Based on the first-order Taylor expansion, an efficient Rigorous Coupled-Wave Analysis (RCWA) for one-dimensional ultrathin periodic structures is proposed in this paper. The derivation of the ultrathin form RCWA method is completed by using the first-order Taylor expansion to rearrange the matrix in the equations of boundary conditions. Then, the reliability of the proposed algorithm is verified by two examples. Finally, it is concluded that the proposed algorithm can reduce the CPU time of TE polarization and TM polarization by more than 50%. Meanwhile, compared with the conventional algorithm, the proposed algorithm also needs less memory.
