A planar dielectric waveguide is fabricated by sputtering a thin glass film (n2 = 1.62) on top of a glass substrate (n3 = 1.346). The light source is a He-Ne laser operating at wavelength λ0 = 6328 A....

A planar dielectric waveguide is fabricated by sputtering a thin glass film

(n2 = 1.62) on top of a glass substrate (n3 = 1.346). The light source is a

He-Ne laser operating at wavelength λ0 = 6328 A. ˚

(a) What is the maximum thickness of the waveguiding layer for the guide to

propagate only one mode?

(b) If the propagation constant in the direction of propagation is β = 1.53 ×

105 cm−1, what is the bounce angle θm of the mode? (Make a sketch and

label the angle for clarity.)