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Variable power splitting ratio 2×2 MMI couplers using multimode waveguide holograms are analyzed. Theoretical analysis shows that variable splitting ratios can be obtained with surface relief holograms on MMI couplers with fixed dimensions. Devices with paired-imaging lengths are designed on a silicon-on-insulator (SOI) platform. Beam propagation simulations are used to verify a matrix theory analysis and to investigate proposed device performance. Fabrication tolerance of the proposed devicedoi:10.1364/oe.15.009015 pmid:19547241 fatcat:ntuuzafez5h4vo6tk43rywxx54