Light wave propagation within complex liquid crystal structures is undertaken by the FDTD method, a purely numerical method that explicitly solves Maxwell's equations in space and time. A specific FDTD arrangement suitable for liquid crystal applications is described, allowing for efficient space termination, oblique angles of illumination, and correct phasor representation. Two application examples are considered: a two-domain twisted pixel formed by two oppositely twisted sub-domains, and a helical ferroelectric liquid crystal material. In each case comparison is also made with the optical prediction obtained by the Berreman method.