The finite difference time domain (FDTD) method [Taflove and Hagness, 2000] with the periodic boundary condition (PBC) is one of the most popular numerical methods for the efficient analysis of periodic structures. Several techniques for the analysis at oblique incidence have been proposed and applied to the periodic FDTD method [Aminian and Rahmat-Samii, 2006; Taflove and Hagness, 2000; Roden et al., 1998]. It should be noted, however, that the time step size (Δt) of the conventional FDTD method suffers from the Courant-Friedich-Levy (CFL) condition. To remove this, Wang et al.  have applied the alternating direction implicit (ADI) scheme [Namiki, 1999; Zhen et al., 2000] to the periodic FDTD method, in which the cyclic matrix problem resulting from the implicit scheme is solved using the Sherman-Morrison formula [Thomas, 1995]. The implicit scheme allows us to use a large Δt beyond ΔtCFL that is the upper limit determined with the CFL condition. The periodic ADI-FDTD method has also been extended to the analysis at oblique incidence [Mao et al., 2009].
 As an alternative to the ADI-FDTD method, the unconditionally stable locally one-dimensional (LOD) FDTD method [Nascimento et al., 2006; Shibayama et al., 2005, 2006; Tan, 2007] has been proposed. The algorithm of the LOD-FDTD method is quite simple compared to the ADI-FDTD method, maintaining the comparable accuracy. Recently, we have introduced the PBC into the LOD-FDTD method and confirmed the effectiveness of the LOD technique [Shibayama et al., 2009]. It should be noted, however, that the formulation has been limited to the case at normal incidence.
 From this viewpoint, we have begun to investigate the possibility of deriving the periodic LOD-FDTD method for the analysis at oblique incidence [Shibayama et al., 2010; Wakabayashi et al., 2010]. In this paper, we systematically formulate the LOD-FDTD method at oblique incidence. The two-dimensional problems for obliquely incident transverse electric (TE) and transverse magnetic (TM) waves are treated with the aid of the split-field technique [Roden et al., 1998]. In the light of the advantage of the implicit FDTD method, we introduce the dispersion control parameters to reduce the dispersion error caused by a large Δt [Li et al., 2007; Shibayama et al., 2009]. After the formulation, we analyze a photonic band gap (PBG) structure to confirm the effectiveness of the present algorithm. With the control parameters, the numerical results of the periodic LOD-FDTD method for 8ΔtCFL fairly compare with those of the explicit periodic FDTD method. Thus, the computational time is reduced to ≅16% of that of the explicit FDTD method. Using the derived algorithm, we analyze a broadband mirror consisting of a subwavelength grating (SWG) [Mateus et al., 2004a, 2004b; Wakabayashi et al., 2009].