The Research Of LBO Crystal’s Transformation-Efficiency In Type Ⅰ Frequency-doubling Phase-Matching

Access to a large number of reference literatures, we make a comprehensivesummaries of the nonlinear optical frequency conversion technology’s development, statusand application prospect. LBO crystal is a kind excellent frequency conversion materials,it has lots of features such as high damage threshold, good optical homogeneity, smallwalk-off angle, the wide rang of phase matching and so on.The refractive index, walk-off angle and the interaction angle of every wave arecalculated with numerical methods, while the LBO crystal is under type I collinear phasematching. According to the three-wave coupled equations while the three wave have thewalk-off angles, we make a numerical solution of the conversion efficiency. The mainresults are as follows:1. From electromagnetic field theory, we derive the formulas of the walk-off anglesand the interaction angles of biaxial crystal’s type I phase-matching.2. We make a calculation with numerical methods for the refractive index of the fastand slow waves under type I phase-matching of LBO crystal. The refraction index’s rangof the fast wave whose wavelength is1064nm is1.5905～1.6055; the r. efraction indexrang of the slow wave whose wavelength is532nm is1.5824～1.6065.3. The walk-off angles of the fast wave and slow wave are calculated with numericalmethods under type I phase-matching of LBO crystal. The walk-off angle’s rang of thefundamental frequency wave (wavelength is1064nm) is0°~1.35°, while thephase-matching angle is90°, the walk-off angle is0°, while the phase-matching angleis about36°, the maximum walk-off angle is1.35°; the walk-off angle’s rang of thedoubling frequency wave is0~1.52°, while the phase-matching angle is90°, thewalk-off angle is0°, while the phase-matching angle is about51°, the rang of theinteraction angle between the frequency wave and doubling frequency wave is0~1.15°,while the phase-matching angle is90°, the interaction angle is0°, while thephase-matching angle is about45°, the maximum interaction angle is1.15°.4. The relation curve between the doubling frequency wave-vector amplitude and thelength the wave walked through is calculated with numerical methods, they show therelation of direct ratio, and the ratio is different among the different matching directions,so that this just proves the effect to the conversion efficiecy from the walk-off angle, theinteraction angle and the effective nonlinear coefficient of different directions. 5. The numerical value shows that the conversion efficiency depends on the effectivenonlinear coefficient. At different matching directions, the walk-off angle, the interactionangle and the refractive index make different effects to the conversion efficiency, theeffect is max while the matching angle is18°, compared with not considering thoseeffects, the relative error is about4.7%.6. While the matching angles are about（17.7°，0.6°）,（42.2°，19°）,（86°，0.5°）, the conversion efficiency reaches maximums, of which is （42.2°，19°）,the maximum value is about3.35%. Under every matching angle, the conversionefficiency is direct ratio to the squared value of the length walked through by the wave.After the three-wave coupling, only every wave’s intensity changes, but not thepolarization states.