A multimode waveguide interference (MMI) coupler is combined with a critical linear tapered waveguide on a silicon-on-insulator (SOI) chip. When the TE₀ mode is a critical adiabatic mode conversion from a single-mode waveguide to an extreme linear tapered waveguide combined with an MMI, this linear tapered waveguide is achieved to the maximum divergence angle (i.e., the shortest length). The maximum divergence angle is expressed by θ ≤ 2 tan⁻¹[(0.35W_mmi − W_s)/(0.172L_mmi)] under a 1 × 1 MMI combined with this critical linear tapered waveguide. The expression formula is demonstrated by three different widths of a 1 × 1 MMI of 4 μm/8 μm/12 μm combined with the critical linear tapered waveguide. So, the maximum divergence angle is obtained at θ = 16°/14°/8°, with respect to this linear tapered waveguide loss of 0.022 dB/0.172 dB/0.158 dB, and this linear tapper length is reduced by 93.7%/92.9%/87.5% than the divergence angle θ = 1°. The output power of a 1 × 1 MMI combined with a critical linear tapered waveguide is enhanced at least 1.5 times under 0.95 above condition.

中文翻译：

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临界绝热线性锥形波导与SOI芯片上的多模波导耦合器组合

多模波导干涉（MMI）耦合器与绝缘体上硅（SOI）芯片上的临界线性锥形波导结合在一起。当TE ₀模式是从单模波导到结合MMI的极端线性锥形波导的绝热绝热模式转换时，此线性锥形波导可以达到最大发散角（即最短长度）。的最大发散角被表示为θ  ≤2黄褐色^-1 [（0.35 w ^ _MMI  -  w ^_小号）/（0.172大号_MMI）]下一个1×1 MMI与此临界线性锥形波导相结合。表达公式由4的1×1 MMI的三个不同宽度证实 μm / 8个 μ米/ 12  μ米与临界线性锥形波导相结合。因此， 相对于此线性锥形波导损耗0.022 dB / 0.172 dB / 0.158 dB，在θ = 16°/ 14°/ 8°处获得了最大发散角，并且该线性锥孔长度减少了93.7％/ 92.9比发散角θ  = 1°为％/ 87.5％。在高于0.95的条件下，结合了临界线性锥形波导的1×1 MMI的输出功率至少提高了1.5倍。