Correction to Theoretical Prediction of Umbilics Creation in Nematic Liquid Crystals with Positive Dielectric Anisotropy

On page S1 in the Supporting Information, the current text “In one-dimension (1D), the excess carrier density δN(=(N_i(x) – N₀), where N₀ (=9.25 × 10²⁰ cm^–3) being the bulk free carrier density of ITO⁴) induced in the accumilation layer can be calculated from the Poisson equation⁴, as” should be changed to “In one-dimension (1D), the excess carrier density δN induced in the accumulation layer in a cross section through the beam center along the x-axis supposed at y = 0 μm and z_i = 30 μm relative to the Fe:LN interface with LC (as seen in Figure S1) can be calculated from⁴”

The text “where e is the unit charge, ε₀ and ε_ITO = 9.3^3,4 are the vacuum and the relative static permittivity of ITO, respectively.” should be changed to “where e is the unit charge, ε₀ and ε_ITO = 9.3^3,4 are the vacuum and the relative static permittivity of ITO, respectively. Voltage at the ITO surface was determined relative to z_f → ∞.”

The text “which was calculated with respect to the outer surface of glass, where the electric field goes to zero, as a result ΔU = U holds. The electric potential was numerically calculated from the electric field distribution stemed only from the photoinduced charge densities in the Fe:LN substrate.” should be changed to “which was calculated with respect to the outer surface of glass (f → ∞), where the electric field goes to zero because of the high thickness of glass (more than 100 μm), hence U_∞ = 0, as a result ΔU = U (U: electric potential at ITO surface U = U_i) holds. The electric potential was numerically calculated from the electric field distribution stemming only from the photoinduced charge densities in the Fe:LN substrate (see from Figure S1).”

On page S2, the text “By substituting the numerical values obtained for U, the excess carrier density (δN = N_i – N₀) was obtained from eq (1), where the excess electric charge density can be calculated from σ = eδN, with e the unit charge. The corresponding induced charge density in 2D is shown in Figure S3.” should be changed to “By substituting the numerical values obtained for U, the excess carrier density δN was obtainedin in two dimensions (2D), where the excess electric charge density can be calculated from σ = eδN, with e is the electron unit charge. The corresponding induced charge density in 2D is shown in Figure S3.”