Theoretical analysis and correction of a tight focusing field within <i>z</i>-cut uniaxial crystals

Ultrafast laser processing is a cutting-edge technology used in three-dimensional nanofabrication owing to its unique multiphoton absorption scheme, making it essential for applications such as microfluidics, photonic devices, and integrated optics. Nevertheless, the precise fabrication of three-dimensional structures within birefringent crystals faces challenges arising from a significantly distorted focused field caused by a refractive index mismatch and birefringence under tightly focused conditions. In this study, we extend the vectorial Debye diffraction theory to incorporate birefringence and deduce an analytical solution to accurately model the distorted focused patterns inside z-cut uniaxial crystals. Practical methods are also proposed to achieve a perfectly focused spot by simultaneously compensating for spherical aberration and birefringence. These findings provide valuable insights for the accurate fabrication of large-scale three-dimensional structures in crystals.