Page 351 - Tunable Lasers Handbook

7 Optical Parametric OsciIIators 3
pensating variation in the other wavelength. Keeping the pump wavelength fixed
and taking the derivative of the mismatch with respect to the signal wavelength
produces

When taking the derivatives of the phase mismatch with respect to the wave-
length. the pump wavelength can be considered to be fixed. Evaluating the par-
tial derivatives in Eq. (34) yields

(35j

Derivatives of the refractive index with respect to wavelength can be determined
using experimental refractive index data or curve fits to the experimental refrac-
tive index data. If a standard two-pole Sellmeier expression is used. then

With these expressions, the single-pass spectral bandwidth of a difference fre-
quency interaction can be calculated.
To calculate the spectral bandwidth of an optical parametric oscillator. the
number of passes of the signal through the nonlinear crystal must be taken into
account. Calculated using equations 31 and 34 is the spectral bandwidth for a
single pass. However, during the pulse evolution, the signal makes repeated
passes through the nonlinear crystal. Subsequent passes through Lhe nonlinear
crystal will continue to narrow the spectral bandwidth of the parametric oscilla-
tor. It has been shown [17-191 that the spectral bandwidth depends on the num-
ber of passes the radiation makes through the spectral narrowing device. in this
case the nonlinear crystal. To take this effect into account, the calculated single-
pass spectral bandwidth should be divided by the p’ , where p is the number of
passes that occur during the pulse evolution time interval. An estimate of the
number of passes the signal makes through the nonlinear crystal can be obtained
from the pulse evolution time interval T~ using the relation

where c is the speed of light and 1, is the length of the parametric oscillator
resonator.