Manipulation of Goos–Hänchen shift via phase and angular momentum in Doppler-broadened systems

This study exploresthe Goos–Hänchen (GH) shift in both reflection and transmission within a Doppler-broadened four-level atomic system, emphasizing the pivotal role of phase factors and the angular momentum quantum numbers of the control fields. The GH shifts are found to be strongly affected by factors such as the direction, incident angle, and detuning of the probe and control fields. By precisely adjusting the parameters of the driving fields, both small and large negative and positive GH shifts in transmission and reflection can be finely controlled. Notably, negative GH shifts in transmission are significantly enhanced, while positive GH shifts in reflection are enhanced, eventually reaching a saturation point as the Doppler width increases or the influence of inverse Doppler broadening becomes dominant. The maximum small GH shift in both transmission and reflection is approximately ±2.1λ, while the large GH shifts vary between ±20λ and ±100λ. These findings provide valuable understanding of the precise control of light in intricate atomic systems, with far-reaching applications in fields like micro- and nano-optics, quantum mechanics, and plasma physics. This work opens up new possibilities for the development of cutting-edge optical technologies, quantum sensing devices, and high-precision metrology systems, where fine-tuned control of light propagation is of paramount importance.