  We report the realization of simultaneously negative effective mass density
and shear modulus in a single-phase asymmetric double-sided pillared
metamaterial. The negative effective mass density is achieved by the
combination of bending and compressional resonances of one pillar whereas the
rotational resonance of the other pillar leads to the negative effective shear
modulus. The coupling between these two pillars is investigated to describe the
formation of the doubly negative property. Then, a pillared system featuring
chirality is designed in order to make efficient the excitation of the
rotational vibration, the occurrence of which is demonstrated by the
transmission spectrum. Finally, numerical simulations of the zero-index
refraction are carried out to prove the occurrence of the doubly negative
property.
