Fig. 1. (a) Schematic of the proposed polarization-insensitive 2×2 MMI (SiO2 cladding is not shown for clarity). (b) Top view of the taper from input silicon wire to bricked SWG waveguide. (c) Top view of the bricked SWG multimode waveguide.

Fig. 2. (a) Procedure employed for modeling the bricked SWG. (b) Calculated refractive index components for a bricked SWG waveguide with h=220  nm, Λx=200  nm, DCx=50%, Λz=240  nm, and DCz=50% at the wavelength λ=1.31  μm. (c) Beat length for wMMI=3  μm using the 2D anisotropic model (solid curves) and full 3D simulations (dotted curves).

Fig. 3. Design methodology used in this work, comprising two main stages: (a) design of the bricked SWG multimode waveguide and (b) optimization of the complete device using a 3D-FDTD simulator.

Fig. 4. Absolute value of the relative difference between TE and TM beat lengths |ΔLπ¯|=|ΔLπ/Lπ¯|, where ΔLπ=Lπ(TE)−Lπ(TM) and Lπ¯=(Lπ(TE)+Lπ(TM))/2, calculated using the anisotropic 2D model. Simulation parameters of the unit cell are h=220  nm, DCz=DCx=50%, Λx=200  nm, and λ=1.31  μm. The dashed line represents the points (dz,Λz) for which ΔLπ¯=0. The optimal parameters Λz=240  nm and dz=Λz/2 are marked with a green dot.

Fig. 5. Beat length as a function of wavelength obtained from 3D Floquet–Bloch simulations of the (bricked) SWG waveguide. Solid lines correspond to dz=0, while dashed lines correspond to dz=0.48Λz. Other geometrical parameters are: wMMI=3  μm, h=220  nm, Λx=200  nm, DCx=50%, Λz=220  nm, and DCz=50%.

Fig. 6. Final design performance of the optimized polarization-independent 2×2 MMI.

Fig. 7. Dependence of the bandwidth and center wavelength of the MMI on fabrication error δ. The bandwidth is defined as the wavelength range in which PDL, EL, and |IB| are simultaneously below 1 dB, and |PE| is less than 5°. The inset shows the effect on the in-plane geometry of positive and negative values of δ. The original geometry (top view, i.e., in the chip plane) is represented with a continuous line, while the over/under-etched geometry is represented with a dashed line.

Fig. 8. Calculation of |ΔLπ¯| as performed in Fig. 4 for different transversal periods Λx and duty cycles (DC=DCx=DCz) and the wavelength of λ=1310  nm. The dashed line corresponds to |ΔLπ|=0. The design point is marked with a green dot in (d). For Λx>200  nm or DC≠50%, the design space for |ΔLπ¯| is closer to the Bragg zone [see cases (a), (e), and (g)] or no solution can be found, as shown in (b), (c), (f), (h), and (i).