多模干涉耦合器一般成像位置分析

自映像效应是多模波导的一个重要特性，利用多模波导自映像效应制成的多模干涉耦合器被广泛地应用于集成光学回路中。然而根据以往的文献要得出多模干涉耦合器的成像位置要经过一系列复杂的计算。根据多模干涉耦合器的自映像原理，对多模干涉耦合器的成像位置进行分析。成像位置与输入场位置和位置数密切相关，给出了成像位置的解析表达式，得出奇数、偶数的位置数的成像位置分别对应相同，并且奇、偶数的位置数所对应的成像位置之和为多模波导宽度的成像规律。用导模传输分析法验证了表达式和成像规律的正确性。根据成像位置的表达式和成像规律可以直接得出任意输入场位置和位置数所对应的成像位置。为一维和二维限制的多模干涉耦合器的设计提供了理论基础。

Analysis of General Self-Imaging Positions in Multimode Interference Couplers

Self-imaging effect is one of the most important properties of the multimode waveguides,and multimode interference couplers based on the self-imaging principle are widely used in integrated optical circuit. But to predict the positions of the images, a series of complex calculation is needed according to the previous method. Based on the self-imaging effect of multimode interference couplers,general self-imaging positions are analyzed in detail. The positions of the images are directly related to the position of the input field and positional number. Simple expressions for positions are derived. The following rule is concluded that the output images for all odd positional numbers have the same positions. So do all even positional numbers. Adding the positions for the odd positional number to the positions for the corresponding even positional number gets the width of the multimode waveguide. The guided-mode propagation analysis is used to confirm the analytical results. These formulae and conclusions can be used to indicate the positions of the images with the arbitrary input field and positional number without complex calculations,which provide a useful tool for the design of multimode interference couplers with one-and two-dimensional confinement.