10.1

For incidence from glass with n = 1.5 to air, calculate the Goos-H nchen phase shift ? for both TE and TM waves. Plot ? as a function of the incidence angle ? ₁.

10.2

Show that the normal component of the time-averaged Poynting vector is zero in both media when total internal reflection occurs. Prove Eq. (10.8).

10.3

Calculate the Goos-H nchen lateral shift upon total internal reflection from a dielectric with n = 2 to air. Plot the lateral shift for both TE and TM waves as a function of ? ₁. Discuss the cause and the physical significance of the lateral beam shift.

10.4

A perfect conductor can be understood based on the Drude free-electron model by neglecting the collision term. The dielectric function becomes ?( ?) = 1 ? ? ² _p/ ? ², where ? _p is the plasma frequency. For radiation incident from air to a perfect conductor, calculate the phase shift when ? = ? _p/2 for TE and TM waves as a function of the incidence angle. Use Eq. (10.9) to calculate the lateral beam shift for a TM wave and modify it for a TE wave. Do you expect a sign difference between the TE and TM waves?

10.5

For a planar waveguide with n ₁ = 1.54 and n ₂ = 1.23, with a thickness of d = 200 nm,...