Symmetries and relationships between elements of the Mueller matrix spectra of the cuticle of the beetle Cotinis mutabilis

The optical properties of light reflected from the cuticle of the scarab beetle Cotinis mutabilis are studied using variable angle Mueller matrix spectroscopic ellipsometry. Reflection of left-handed polarized light is demonstrated. Large amplitude interference oscillations in the elements of the normalized Mueller matrix (M) reveal highly transparent materials comprising the beetle cuticle. Off-diagonal elements in M obey simple symmetry relationships due to the constraint in the cross-polarized reflection coefficients between p and s polarizations of chiral systems, rps = − rsp. Based on the latter constraint and further interrelationships experimentally investigated, the number of independent elements in M resulted in only six. Reciprocity is probed from measurements performed in opposite sample orientations and the effects on M due to sample rotation by 90° are discussed. The results suggest relatively large areas in the cuticle of C. mutabilis with a helicoidal structure comprised of fibrils with a well-defined orientation.