采用三维波束传输法的多模干涉耦合器成像位置的数值计算

Numerical Calculation of Imaging Positions in Multimode Interference Couplers by the Three-Dimensional Beam Propagation Method

多模干涉(MMI)耦合器需要精确定位成像位置,以便器件的设计制作。针对强限制和弱限制的三维多模波导干涉耦合器,采用三维交替方向隐式有限差分光束传输法(BPM),数值计算得出多模波导长度、输入波导和输出波导位置。首先通过对对称干涉多模干涉耦合器的数值分析求得多模干涉耦合器的等效宽度Weq及最低二阶模之间的拍长Lc,然后将这些参量结合光束传输法直接用于器件设计。计算显示该方法得到的成像位置和导模传输分析法(MPA)的理论预测比较接近,但Weq和Lc却是由光束传输法计算得到的,导模传输分析法理论只能在得到Weq和Lc的前提下才能得到成像位置。该方法直接针对三维波导进行,没有采用基于等效折射率方法的从三维波导到二维波导的简化处理,并且也没有采用导模传输分析法所采用的近似,保证了计算精度,对于实际多模干涉器件的设计制作可起参考作用。

In order to design and make multimode interference （MMI） couplers, the imaging positions must be located accurately. The implicit finite difference beam propagation method （BPM） in three-dimensional alternate directions is used for the analysis of strongly guided and weakly guided multimode interference couplers. The length of multimode waveguide, the positions of input guides and output guides are determined precisely. The equivalent width Weq and the beat length Lc of two lowest modes of multimode waveguide are obtained first by the numeric modeling of a symmetric interference MMI, and then these parameters together with BPM are used for the device design. The imaging positions showed the close results between BPM and the predictions of the mode propagation analysis （MPA） theory, however, Weq and Lc were obtained by the BPM, MPA theory will not give any result without these parameters. The three dimensional （3D） waveguides are not treated as 2D waveguides by means of effective index method （EI）, therefore, this method can be used directly to 3D waveguides. As a kind of numerical method, some normal approximations are not introduced as MPA theory, so it will ensure the precision of calculation and can afford reference for practical MMI device design.