Page 355 - Electrical Properties of Materials

Exercises 337

12.5. In a laser material of 3 cm length the absorption coeffi- 12.9. Can the inverted population be saturated in a semi-
–1
cient is 0.14 cm . Applying a certain amount of pump power conductor laser? Can one make a Si or Ge p–n junction
–1
the achieved gain coefficient is 0.148 cm . One of the mirrors ‘laser’?
at the end of the laser rod has 100% efficiency.
12.10. Determine the threshold current density of a GaAs
Determine the minimum reflectivity of the second mirror
junction laser which has a cleaved edge. Assume the fol-
for laser action to be possible.
13
lowing values: linewidth = 10 Hz, attenuation coefficient,
–1
3
12.6. A typical argon ion laser has an output of 5 W and an α =10 m , l = 0.2 mm, d =2 μm, n = 3.35, η =1.
input current of 50 A at 500 V. What is the efficiency of the
12.11. A microwave cavity of resonant frequency ω is filled
laser?
with a material having a two-level system of electron spins, of
12.7. Assuming that the inversion curve of a laser is wide energy difference ω. The microwave magnetic field strength
enough to permit several axial modes, determine the fre- H can be considered uniform throughout the cavity volume V.
quency difference between nearest modes. Show that the rate of energy loss to the cavity walls is
12.8. The Doppler broadened lineshape function is given by ωμ 0 H V
2
eqn (12.26). ,
Q
(i) Show that the half-power bandwidth is given by the where Q is the quality factor of the cavity.
expression If the probability for induced transitions between levels per
1/2 2
2 k B T1n2
unit time is αH and spontaneous emission is negligible, show
ν =2ν 0 . that the condition for maser oscillation is
Mc 2
μ 0
(ii) Work out the half-power bandwidth for an argon laser N > ,
α Q
emitting at 514.5 nm at a temperature of 5000 K.
(iii) How many longitudinal modes are possible at this line if where N is the excess of upper level population density over
the length of the cavity is 1.5 m? lower. [Hint: Q = ω× energy stored/energy lost per second.]