Page 340 - Electrical Properties of Materials

322 Lasers

(the set travelling in the opposite direction will make a similar contribution).
The electric field may then be written in the form,

N/2

E (z, t)= E 0 exp[–i(ω 0 + lω)(t – z/c m )]
l =–N/2
= E 0 exp[–iω 0 (t – z/c m )]F(t – z/c m ), (12.50)

where E 0 is a constant, and

1
sin( Nωx)
F(x)= 2 1 . (12.51)
sin( ωx)
2
Equation (12.50) represents a travelling wave, whose frequency is ω 0 , and its
shape (envelope) is given by the function, F.If N 1, F is of the form of a
sharp pulse of width 4π/Nω, and it is repeated with a frequency of ω. Taking
N = 100, a resonator length of 10 cm, and a refractive index of 2, we get a
pulsewidth of 27 ps and a repetition frequency of 750 MHz. The situation is, of
course, a lot more complicated in a practical laser, but the above figures give
good guidance. The shortest pulses to date have been obtained in dye lasers
with pulsewidths well below 1 ps.
How can we lock the modes? The most popular method is to put a satur-
These are usually two-section able absorber in the resonator which attenuates at low fields but not at high
devices, one section to provide op- fields. Why would a saturable absorber lock the modes? A rough answer may
tical gain, and the other one to act be produced by the following argument: when the modes are randomly phased
as a saturable absorber. relative to each other, the sum of the amplitudes at any given moment is small,
hence they will be adversely affected by the saturable absorber. However, if
they all add up in phase, their amplitude becomes large, and they will not be
affected by the saturable absorber. Thus, the only mode of operation that has
a chance of building up is the one where the modes are locked; consequently,
that will be the only one to survive in the long run (where long means a few
nanoseconds). This is another example of optical Darwinism.

12.9 Parametric oscillators
In principle, this is the same thing as already explained in connection with
varactor diodes in Section 9.13. The main differences are that in the present
case (i) the nonlinear capacitance is replaced by a nonlinear optical medium,
(ii) the dimensions are now large in comparison with the wavelength; hence
wave propagation effects need to be taken into account, and (iii) instead of
amplifiers, we are concerned here with oscillators (although optical paramet-
ric amplifiers also exist). What is the advantage of parametric oscillators?
Why should we worry about three separate frequencies, when we can easily
build oscillators at single frequencies? The reason is that we can have tuneable
outputs.
A schematic diagram of the optical parametric oscillator is shown in
Fig. 12.23. The parametric pump (not to be confused with the pump needed
to make the laser work) is a laser oscillating at ω 3 . There is also a resonator