Fig. 1. Schematic configurations of the proposed calibration-free elementary 2×2 MZS. (a) Overview; (b) cross section of the phase-shifter; (c) TES-bend and the bent-ADC mode filter.

Fig. 2. (a) Local angle θ and the curvature radius R, and (b) the core width w as functions of the curve length L for the first half of the TES-bend.

Fig. 3. Simulation results for the designed 2×2 MZS. Calculated transmissions of the designed TES-bend (a) without and (b) with the bent-ADC mode filter, respectively. Insets, simulated light propagations when the TE₀ and TE₁ modes are launched, respectively. (c) Calculated transmissions of the MMI coupler connected with the TES-bends. Inset, simulated light propagation for the launched TE₀ mode. (d) Calculated transmissions at the cross and bar ports of the designed MZS in the Off state.

Fig. 4. (a) Calculated total phase imbalance for the new MZS consisting of TES-bends as well as arm waveguides with different core widths of 1, 2, and 3 μm; here the mean width difference δw varies from 1 nm to 20 nm; the result for conventional MZSs with 450-nm-wide arm waveguides is also given; (b) the itemized phase imbalance as the core width wco varies. The results for the conventional MZS with 450-nm-wide S-bends are also included for comparison.

Fig. 5. (a) Optical microscope image of the fabricated 2×2 MZS; (b) measured transmissions at the cross/bar ports for the central wavelength when sweeping the heating power Q from 0 to 80 mW; (c) measured transmissions at the cross/bar ports of the present MZS operating at the Off/On (cross/bar) states (i.e., Q=0 and 34 mW, respectively); (d) summary of the measured phase imbalances for all the MZSs (Designs A, B, C, and D) from 11 chips in the same fabrication batch. Design A is with the TES-bends and 2-μm-wide phase-shifters; Design B is with the TES-bends and 1-μm-wide phase-shifters; Design C is with the conventional 0.45-μm-wide S-bends and 2-μm-wide phase-shifters; Design D is with the conventional 0.45-μm-wide S-bends/phase-shifters.

Fig. 6. (a) Optical microscope image, and (b)–(e) measured all-cross transmissions Tij at the output port Oj with the port Ii importing when i=1, 2, 3, and 4, respectively, with no calibration for all the six MZSs. (f)–(i) Measured all-bar transmissions Tij, where the signals launched from input ports I1, I2, I3, and I4 are routed to output ports O1, O2, O3, and O4, respectively.

Fig. 7. Synthesized eye-diagrams at port (a) O1, (b) O2, (c) O3, and (d) O₄ of the present 4×4 MZS in the all-cross states. Here the bit rate is 30 Gb/s.

Fig. 8. Adiabatic taper with different shapes. (a) Structure. (b) Calculated excess loss for the TE0 mode. (c) Calculated mode excitation ratio to the TE1 mode. Here wco=2  μm and w1=0.9  μm.

Fig. 9. Simulated transmission spectra of the 2×2 MMI coupler, including the TE0 and TE1 modes at the cross and through ports.

Fig. 10. Calculated effective indices of the TE modes of 220-nm-thick silicon waveguides.

Fig. 11. (a), (b) Optical microscope images of TES-bend. (c) The measured transmissions for the testing structures with a number of TES-bends in cascade.

Fig. 12. Measured transmissions of the fabricated 4×4 MZS with Benes network in (a), (b) (10|00|00) state; (c), (d) (01|00|00) state; (e), (f) (00|10|00) state; (g), (h) (00|01|00) state; (i), (j) (00|00|10) state; (k), (l) (00|00|01) state.