Fig. 1. Structure of optical beamforming network (OBFN). (a) Three microring resonators (MRR) basic delay unit; (b) 1×N binary tree OBFN chip

Fig. 2. Simulated delay spectra of MRR at various coupling coefficients

Fig. 3. Simulated delay results of OBFN. (a) Delay spectra of the longest path in different stages of OBFNs with each BDU continuously tuned to 5 ps; (b) delay bandwidth of the longest path in different stages of OBFNs with one MRR continuously tuned in each stage

Fig. 4. Pictures of chip before and after packaging. (a) Microscopy image of BDU chip; (b) cross section of Si₃N₄ waveguide; (c) microscopy image of 1×8 OBFN chip; (b) picture of packaged chip with optical and electrical connections

Fig. 5. Schematic of experimental setup for optical and microwave measurement

Fig. 6. Flowchart of optical and microwave group delay calibration

Fig. 7. Optical calibration of MRRs. (a) Measured thermal efficiency of MRR phase shifter (MRR PS); (b) simulated transmission spectra of an MRR at various coupling coefficients; (c) MSE of optical transmission as a function of MZI PS power for K＝1 state calibration; (d) measured optical transmission of a BDU at the shortest and the longest delay states

Fig. 8. Optical characterization for MRR resonance alignment. (a) Process of MRR resonance alignment; (b) power relationship between MZI phase shifter and microring phase shifter for resonance alignment

Fig. 9. Measured delay spectra of a continuously tuned MRR at different coupling coefficients

Fig. 10. Experimental results of microwave delay characterization. (a) Microwave delay spectra of optical characterization results, where MRRs are affected by thermal crosstalk; (b) measured microwave delay spectra of path 7 as MRRs are digitally tuned from K＝0 state to K＝1 state one by one, where MRR states are optimized to eliminate the effect of thermal crosstalk; (c) microwave delay spectra of three continuously tuned MRRs at various delay increments; (d) delay fluctuation of three continuously tuned MRRs over the frequency of 08 GHz at various delay increments