Application: Optical waveguide. An optical waveguide is made in the form of a rectangular cross-section channel in a silicon substrate, as shown in Figure 17.31. The channel is 2μm wide, μm high, and ε= 2ε0.
(a) Explain why this structure can function as a rectangular waveguide and outline the conditions necessary for it to operate. Hint: Consider the conditions for total reflection in a dielectric.
(b) Calculate the lowest frequency that can be propagated. Which mode is it and in what range of the spectrum is this propagation possible?
(c) Calculate the peak power that can be propagated at twice the frequency calculated in (b) if the peak electric field intensity cannot exceed 1000 V/mm.
