Nonlinear beam splitter based on second-harmonic generation by femtosecond laser-induced phase gratings in lithium niobate

Parametric processes such as second-harmonic generation (SHG) and sum-frequency generation (SFG) are often realized in nonlinear optical crystals by collinear phase matching. However, it is known that noncollinear phase matching (NCPM) offers an additional degree of freedom by intersecting the fundamental waves under an angle to compensate for not only the phase mismatch but also the group velocity mismatch. The latter one is especially important for parametric processes using ultrashort laser pulses. NCPM can be typically achieved in the same wavelength range where birefringent phase matching is possible. However, the angular tuning range is strongly limited by the specific cut of the crystal. One can omit an external beam splitter if a diffraction grating is integrated in the crystal which allows for NCPM over a large wavelength range in a single crystal. The diffraction grating splits the fundamental beam into two or more beams which are intersecting inside the crystal at the appropriate NCPM angle. This process has been demonstrated in KH₂PO₄ and β-BaB₂O₄ by directly writing of relief gratings at the crystal surface with femtosecond laser pulses.