Page 334 - Tunable Lasers Handbook

294 Norman P. Barnes

In this expression, the subscript 1 denotes the pump, 2 denotes the signal. and 3
denotes the idler. By convention, the signal is the higher of the two generated
frequencies. Any pair of frequencies can be generated, but only frequencies that
satisfy the conservation of momentum will be generated efficiently. Conserva-
tion of momentum can be expressed as
k, = k2 +k; .

In this expression, kl is the wave vector at frequency v,. For the most common
situation where the interacting beams are collinear, the vector relation simplifies
to an algebraic relation. Substituting 2nnlhvi for the wave vector, the relation
becomes

where nl is the refractive index at the i'th frequency. In practice, the conservation
of momentum will limit the generated wavelengths to a relatively narrow spec-
tral bandwidth.
Optical parametric oscillators have several desirable features including a
wide range of tunability. In practice, the ultimate tuning range of the optical para-
metric oscillator is limited only by the conservation of momentum or the range of
transparency of the nonlinear material. Consequently, the practical range of tun-
ing is usually very wide and is set by the available transmission properties of the
ancillary optics. Not only is the tuning range wide. the gain is relatively flat. To
first-order approximation, the gain of the optical parametric device is maximized
at the degenerate wavelength, which is where the signal and idler are equal. Away
from the degenerate wavelength, gain decreases relatively slowly as the wave-
length of the device is tuned to other wavelengths. Another advantage of this
device is the inherent wavelength selectivity of the device. Although lasers with
wide spectral bandwidths are available. several wavelength control devices are
often used to effect the tuning. Optical parametric oscillators. on the other hand.
have a built-in wavelength control mechanism, namely, the requirement to satisfy
the conservation of momentum. Conservation of momentum does not provide
fine wavelength control, but it does provide broad wavelength control.
Optical parametric oscillators have several other desirable features includ-
ing a compact size, good beam quality, and the potential of high-gain ampli-
fiers. A simple optical parametric oscillator consists of a nonlinear crystal in a
resonator. As such, these devices can easily be hand-held items. In principle,
the mirrors could be coated on the nonlinear crystal if a more compact device is
required, however, this would limit the flexibility of the system. The beam qual-