Richard Soref, "Mid-infrared 2 × 2 electro-optical switching by silicon and germanium three-waveguide and four-waveguide directional couplers using free-carrier injection," Photonics Res. 2, 102 (2014)

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- Photonics Research
- Vol. 2, Issue 5, 102 (2014)

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 Δ β L = π and Δ k 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) L c = 750 μm and (b) L c = 370 μm when Δ n = Δ k = 0 (solid lines), Δ β L = 14.3 and Δ k = 0 (dashed lines), and Δ β L = 14.3 and ρ = Δ n / Δ k = 10 (dotted lines).

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

Fig. 12. Beam-propagation simulation at 1.32 μm for (a) Si 4w with L c = 750 μm and (b) 3w with L c = 1500 μm when Δ n = Δ k = 0 (solid lines), Δ n = 0.004 and Δ k = 0 (dashed lines), and Δ n = 0.004 and Δ k = 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).
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Table 1. Change in Silicon Waveguide Core Index at a Carrier Injection Level of
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Table 2. Change in Germanium Waveguide Core Index at a Carrier Injection Level of
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Table 3. Minimum Device Length in Si and Ge Required to Meet the -for-3w and -for-4w Criteria at the Carrier Injection Level of

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