Homework 3 (due
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.
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?
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.