Page 345 - Tunable Lasers Handbook

7 Optical Parametric Oscillators 305

Using the gain defined in Eq. (25). the number of times over threshold, N. can be
defined by using

where Rm is the mean reflectivity of the mirrors at the resonant wavelength and
T, is the tmnsmission of the nonlinear crystal. With these definitions, an observ-
able threshold will be achieved at an approximate time when

In this expression, the pump pulse length tl is related to the full width at half-
maximum (FWHM) pulse length tpl through the relation

T~, 0.82~~ (28)
.
=
If time t is less than the time at which the gain falls below the positive value, that
is. t7, an observable threshold will be achieved.
-
A slope efficiency can also be estimated for an optical paramelric oscillator.
Eventually. the slope efficiency will be limited by the ratio of the photon ener-
gies. At best. each pump photon will produce a single photon at both the signal
and idler wavelengths. Thus, the energy conversion efficiency will be limited by
the ratio of the photon energy at the output wavelength to the photon energy at
the pump wavelength; that is. the slope efficiency will be limited to 3L,/h2 when
the output is at the signal. In a singly resonant oscillator, in essence, all of the
generated signal photons will be available for the output. However. for a doubly
resonant oscillator. some of the generated photons will be dissipated by losses
within the resonator. Consequently, for a double resonant oscillator. the ultimate
slope efficiency will b: limited by the ratio of the fractional output to the total
losses in thE resonator. If R,n, represents the output mirror reflectivity wave-
length and represents the other losses at the signal Wavelength. the ultimate
slope efficiency will be further limited by the ratio of the output to the total
losses, that is I~z(R,,,~)//~(R,,~~R:,). In many instances the losses in the parametric
oscillator resonator can be kept small so that this ratio can be relatively high.
Experiments have demonstrated the validity of the basic approach [ 16.171. For
one set of experiments. an Er:YLF pump laser was used with a singly resonant