On the Complexity of Optical Cross-Connects under Flat and Recursive Shared Wave-Mixing Converters

Wave-mixing Optical Cross-Connects (WM-OXCs) reduce complexity by using bulk wavelength converters (BWCs) to simultaneously convert multiple distinct wavelength channels. This letter investigates the complexity of WM-OXCs under two BWCs sharing schemes, namely, the recursive and flat sharing. It is shown that: (1) recursive sharing requires at least twice as many converters as those used in an optimal OXC with single-channel converters, (2) flat sharing requires strictly less number of native converters compared to the optimal OXC when W log W/ W-1 _≤ C ≤ (W is the number of wavelengths per fiber, and C is number of simultaneously converted channels per BWC).