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Based on a unified formulation, a new split formulation of perfectly matched layers (PML) and quasi-PML are presented. Numerical results of both schemes agree well with analytical solutions although the quasi-PML can be shown theoretically not perfectly matched. A nonuniform grid in cylindrical coordinates is used for the 3-D FDTD method. The new split formulation of PML is an important absorbing boundary condition (ABC) for spectral-domain methods such as the pseudospectral time domain (PSTD) method in cylindrical coordinates.