracavity medium becomes negative and positive for the corresponding negative and positive group index of the intracavity medium, respectively, however, it remains positive for the transmitted light. xTo reduce the strong absorption during super-luminal propagation of light, we suggest a gain-assisted model to control the GH shifts which is experimentally more viable scheme. In this scheme, a similar kind of control over sup- and sub- luminal light propagation can be achieved using three- and four-level atoms inside the cavity following one and two-photon Raman transitions. Both atomic systems exhibit gain-assisted super-luminal propagation of the light. First we consider three-level atomic system and observe a control over GH shift in the reflected and transmitted light via probe field detuning and intensity of the control field using three-level system. We observe negative GH shifts in the transmitted light and both positive and negative GH shift in the reflected light via manipulation of the optical susceptibility of the atomic medium. This is again due to the fact that the group index of the total cavity remains negative for the transmitted light whereas it could be positive and negative for the reflected light. Next, we consider four-level atomic system with N-type configuration and study the behavior of spatial as well as angular GH shifts for different choices of the control field. Finally, we consider a duplicated two-level atomic system, which is a degenerated double lambda system, inside the cavity and study the GH shift behavior corresponding to the super- and sub-luminal propagation of an incident Gaussian- shaped probe light. The system has a coherent control over the group velocity via the phase shift associated with the driving and probe fields and is independent of the intensity of the field in the low optical regime. We study influence of the width of the incident Gaussian probe light on GH shift and distortion. We observe a strong dependence of the GH shift and distortion of the pulse on the width of the incident light.