A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials. This model studies light distribution from the main fiber into other branch fibers, which can be one or more than one. So, for this reason, twin couplers and multiple core couplers are studied in this paper. Further two cases in multiple core couplers namely multiple core couplers near the neighbor and multiple core couplers with a complete neighbor are exhaustively discussed. The non-linearity type that is considered here is Kerr Law. The obtained solutions set is more generalized than the existing solution as it is transformed into fractional-order derivative because it gives the solutions of problems with heavy tails or infinity fluctuations. Furthermore, the obtained solutions contain almost all types of solitons such as dark, bright, dark-bright, rational, periodic, breather, and singular soliton solutions, etc. Moreover, the obtained solutions are fractional solitons with Atangana-Baleanu and modified Riemann–Liouville fractional operator. These non-linear directional couplers also act as limiters in intensity-dependent switches. The propagation constants of the modes of a system are changed by non-linearity. In order to discuss the physical nature of couplers, 2D and 3D figures are also shown.

应用一种新的扩展直接代数方法为具有光学超材料的非线性定向耦合器提取新的行波解。该模型研究从主光纤到其他分支光纤的光分布，可以是一根或多根。因此，出于这个原因，本文研究了双耦合器和多芯耦合器。详细讨论了多芯耦合器中的另外两种情况，即邻近的多芯耦合器和具有完全邻居的多芯耦合器。这里考虑的非线性类型是克尔定律。得到的解集比现有解更具有泛化性，因为它被转化为分数阶导数，因为它给出了重尾或无穷大涨落问题的解。此外，得到的解几乎包含暗、亮、暗-亮、有理、周期、呼吸和奇异孤子解等所有类型的孤子。而且，得到的解是带有Atangana-Baleanu和修正Riemann-Liouville分数的分数孤子操作员。这些非线性定向耦合器还充当强度相关开关中的限制器。系统模式的传播常数因非线性而改变。为了讨论耦合器的物理性质，还显示了 2D 和 3D 图形。这些非线性定向耦合器还充当强度相关开关中的限制器。系统模式的传播常数因非线性而改变。为了讨论耦合器的物理性质，还显示了 2D 和 3D 图形。这些非线性定向耦合器还充当强度相关开关中的限制器。系统模式的传播常数因非线性而改变。为了讨论耦合器的物理性质，还显示了 2D 和 3D 图形。