Traditional optical beam splitters are limited by their fixed geometric structures and static working modes, making it challenging to meet the demands of dynamically reconfigurable photonic systems. To achieve polarization-controllable laser beam splitting, this study developed a programmable optical device based on liquid crystal gradient refractive index distribution. By establishing an equivalent refractive index model for liquid crystal planar structures, triangular-patterned liquid crystal cells with alignment angles of 30°, 45°, 60°, and 90° were fabricated using digital mask lithography via a digital micromirror device (DMD) chip, systematically constructing the mapping relationship between alignment angles and effective refractive indices. Experimental results revealed that as the alignment angle increased from 30° to 90°, the corresponding effective refractive index exhibited a monotonically increasing trend. Under horizontally linear polarized light incidence, the refraction angle of extraordinary light (e-light) showed a linear growth with increasing incident angle (15°~75°), confirming the applicability of Snell's law in liquid crystal media. During continuous polarization state modulation from horizontal to vertical orientations, the intensity ratio between e-light and ordinary light (o-light) demonstrated regular evolution, reaching a 1∶1 balanced state at a 46° polarization angle. Circularly polarized light excitation generated symmetrical dual beams, revealing the regulatory mechanism of birefringence phase difference on beam splitting behavior. This work realizes polarization-encoded beam splitting through gradient refractive index design in patterned liquid crystal devices, with its dynamically tunable characteristics providing both theoretical foundation and technical pathways for developing novel reconfigurable photonic devices.