Helix photonic crystal is one type of three-dimensional periodic chiral structure, which attracts considerable attention owing to many interesting optical properties [1]. To characterize electromagnetic waves propagating in a helical structure, a number of analytical and numerical methods have been implemented. For example, some studies model the helical nonhomogeneity of the materials by effective constitutive parameters, which has been commonly employed to study light propagation in helicoidal bianisotropic media. Numerical analysis based on finite-difference time-domain (FDTD) method are also widely used. For periodic structures, it is also possible to find exact solutions of Maxwell’s equations by some semi-analytical method, such as the rigorous coupled wave analysis (RCWA) approach. Compared to the time-domain approach, the RCWA has been shown to be a more efficient method to calculate diffraction from periodic grating structures.

Rigorous Couple-Wave Analysis (RCWA), also called Fourier Modal Method (FMM), is widely used in studying diffraction field in periodic media. This method gives rigorous conditions to solve Maxwell’s equation. A formulation of the RCWA is published by Moharam and others in 1995, but it was found that the convergence for TM polarization was worse than TE polarization. Afterwards, Lalanne and Morris modified the formulation and got a considerable improvement for TM polarization. Thanks to Lalanne and Li, the treatment of products in the truncated Fourier space was corrected in the RCWA method. Nevertheless, there still has been a convergent issue of metallic gratings.

In this study, we present the optical characterization of the 3D helix photonic crystals based on the RCWA. To resolve the convergence problems often encountered, a normal vector field formulation is included. In the first part of the study, we present the convergent conditions for parameters used in the RCWA by varying the truncation order N. In the second part of the study, the optical properties are calculated by the RCWA based on different geometrical arrangements. The results will be compared with those obtained by FDTD and the differences between the two methods will be discussed. The presented approach allows us to analyze mode diffraction efficiency in a 3D chiral structure, which may be of great interest for the design and applications of other 3D periodic structures.

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