Abstract

The dynamics of a field in a thin waveguide surrounded by helically arranged two-level atoms is studied. The interaction of the induced polarizations of atoms with the field propagating inside the waveguide is described by a system of reduced Maxwell–Bloch equations (RMBEs) in the approximation of unidirectional propagation of the field. Nonlocal dipole–dipole interaction (DDI) of the polarizations of atoms in the helix is described in the approximation of the interaction of nearest neighbors in a curvilinear medium. Soliton solutions of an integrable reduction of the system of equations describing the asymmetric propagation of field pulses in the waveguide in the forward and backward directions are found by the method of Riemann problem with zeros. It is shown that, depending on the chirality sign or the propagation direction, a field pulse in the waveguide can have either the shape of a sharp peak or a nearly rectangular shape. Solutions describing the evolution of field pulses on a nonzero pedestal show that the shape and amplitude of the field pulses can be controlled by the external pumping parameters.

中文翻译：

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手性介质中的孤子

摘要

研究了由螺旋排列的两级原子包围的细波导中的场动力学。通过简化的麦克斯韦-布洛赫方程（RMBE）的系统来描述原子的感应极化与在波导内部传播的场之间的相互作用，该系统近似于场的单向传播。螺旋中原子极化的非局部偶极-偶极相互作用（DDI）是在曲线介质中最邻近原子的相互作用的近似值中描述的。通过具有零的黎曼问题的方法，找到了描述方程组的可分解式方程组的孤子解，该方程式描述了场脉冲在波导中在向前和向后方向上的不对称传播。结果表明，根据手性符号或传播方向，波导中的场脉冲可以具有尖峰的形状或接近矩形的形状。描述场脉冲在非零基座上的演化的解决方案表明，场脉冲的形状和幅度可以由外部泵浦参数控制。