A novel numerical technique for simultaneous calculations of type II phase matching angle and temperature for second harmonic generation in negative uniaxial crystals

In the present work, the phase matching type II conditions using birefringence for second harmonic generation (SHG) in negative uniaxial crystals were studied. A novel numerical method allowing the simultaneous and reliable calculations of the type II phase matching angle and temperature versus fundamentals wavelengths for SHG in Lithium Niobate (LiNbO3) was proposed. The angles and temperatures were determined for values less or equal to 5 × 10−6 of uncertainty. Indeed, SHG efficiency curves at fundamental frequency f = 1.6 THz obtained for various error values highlighted the validity and accuracy of the calculations. The proposed method was also applied in the case of the type I phase matching SHG using both the same crystal and precision. A good agreement between the analytical and numerical results was obtained.