Page 343 - Tunable Lasers Handbook

7 Optical Parametric OsciIIators 303

Considerable simplification can result in this expression depending on whether
the optical parametric oscillator is singly or doubly resonant.
In singly resonant oscillators, only one of the generated waves is resonant,
Either the signal or the idler could be the resonant wave. In general, singly reso-
nant oscillators are Freferred for pulsed applications where the gain is high. In
doubly resonant oscillators, both the signal and the idler are resonant. Doubly
resonant oscillators are often used for cur applications because of the loner
threshold. Doubly resonant oscillators are often more challenging to control
spectrally because generated wavelengths must satisfy conservation of energy,
conservation of momentum. and the resonant condition. If the parametric oscil-
lator is a singly resonant device, only one of the generated waves has a beam
radius determined by the configuration of the resonator. If, for example, the sig-
nal is resonant, the idler beam radius will be given by

In this situation. the gain coefficient simplifies to

A similar expression can be obtained if the idler is resonant by interchanging the
subscripts. To maximize the gain, the pump beam radius and the resonant beam
radius can be minimized. However. eventually laser induced damage or hirefrin-
gence effects will limit the minimum practical size for the beam radii.
If the parametric oscillator is a doubly resonant device, both of the gener-
ated waves have a beam radius determined by the configuration of the resonator.
To maximize the gain for a doubly resonant device. the beam radius of the pump
can be optimized. Performing the optimization yields a beam radius for the
pump, which is given by

Utilizing the optimum pump beam radius yields a gain coefficient given by

(21)

As in the case of the singly resonant oscillator. gain can be increased by decreas-
ing the beam radii of the resonant beams. However, also as in the singly resonant