中文摘要：

理论分析了闭路光伏晶体中灰孤子诱导的波导。研究发现，闭路光伏灰孤子诱导的波导在所有孤子灰度值，电流密度和光强比率下均为单模，这一光强比率为孤子峰值强度与暗辐射之比。这一研究结果解释了闭路光伏灰孤子限制在中心的能量随着电流密度的增加而增加，随着孤子灰度值和光强比率的增加而减小。文章还提供了光伏晶体的相关例子。

英文摘要：

The theory of waveguides induced by gray solitons in closed-circuit photovoltaic crystals is analyzed. The study shows that waveguides induced by gray closed-circuit photovoltaic solitons are only a single guided mode for all soliton graynesses and all values of both the electric current density and the ratio between the soliton peak intensity and the dark irradiance. The results explain that the confined energy near the center of a gray closed-circuit photovoltaic soliton increases with the electric current density and decreases with an increase in both the soliton grayness and the ratio between the soliton peak intensity and the dark irradiance. Relevant examples are provided where the photovoltaic crystal is assumed to be LiNbO3.