Optimal exposure distances for 3-D optical circuits induced by laser micromachining in LiNbO₃ crystals

The optimal exposure distances for 3-D optical waveguides induced by laser micromachining in LiNbO₃ crystals are theoretically and experimentally investigated. By solving the photorefractive dynamic equations, the optimal distances for waveguide fabrications are numerically specified when the focused laser beams scans along the different directions. The simulations show that the optimal exposure distance is not dependent on the scanning directions of the writing beam, but the index distributions of the fabricated waveguides are seriously dependent on them. When the writing beam scans the crystal along the axis c, optical waveguides cannot be fabricated efficiently. However, in this case, symmetric refractive index changes can be obtained, so called as sandwich illumination method. By scanning LiNbO₃: Fe crystal with a focused green laser beam, experimental demonstrations are performed. The light-induced index changes are measured by employing digital holography. The experimental results coincide with the theoretical analyses. Additionally, a curved waveguide is experimentally formed. The near field pattern and the results of the guiding tests show that the waveguide are successfully written in the LiNbO₃:Fe crystal.