Directional Coupler
Directional coupler made of Si wire waveguides (wavelength=1550 nm)Fabrication technology of directional coupler is here and here
It is important component of many devices made of Sinanowire waveguide. Depending on device, a different coupling ratio is required: 1) polarizer and polarization beam splitter100 % for TM mode, small for TE mode 2) Machâ€“Zehnder interferometer50 % 3) ring resonatorsmall
comsol+ matlab files for calculation can be downloaded here DirectionalCoupler2.m DirectionalCoupler2.mph: Calculation for a fixed gap

Fig..2 The length of full conversion of waveguide mode from a waveguide to a waveguide as function of gap between two parallel Si waveguides. The waveguides are not covered by SiO2. Thickness of Si waveguides 220 nm, width 450 nm. 
Fig.2a Conversion of TE mode of two parallel waveguides. Gap between waveguides is 250 nm. Thickness of Si waveguides 220 nm, width 450 nm. The conversion length of light from one waveguide to another is 68 um (See Fig.2) 
Fig..3 The length of full conversion of waveguide mode from a waveguide to a waveguide as function of gap between two parallel Si waveguides. The waveguides are covered by SiO2. Thickness of waveguides 220 nm, width 450 nm. 
Fig.3a Conversion of TM mode of two parallel waveguides. Gap between waveguides is 450 nm. Thickness of Si waveguides 220 nm, width 450 nm. The conversion length of light from one waveguide to another is 15 um (See Fig.2) 
Directional coupler as a polarizer 
Fig.5 Maximum polarization ratio, which can be achieved by a directional coupler as function of gap in the coupler. For each gap the length of the coupler is adjusted to 100 % of TM mode conversion (See red line in Fig.2 and 3). The distance of The width of Si waveguides is 450 nm 
The fabrication technology of polarizer made of Sinanowire waveguides is here
It is relatively easy to make a polarizer of polarization beam splitter using a directional coupler.
As can be seen from Fig.2 and 3, the distance for 100% conversion is significantly different for TM and TE modes. For example, from Fig 3 for 400 nm gap the distance for 100% conversion is ~11 um for TM mode and ~150 um for TE mode. In case of length of coupler of 11 um, 100 % of TM polarization is converted into output 2, but there is only a very little conversion of TE polarization and near all TE polarized light goes to output 1. Therefore, the coupler splits TMpolarized light to output 2 and TEpolarized light to output 1.
From calculation of Fig.5, a larger polarization ratio can be achieved in coupler with larger gap between the coupling waveguides. From Fig.2 and 3 the larger gap requires a longer interaction distance for required 100 % of conversion of TM mode.