We show that it is possible to obtain 2 x 2 waveguide couplers with arbitrary power splitting ratios by interconnecting a pair of unequal width waveguides as the phase-tuning section into the middle of two short MMI sections. These couplers have simple geometry and low loss. They offer valuable new possibilities for designing waveguide-based photonic integrated circuits.
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Feng et al. (2008) studied this question.