In the case of a prism coupler, explain why the condition βm = 2πnp λ0 sin θm, must be satisfied in order for coupling to occur. Derive the equation from geometric considerations (np: index of...

In the case of a prism coupler, explain why the condition

βm = 2πnp

λ0

sin θm,

must be satisfied in order for coupling to occur. Derive the equation from geometric considerations (np: index of refraction of prism, βm: phase constant of

mthe mode in the waveguide, θm: angle between normal to waveguide surface

and incident ray of light within the prism, and λ0: wavelength of light in air).