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[(0.35Wmmi???Ws)/(0.172Lmmi)] 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.
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