Page 347 - Tunable Lasers Handbook

7 Optical Parametric Oscillators 307
- 1 *:
*
- 1.20
g,
1.10
p 1.00
a, 0.31 Slope
5 0.90 efficiency -e
8
0.80 28
m e
e

k 0.50
a,
5 0.40
L
2 0.30

I I I I I I I I I
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9 0
1.73pm Pump energy (mJ)

FIGURE 4. The 4%GaSe, optical parametric oscillator output energ versus Er:llF pump
enegg.

decreases according to a sin'(s)/,G relation. .4n allowable mismatch can be
defined as

At this point. a nonlinear interaction decreases to about (4/~2) the efficienc] of
the ideally phase-matched interaction. For nonlinear interactions in the optical
region of the spectrum, the ratio of the length of the nonlinear crystal to the
wavelength is a large number. Thus to make the phase mismatch small. the rela-
tion among the three refractive indices becomes relative11 strict. Because the
refractive indices depend on the direction of propagation and temperature as
well as the wavelengths, rather small variances are set for these parameters in
order to satisfy the phase-matching condition.
Allowable variances for these parameters can be calculated by expanding
the phase-matching condition in a Taylor series about the phase-matching condi-
tion. In general. if Y is the parameter of interest. the mismatch can be expanded
as follows ['7]