Propagation dynamics of controlled cross-talk via interplay betweenχ(1)andχ(3

Abstract

We investigate theoretically and experimentally the propagation dynamics of a nonlinear cross-talk effect between two probe channels in a double-ladder system and show that an interplay between χ (1) and χ (3) processes leads to the control of cross-talk. We derive analytical solutions to describe the propagation dynamics of the probe fields with the cross-talk effect built in. From the analytical results we identify and examine the regimes of interest where contributions of either χ (1) or χ (3) or both are significant. The control of cross-talk is demonstrated experimentally, and good quantitative agreement is found between the analytical solutions and the experiment.

Tunable Goos–Hänchen Shift and Polarization Beam Splitting Through a Cavity Containing Double Ladder Energy Level System

“…In the following, we set d 1 = 0.1 μm, d 2 = 5 μm, ε 1 = 2.22 throughout this paper unless specified. The probe fields are assumed to be resonant with the transition 6 2 S 1/2 ↔ 6 2 P 3/2 at wavelength 852.2nm, while the drive fields are resonant with the transition 6 2 P 3/2 ↔ 8 1 S 1/2 at wavelength 794.3nm [51], [55]. The decay rates from 8 1 S 1/2 → 6 2 P 3/2 and from 6 2 P 3/2 → 6 2 S 1/2 is 2π × 1.7 MHz and 2π × 5.2 MHz respectively [51], [55].…”

“…The dark state created by probe field p + and drive field d− is perturbed owing to the presence of drive field d+ , which further increases the absorption of the probe field p + . The population is pumped to the excited state |c via the drive field d− , transferred to the state |a' owing to the stimulated emission via the drive field d+ [51]. Thus, gain is achieved in the probe field p − due to the three photon process * d+ d− p + via the transition |b → |a → |c → |a .…”

“…The above results have demonstrated the polarized beam splitting based on opposite GH shifts, related parameters were also used to control the separate distance. In experiment, the three photon based gain process and the cross talk effect between the two probe beams have been verified using cesium atomic vapor cell [50], [51]. The power of both probe and drive beams can be easily controlled by adjusting a half-wave plate before a polarizer, the polarization state are tuned employing the rotating polarizer and a quarter-wave plate [50], [51].…”

“…In order to modify the reflection coefficient of the cavity, it is necessary to analyze the dielectric function of the double ladder energy level system. The energy level structure could be realized using cesium atoms [46], [50], [51]. As Fig.…”

“…here {}+ is the anticommutators of the operators. For simplicity, we assume the Rabi frequencies | d± | 2 | p ± | 2 and the decay rates 2 = 2 i (i = a, a ), 2γ = 2γ i (i = a, a ) [50], [51]. According to the relation P ± = N ℘ρ ± , the susceptibilities χ ± for LCP and RCP probe beams are given by…”