Mid-infrared 2 × 2 electro-optical switching by silicon and germanium three-waveguide and four-waveguide directional couplers using free-carrier injection

Abstract

New designs are proposed for 2×2 electro-optical switching in the 1.3–12 μm wavelength range. Directional couplers are analyzed using a two-dimensional effective-index approximation. It is shown that three or four side-coupled Si or Ge channel waveguides can provide complete crossbar broad-spectrum switching when the central waveguides are injected with electrons and holes to modify the waveguides’ core index by an amount Δn+iΔk. The four-waveguide device is found to have a required active length L that is 50% shorter than L for the three-waveguide switch. A rule of ΔβL>28 for 3w and ΔβL>14 for 4w is deduced to promise insertion loss <1.5 dB and crosstalk <−15 dB at the bar state. At an injection of ΔNe=ΔNh=5×1017 cm−3, the predicted L decreased from ∼2 to ∼0.5 mm as λ increased from 1.32 to 12 μm. Because of Ge’s large Δk, the Ge bar loss is high in 4w but is acceptable in 3w.