Cascaded quadratic nonlinear compensation of small-scale self-focusing in a kHz, 100-mJ picosecond laser

In pursuing kHz high-power picosecond lasers, small-scale self-focusing becomes an inevitable nonlinear effect as the peak intensity increases. By utilizing cascaded quadratic nonlinear effects to introduce a nonlinear phase with controllable sign and magnitude on the initial fundamental wave, an equivalent nonlinear refractive index n₂ is generated. This property can be used to compensate for the nonlinear phase accumulated during beam propagation, thus mitigating self-focusing. In this paper, we derive and solve the coupled wave equations for second-harmonic generation to simulate the numerical variation of LBO's equivalent nonlinear refractive index under different phase mismatches and light intensities. Using this method in our kilohertz-hundred millijoule picosecond laser system, we successfully observed the compensation of small-scale self-focusing and the pulses being safely amplified from 132 mJ to 170 mJ in a further amplifier without filamentation.