Homework 3 (due 3/11/02)

1. Consider a wave formed by the sum of two identical Gaussian beams propagating in the +z and –z directions. Show that the result is a standing wave. Using the boundary conditions at two identical mirrors placed such that they coincide with the wavefronts, derive the resonance frequencies – this was derived in a different way in the class.

2. Consider a light of wavelength 1.06mm and spectral width Dn=120 GHz. How many modes have frequencies within this linewidth in a one-dimensional resonator of length d=10 cm?

3. Consider a cyclindrical coaxial line which consists of an outer perfect conductor of radius a and an inner perfect conductor of radius b. Show that TEM waves can be propagated in such a structure if the transverse field varies inversely with r, the distance from the axis of symmetry. Find the necessary potential difference between the outer and inner conductors. Find also the magnetic induction vector.