A general design rule of scrambling-type mode (de)multiplexers (mode scramblers) based on silica planar lightwave circuit (PLC) with small mode-dependent-loss (MDL) is presented for a mode-division multiplexing (MDM) system. First, we consider four- and eight-mode scramblers and demonstrate that if the number of modes is 2, it is possible to construct small-MDL mode scramblers by using Y-branch waveguides and mode rotators. Next, a 6-mode scrambler, which can be used for four linearly polarized (LP) mode transmission in MDM system, is considered, and the MDL is large if Y-branch waveguides are cascaded simply, originating from the radiation loss of unwanted modes at the Y-branch. We propose a 2 + 4-type mode scrambler by combining 2- and 4-mode scramblers and demonstrate that it is possible to design a small MDL 6-mode scrambler.
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