1. [20 points] A pulse consisting of multiple optical waves with different wavelengths is
propagating in a medium with the following dispersion characteristic. The center wavelength of
the pulse is 900 nm. Find the speed of the pulse propagation.
2. [20 points] NASA installed a mirror on the lunar surface to measure the distance between the
Earth and the moon. A giant laser beam was shot from Steward Observatory. The laser was a
Helium-Neon laser (λo = 632.8 nm) from a cylindrical cavity. The output beam diameter was 2
cm and the wavefront was flat at that point.
(a) Calculate the beam diameter at the lunar surface (approximately 385,000 km away).
(b) Calculate the beam diameter at the lunar surface if the original beam diameter was expanded
to 2 m using a telescope.
3. [20 points] A HeNe laser (λo = 632.8 nm) beam is incident on a glass (n=1.5) surface relief
grating with pitch Λ = 350 nm. Assuming 45° incidence angle, determine the number of allowed
reflection and transmission diffraction orders and their angles.
4. [10 points] A symmetric dielectric slab waveguide has core index of 1.51, cladding index
1.505, and 8 μm core thickness. Find the single mode cutoff wavelength, numerical aperture, and
acceptance angle.
5. [10 points] At 1550 nm, the output power of a 20 km-long optical fiber was measured to be 4
mW. When the input power was 150 mW, what is the attenuation coefficient of the fiber in
[dB/km]?
6. [10 points] A circular lens with 5 cm diameter and 10 cm focal length was used to focus a
plane wave (free-space wavelength = 632 nm). Find the radius of the focal spot.
7. [10 points] A Fabry-Perot resonator is implemented with two perfect metal mirrors separated
by 50 cm in parallel to each other. The space between the mirrors is glass (n = 1.5). What will be
the frequency spacing between the cavity resonance peaks?