Abstract

In the paraxial wave equation for a complex gaussian duct the term describing the combined effect of thermal lensing and gain guiding is given by the complex expression in the round brackets with the real and the imaginary part corresponding to thermal lensing and gain guiding, respectively. If both parts are of comparable magnitude or if the imaginary part is smaller than the real one, as found in many practical resonator configurations, the expression obtained from this equation for the spot size is dominated by the real part, the expression obtained for the phase front curvature on the other hand is dominated by the imaginary part. Therefore, in monolithic configurations with short resonators gain guiding must only be taken into account for laser materials with negligible thermal lensing i. e. with very small or negative derivative of the index of refraction with respect to temperature. This case has been analyzed in previous papers. However, in heterogeneous resonator configurations e.g. with external mirrors or other mode shaping elements the additional phase front curvature due to gain guiding may become very important even in the presence of thermal lensing. An example for this situation is shown in Fig. 1 where a short crystal is combined with an external mirror and where the distance between crystal and mirror is chosen several times larger than the crystal’s length. As one can see, in this case the splitting of the mode shape for both directions of propagation due to gain guiding can be considerable. As can be shown by parameter variation, this splitting depends very sensitive on the relative values of the resonator’s length, the mirror’s curvature, and the parabolic coefficients n₂ and α₂ of refractive index and gain, respectively. In the present example, for fixed values of n₂ and α₂ the splitting can be nearly suppressed by an appropriate choice of the mirror’s curvature. The configuration, however, remains sensitive with respect to fluctuations of pumping power and temperature distribution. An even more complicated situation arises, if a frequency doubler is present in the resonator, which induces an antiguiding effect due to a transversely varying conversion efficiency. This examples show that a parametric study of the combined effect of thermal lensing and gain guiding can be very important to find out an appropriate resonator design. For this purpose a program was developed by the use of the complex ABCD matrix formalism which offers a very fast and valuable tool to get better insight into the behavior of resonator configurations even though it allows only a parabolic approximation.

© 1996 IEEE