Theoretical discussion and numerical results for experimentally obtained new kind of the optical waveguide has been presented. Discussed waveguide is optically self-induced during light beam propagation along boundary between liquid crystal and semiconducting polymer. Light is propagated in electrically driven liquid crystal (LC) cell. Experimental results obtained earlier are reported in here shortly, and theoretical model of the observed phenomena is discussed as well as numerical outcome. Exploited nematic liquid crystal was of high birefringence near to 0.35. Experimental data have been obtained in the case of poly (N-vinyl) carbazole as photorefractive polymer doped with 2, 4, 7-trinitro-fluorenone, and numerical simulation has been done for this case.