Implications of spectral hole burning on the manipulation of spatial Goos–Hänchen shift in an atomic cell

Abstract

We present a new scheme to report on Goos–Hänchen (GH) shift experienced by the Gaussian light beam interacting with an optical cavity filled with four-level sodium atomic medium in the spectral hole burning region with and without Doppler broadening effect. Theoretical atomic density-matrix formalism is employed to obtain the susceptibility of atomic medium while the stationary-phase-theory is used to compute the GH shift in the reflected and transmitted probe beams subjected to control fields. A steep normal slope of dispersion is observed with a maximum and zero probability of transmission and reflection coefficients, respectively, at the regions of the spectral holes burning. In the normal dispersion spectrum at the region of spectral hole burning, positive and negative GH shift is observed, respectively, in the transmitted and reflected light beams. However, at anomalous dispersive regions negative GH shift in the transmission beam and positive GH shift in the reflection beam is observed. The reflection and transmission coefficients as well as the spatial GH shift are the functions of probe detuning, collective phase of control fields, beam incident angle and inverse Doppler broadening effect in the spectral hole burning region. The position and number of spectral holes also depend on the same spectral parametrs as stated above. The study is expected to be useful for optoelectronic devices and optical-clocking applications.