Page 340 - Tunable Lasers Handbook

300 Norman P. Barnes
1
1 t(rl)’sin’ (AkZ/2)/(Ak1/2)2 .

In this case, energy can be transferred between the pump and the signal and idler
beams and back again.
When a Gaussian beam enjoys a gain profile created by a Gaussian pump
beam, an average-gain concept can accurately describe the situation. An average
gain can be computed by integrating the product of the initial signal and the gain
created by a Gaussian pump beam. With a Gaussian pump beam, the square of
the electric field can be expressed as

where c is the speed of light, P, is the power of the pump beam, w1 is the beam
radius, and p is the radial coordinate. When the electric field of the pump varies
with radial position, the gain also varies radially since r depends on the electric
field of the pump. An average gain G, can be defined as [ 151
(
G, = [- 5 T) cosh’ (rl)2npdp .
exp
2pl
-
-0 -
Although this expression cannot be integrated in closed form, it is readily
amenable to integration using numerical techniques. Note that this expression
represents a power gain. Energy gain can then be readily computed by integrat-
ing this expression over time.
Gain in parametric amplifiers has been characterized experimentally and
found to agree with the predictions of the model. For these experiments, a contin-
uous wave (cw) HeNe laser operating at 3.39 pm was used as the signal, and a
pulsed Er:YLF laser, operating at 1.73 pm, was used as the pump. Both the
energy and the pulse length of the pump laser were measured to determine the
power of the laser. Beam radii of both the pump and the signal beam were mea-
sured using a translating knife-edge technique. Pump energies ranged up to 15 mJ,
and the pulse lengths, represented by rl, were typically around 180 ns. Even with
this relatively low power, single-pass gains in excess of 13 were observed. In Fig.
1, the experimental gain of the signal versus (El/~l)’5 is plotted along with the
average gain computed from Eq. (15). To within experimental error. the agree-
ment between the experiment and the prediction of the average gain is found to be
reasonable. High single-pass gains available with optical parametric amplifiers
make their use attractive in high-energy-per-pulse situations.
While high-gain optical parametric amplifiers are possible, amplified sponta-
neous emission (ASE) does not affect these devices like it affects laser amplifiers.