Extremely sub-wavelength magnetic metamaterials without using lumped elements

Electrical smallness is one of the most fundamental properties of metamaterials. Generally, the size of a metamaterial unit cell must be less than λ/10. In this paper, we propose the design of extremely sub-wavelength magnetic metamaterials that can be made far less than λ/1000. Based on broadside capacitive couplings, the magnetic resonant frequency of split-ring resonator magnetic metamaterials can be drastically reduced by introducing more shunt capacitances. As an example, we demonstrated by experiment a polarization-independent sub-wavelength magnetic metamaterial that is as small as λ/38. This design avoids the use of lumped elements whose capacitances/inductances usually vary with frequencies and thus provides an efficient route to deep sub-wavelength metamaterials with stable performances for practical applications.