A dual channel directional coupler is made from square 400 × 400 nm waveguides with index of refraction = 3.45 formed in a substrate with index =3.35.The separation between waveguides is 500 nm. For a...

A dual channel directional coupler is made from square 400 × 400 nm

waveguides with index of refraction = 3.45 formed in a substrate with index

=3.35.The separation between waveguides is 500 nm. For a TE mode with a

vacuum wavelength of 900 nm, how long must this coupler be to make a 3 dB

coupler if the coupling coefficient κ = 1.229 × 10−5 nm−1?

Hint: You may not need all of the given information to solve this problem.