Second-harmonic generation driven by beams with engineered two-dimensional spatial coherence

We theoretically investigate second-harmonic generation driven by random structured pump beams with engineered two-dimensional spatial coherence distributions. Taking a multi-Gaussian correlated Schell-model beam as a representative example, we derive the analytical cross-spectral density of the generated second-harmonic field and analyze its focusing characteristics. The results show that the pumps spatial coherence structure is transferred to the frequency-doubled field through nonlinear interaction, resulting in pronounced intensity self-shaping. The flat-top shaping effect is significantly enhanced by increasing the beam order, decreasing the coherence width, and extending the nonlinear crystal length, demonstrating that coherence-structured nonlinear interaction governs the redistribution of second-harmonic intensity. These findings provide new insight into coherence engineering in nonlinear frequency conversion.