An MMI-based six-port circulator is analyzed by 3-D magneto-optical (MO) beam propagation method (BPM). Since opposite nonreciprocal $4\pi/3$-phase shifts are introduced into the two sided interferometric arms of 3$\,\times\,$3 mirror-image MMI coupler, light travels through this device in a nonreciprocal fashion and obeys the sequential order. After using the Ce:YIG/SOI bonding waveguide to construct the proposed circulator, the 3-D MO BPM formula are validated for the first time to simulate nonreciprocal device with external magnetization perpendicular to the light propagation direction. Simulation shows that this device features in easy fabrication, good operation bandwidth, ability to reduce the port count number.
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