ED II. Homework 2 (due 2/27/02)

- Derive the phase change of a plane wave
undergoing total internal reflection from
a medium with index of
refraction n
_{1}to a medium with n_{2}(n_{1}>n_{2}).

_{} _{}

(This is the first equation on page 2 of the 2/20/02 handout). Note that the angle q is defined from the plane, not from the normal to the plane. You may want to use the equations derived in Jackson directly.

- For
the planar dielectric waveguide, consider the example with d=10mm,
n
_{1}=3.5, n_{2}=3.45, and the wavelength in vacuum is 0.9mm. Calculate**all**the allowed modes, the phase velocity and the group velocity of each mode.

(you may want to write a simple code to get the answers).