Department of Engineering Science
Sonoma State University
ES 445
Photonics
HW 10
Solutions must be written clearly and explained thoroughly.
Diagrams must be drawn with care
1. Consider a cylindrical Ruby laser, 10 cm long and 1.0 cm in
diameter, in which the concentration of Cr3+ ions is 8.5 x 1018 cm-3.
Assume the energy of the pumping photons to be 2.25 ev, and the
minimum necessary pumping power for achieving population
inversion is 4.0 kW. Further, consider the Ruby laser to have a 3level laser system. The pumping light forces Cr atoms to transition
from the ground energy level E1 to the excited energy level E3,
from which the atoms spontaneously transition to energy level E2.
E2 is a long-lived energy state with a spontaneous emission
lifetime τsp.
(a) Draw a 3-level energy diagram and indicate energy states E1,
E2, and E3.
(b) Determine the wavelength of the pumping light.
(c) Calculate the spontaneous emission lifetime τsp.
(d) The wavelength of the output light of Ruby laser is 694.3 nm.
Calculate the energy of the long-lived state E2 with respect to
the ground state energy (E2 – E1).
2. Consider an 18-cm long Nd3+-doped silica-based glass fiber
amplifier with the doping concentration of 8.5 x 1018 cm-3.
Assume a 4-level energy system for this amplifier. The light output
of this amplifier due to the stimulated emission has a wavelength
of 1.05 μm and the emission cress-section of the long-lived state is
2.8 x 10-20 cm2.
(a) Draw the 4-level energy level diagram of this amplifier.
(b) Determine the energy of the emitted photos due to stimulated
emission.
(c) Calculate the gain factor of the amplifier.
(d) Calculate the maximum theoretical gain for this amplifier in
dB.
3. Consider a 3.5 m long Erbium-Doped Fiber Amplifier (EDFA)
with a core diameter of 6 μm, and an Er3+ doping concentration of
8.5 x 1018 cm-3. Assume the spontaneous decay lifetime of Er3+ at
the long-lived energy state to be 12 ms. The pumping source for
this fiber amplifier is a 980 nm laser diode, which couples 25 mW
Department of Engineering Science
Sonoma State University
of optical power into the fiber. Assume that the maximum fiber
length beyond which the gain is lost rapidly (Lp) is 4.0 m. Assume
the emission cross-section to be 3.2 x 10-21 cm2 and the absorption
cross-section to be 2.4 x 10-21 cm2. Calculate:
(a) The confinement factor for this fiber amplifier. This is the
percentage of the light pumped into the fiber which confined
within the fiber.
(b) The gain in dB for full population inversion.
(c) The gain in dB for 85% population inversion.