Pintus Paolo
Opt Express. 2014 Jun 30;22(13):15737-56. doi: 10.1364/OE.22.015737.
In this work, a dielectric waveguide mode solver is presented considering a general nonreciprocal permittivity tensor. The proposed method allows us to investigate important cases of practical interest in the field of integrated optics, such as magneto-optical isolators and anisotropic waveguides. Unlike the earlier developed mode solver, our approach allows for the precise computation of both forward and backward propagating modes in the nonreciprocal case, ensuring high accuracy and computational efficiency. As a result, the nonreciprocal loss/phase shift can be directly computed, avoiding the use of the perturbation method. To compute the electromagnetic modes, the Rayleigh-Ritz functional is derived for the non-self adjoint case, it is discretized using the node-based finite element method and the penalty function is added to remove the spurious solutions. The resulting quadratic eigenvalue problem is linearized and solved in terms of the propagation constant for a given frequency (i.e., γ-formulation). The main benefits of this formulation are that it avoids the time-consuming iterations and preserves the matrix sparsity. Finally, the method is used to study two examples of integrated optical isolators based on nonreciprocal phase shift and nonreciprocal loss effect, respectively. The developed method is then compared with the perturbation approach and its simplified formulation based on semivectorial approximation.
在这项工作中，提出了一种考虑一般非互易介电常数张量的介质波导模式求解器。所提出的方法使我们能够研究集成光学领域中具有实际意义的重要情况，例如磁光隔离器和各向异性波导。与早期开发的模式求解器不同，我们的方法允许在非互易情况下精确计算正向和反向传播模式，确保高精度和计算效率。结果，可以直接计算非互易损耗/相移，避免使用微扰法。为了计算电磁模式，针对非自伴情况推导了瑞利 - 里兹泛函，使用基于节点的有限元方法对其进行离散化，并添加惩罚函数以消除虚假解。将得到的二次特征值问题线性化，并针对给定频率根据传播常数进行求解（即γ公式）。这种公式的主要优点是它避免了耗时的迭代并保持了矩阵的稀疏性。最后，该方法分别用于研究基于非互易相移和非互易损耗效应的集成光学隔离器的两个示例。然后将所开发的方法与微扰方法及其基于半矢量近似的简化公式进行比较。
