In this paper we control the negative refractive index of a four-level left-handed medium by applying different waveforms to excite the atomic system. The control field is a few-cycle strong pulse described by a double exponential function, and its modified forms, a Gaussian field, and a tan-hyperbolic pulse. The considered four-level system was fully analyzed in terms of the density matrix formalism under the rotating wave approximation, and the refractive index for various control fields was obtained. Hence, under specific conditions, the tunneling, and the modulation of the negative refractive index are achieved for various shaped waveforms. Such strong-shaped laser pulses open the way to fully control the system.

在本文中，我们通过应用不同的波形来激发原子系统来控制四级左手介质的负折射率。控制场是由双指数函数描述的几个周期的强脉冲，及其修改形式，高斯场和正切双曲线脉冲。根据旋转波近似下的密度矩阵形式对所考虑的四能级系统进行了全面分析，并获得了各种控制场的折射率。因此，在特定条件下，可以实现各种形状波形的隧道效应和负折射率的调制。这种强形状的激光脉冲为完全控制系统开辟了道路。