A grating with spacing Λ = 0.4 μm, situated on a GaAs planar waveguide, is to be used for coupling a beam of light from a He-Ne laser (λ0 = 1.15 μm) into the waveguide. If the propagation constant for...

A grating with spacing Λ = 0.4 μm, situated on a GaAs planar waveguide, is

to be used for coupling a beam of light from a He-Ne laser (λ0 = 1.15 μm)

into the waveguide. If the propagation constant for the lowest-order mode in

the guide is β0 = 3.6 k, what angle must the laser beam make with the surface

of the waveguide in order to couple to this mode? Assume first-order coupling,

i.e. |ν| = 1.