The height of the molten zone was modulated during single crystal fiber pulling by the laser-heated pedestal growth technique to create a periodically doped fiber. Different frequencies, in the order of $10^{-3}$ Hz, were used to modulate the molten zone during the growth of LaAlO$3$:Cr$^{3+}$ fibers, a material model. We demonstrated that the axial Cr$^{3+}$ distribution varied periodically along the length of the fiber at the same frequency as the molten zone oscillations. A dopant distribution model, based on mass conservation, was successfully applied to predict the axial Cr$^{3+}$ concentration profile. The effective segregation coefficient ($k\textrm{eff}$) of the LaAlO$_3$:Cr$^{3+}$ was determined to be 4.6 (without molten zone oscillation). The growth temperature was $(2340 ± 10)^∘$C and growth was carried out in an air atmosphere. The fiber/pedestal-pulling ratio was equal to 1.0. Transparent fibers 450 μm in diameter and 3 cm in length were obtained.