In this case of course the two waveguides have to be identical. Now taking , we get
The power is therefore equally divided between the two waveguides.
Wavelength Filter
Since the coupling coefficient and hence the coupling length is a function of wavelength, we can design the coupler is such a way that is odd and is even, where are the coupling lengths at the two wavelengths respectively.
Then wavelength will appear at the output of waveguide A, and will appear at the output of waveguide B. The two wavelengths can therefore be separated by the directional coupler.
, we get 
is odd and 
is even, where 
are the coupling lengths at the two wavelengths 
respectively. 
will appear at the output of waveguide A, and 
will appear at the output of waveguide B. The two wavelengths can therefore be separated by the directional coupler. 
