The cuticle of the beetle Chrysina chrysargyrea reflects left-handed polarized light in the broad spectral range from 340 to 1000 nm. Interference oscillations in the experimental Mueller-matrix spectroscopic ellipsometry data reveal that transparent materials comprise the cuticle. A spectral analysis of the interference oscillations makes evident that the pitch profile across the cuticle is graded. The graded pitch and effective refractive indices are determined through non-linear regression analysis of the experimental Mueller matrix by using a cuticle model based on twisted biaxial dielectric slices. Non-uniformity in cuticle thickness as well as in pitch profile near the cuticle surface account for depolarizance of the Mueller matrix. Transmission electron microscopy supports the reliability of the results.