Fig. 1. MZI 2×2 at (a) cross state with zero bias, (b) lossless bar state with π shift in one arm, and (c) bar state with π shift and free-carrier-induced loss in one arm.

Fig. 2. MZI 2×2 bar-state IL (solid line) and CT (dashed line) versus ρ when ΔβL=π and Δk is induced in one arm.

Fig. 3. Top view of three-waveguide directional coupler 2×2 EO switch.

Fig. 4. 4×4 crossbar matrix switch composed of 16 “2w” switches.

Fig. 5. 4×4 permutation matrix switches made from six “3w” switches.

Fig. 6. 4×4 permutation matrix switches made from six “4w” switches.

Fig. 7. Top view of 3w symmetric coupler with one central active waveguide and two adjoining passive waveguides. CW light is launched from WG1.

Fig. 8. “2w” and “3w” 2×2 switching characteristics compared. The output of the two outer waveguides is shown as a function of phase shift induced in the central waveguide.

Fig. 9. Parameters of Si (a) 3w and (b) 4w used in 1.32 μm simulations.

Fig. 10. Beam-propagation simulation at 1.32 μm for Si 4w with (a) Lc=750  μm and (b) Lc=370  μm when Δn=Δk=0 (solid lines), ΔβL=14.3 and Δk=0 (dashed lines), and ΔβL=14.3 and ρ=Δn/Δk=10 (dotted lines).

Fig. 11. (a) IL and (b) CT versus ΔβL in Si 3w (dashed line) and 4w (solid line) at 1.32 μm with coupling length engineered for Lc=750  μm. This is the lossless Δk=0 case.

Fig. 12. Beam-propagation simulation at 1.32 μm for (a) Si 4w with Lc=750  μm and (b) 3w with Lc=1500  μm when Δn=Δk=0 (solid lines), Δn=0.004 and Δk=0 (dashed lines), and Δn=0.004 and Δk=0.001 (dotted lines).

Fig. 13. Bar-state IL and CT as a function of ρ for both switch configurations.

Fig. 14. Parameters of Ge (a) 3w and (b) 4w used in 12 μm simulations.

Fig. 15. Beam-propagation simulation at 12 μm for (a) Ge 4w and (b) Ge 3w at zero bias (solid lines), lossless injection (dashed lines), and lossy injection (dotted lines).