The present study aims to investigate the transmitted and reflected light beams from a one-dimensional defect photonic crystal (1DPC) composed of a three-level ladder-type quantum system. The lower leg of the ladder scheme is driven by a weaker probe beam, while the upper leg is driven by a stronger control beam. Unlike natural atoms, this type of model with broken symmetry permits the generation of a sum-frequency signal beam between the majority of higher and lower quantum states, resulting in the formation of a cyclic closed-loop arrangement for the interaction between light and matter. The Laguerre Gaussian (LG) field with strong coupling and a weak probe light interact with the quantum system. A new weak signal light is produced as a result of the system’s symmetric breakdown, and the medium becomes azimuthal dependent. We investigate the spatial dependence of the transmitted and reflected light from a defect 1DPC by using azimuthal modulation of the LG light. Additionally, we will discuss how the absorption spectrum’s spatial modulation varies with winding numbers. We discover that in certain regions, the gain can be realized without population inversion under certain specified parametric parameters.

中文翻译：

---

通过高效非线性混频通过 1DPC 进行光传播的方位角调制

本研究旨在研究由三能级梯型量子系统组成的一维缺陷光子晶体（1DPC）的透射和反射光束。梯子方案的下腿由较弱的探测光束驱动，而上腿由较强的控制光束驱动。与自然原子不同，这种对称性破缺的模型允许在大多数较高和较低量子态之间生成和频信号束，从而形成光与物质相互作用的循环闭环排列。强耦合的拉盖尔高斯 (LG) 场和弱探测光与量子系统相互作用。由于系统的对称击穿，产生了新的微弱信号光，并且介质变得与方位角相关。我们通过使用 LG 光的方位角调制来研究缺陷 1DPC 的透射光和反射光的空间依赖性。此外，我们将讨论吸收光谱的空间调制如何随绕组数变化。我们发现，在某些区域，在某些指定的参数参数下，无需总体反转即可实现增益。