ECE/PH 482/582 Fall 2009 Problem Set #6
Due: Wednesday, December 2, 2009 in class
1. Kuhn: Problem 5.4 on rate equations
2. A laser at λo = 1.0 μm, which is to be Q-switched, has an initial population inversion of 1018
atoms, a factor of 3 above the threshold value required for CW oscillation in the high Q cavity.
There are three types of photon losses in the cavity: coupling through one mirror to the outside
world at a rate of 5 x 107/sec, loss in the electro-optic Q-switch at a rate of 107/sec, and useless
losses at the air-rod-switch interfaces at a rate of 1 x 107/sec. The inversion after the Q-switched
pulse is over is 5.9 x 1016 atoms.
a) Find the peak power out of this laser.
b) Find the output energy in the Q-switched pulse.
c) Estimate the pulse width.
3. (Good review for final exam)
A HeNe laser at λo = 632.8 nm operating in the fundamental transverse mode has mirrors
separated by 30 cm and an active gain length of 20 cm. The Doppler-broadened linewidth is 1.5
GHz, and the effective refractive index is n = 1. The output mirror is flat, and the other mirror is
spherical with a radius of curvature of 4 m.
a) What is the frequency difference between longitudinal modes in the resonator?
b) Show that the resonator is stable.
c) What would the Doppler width become if the temperature of the laser medium were
doubled?
d) What is the spot size at the flat mirror?
e) If the output is taken from the flat mirror, what is the spot size 10 m away?
f) Given that the distributed cavity loss (over the whole cavity length) coefficient is
10-4/cm, the small signal gain coefficient is 10-3/cm, and the reflection coefficient of
the spherical mirror is 1.0, what is the reflection coefficient, R, of the output mirror
that will give the maximum output power?
g) A thin lens of focal length f is placed against the output mirror. Find the radius of
curvature of the Gaussian beam at a distance d = f from the lens.
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Grad Students only (Bonus credit for Undergrads)
4. Kuhn: Problem 6.4