any state of polarization the waveguides 20 and 22 are designed to be identically or near identically matched in length and width from the signal input up to the input of the 4 u00d7 4 mmi coupler 14 this is to ensure that any birefringence in the waveguides is matched the two waveguides 20 and 22 are coupled to separate specific inputs 24 of the 4 u00d7 4 mmi coupler 14 for 90 u00b0 phase mixer functionality that is the 4 u00d7 4 mmi coupler 14 includes four inputs 24 a d and two of the inputs 24 are respectively coupled to the waveguides 20 and 22 for receiving the input signal while the other two inputs 24 are unused the waveguides 20 and 22 may be coupled to the inputs 24 in any of these specific possible arrangements 24 a and 24 b 24 a and 24 c 24 c and 24 d and 24 b and 24 d phase and auxiliary controls may also be included along the waveguides 20 and 22 specifically one or more phase electrodes 26 may be included along the waveguides 20 and 22 to enable adjustment of the relative optical phases of the signals resistive heaters on the top of the ridge waveguide are used to provide a localised heating of the waveguide core.