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In the application of finite-difference time-domain (FDTD) method to the wideband plane wave scattering analysis of objects embedded in stratified lossy dispersive media, it is a challenge to solve the obliquely incident wave. In this work, a novel configuration of auxiliary one-dimensional (1-D) FDTD grids is proposed to provide the obliquely incident plane wave at the total-field scattered-field (TFSF) boundary in stratified lossy dispersive media. Thus a closed TFSF boundary is formed, where the incident waves are directly obtained from the auxiliary simulations without any interpolation. The formulations of the auxiliary simulations are presented by the modified 1-D Maxwell's equations. Given the dispersion characteristic, perfectly matched layer (PML) is implemented to the 1-D simulations. Examples demonstrate the effectiveness of the proposed technique of obliquely incident wave introduction.