We study analytically and numerically the possibility of vortex modes propagation over planar dielectric rectangular waveguides, and consider the problem of waveguide geometry optimization for the support of vortex modes. The results show, that theoretically rectangular waveguides can provide transmission of quasi-TE and quasi-TM modes with high purity states of orbital angular momentum (OAM) in the dominant field component. However, only for the quasi-generate mode of azimuthal order ±1 the constituent eigenmodes can propagate in a phase-matched regime, and the vortex modes of higher azimuthal orders can propagate only with a certain beat length. Moreover, as the target azimuthal order increases, the normalized power of the corresponding OAM state in the modal superposition decreases. The analytical predictions have been verified by numerical electromagnetic simulations of silicon nitride waveguides providing field distributions and OAM spectra of the corresponding modal superpositions.

中文翻译：

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矩形介质波导中涡模传播的建模和优化

我们分析和数值研究涡流模式在平面介质矩形波导上传播的可能性，并考虑了支持涡流模式的波导几何优化问题。结果表明，理论上矩形波导可以提供准 TE 和准 TM 模式的传输，在主场分量中具有高纯度的轨道角动量 (OAM) 状态。然而，仅对于方位阶 ±1 的准生成模式，组成本征模可以以相位匹配的方式传播，而更高方位阶的涡旋模式只能以一定的拍长传播。而且，随着目标方位角阶次的增加，模态叠加中对应OAM状态的归一化功率减小。