We demonstrated the inverse design of a multifunctional silicon photonic device named wavelength demultiplexing power splitter (WDPS) which can realize dual-band (1310/1550 nm) demultiplexing and 1:1 power splitting simultaneously. We proposed a novel two-step hybrid binary-analog optimization (TH-BAO) method that combines two distinct optimization techniques: direct binary search (DBS) for binary pixel-state optimization and particle swarm optimization (PSO) for analog pixel-position optimization. Compared with the traditional DBS method, the TH-BAO method achieves comparable optimization performance with a reduction of the total simulation runs by 29.2%. The inverse-designed WDPS achieves insertion losses of 0.76 dB and 1.19 dB, as well as channel crosstalks of -17.96 dB and -11.20 dB at 1310 nm and 1550 nm, respectively. Furthermore, the dual-band functionality of our device can efficiently support the development of next-generation passive optical networks.
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