as a function of u03c6 wide u2014 d and u03c6 narrow u2014 u which are themselves given by 7 and 8 u03d5 wide_u arccos ue8a0 u03b1 ue89e ue89e cos ue89e ue89e u03d5 wide_d w wide u03b1 w wide 11 u03d5 narrow_d arccos ue8a0 u03b2cos u03d5 narrow_u w narrow u03b2 w narrow 12 the taper section 2 is now completely defined i e the first outer edge 2 a is defined by equation 1 where u03c6 wide runs between 0 and u03c6 wide u2014 u the quantity u03c6 wide u2014 u is defined in equation 11 where a is defined in equation 6 and u03c6 wide u2014 d in equation 7 the second outer edge 2 b of the taper section 2 is defined by equation 2 where u03c6 narrow runs between 0 and u03c6 narrow u2014 d the quantity u03c6 narrow u2014 d is defined in equation 12 where u03b2 is defined in equation 6 and u03c6 narrow u2014 u in equation 8 the respective edges of the output waveguides 3 and 4 have been defined above however the position of the ends thereof still has not been determined in the aforementioned prior art references several authors have shown that the optical power.