Multilayer terahertz metamaterials: Interactions between layers within the deep-subwavelength limit

Split-ring-resonators (SRR) play a significant role in the design and realization of metamaterials over a wide range of the electromagnetic spectrum. In addition to single SRR layers, a number of demonstrations have been carried out to understand the bulk properties of multiple layer structures. Usually, the SRR layers are separated by dielectrics with a layers spacing > λ_res/30. We present the effect of layer separations on the fundamental inductive-capacitive (LC) resonances for SRR based metamaterials. We have investigated the effect of layer separations for (i) closed split ring resonator (CSRR), (ii) SRR with their splits oriented in the same direction, and (iii) SRR with their splits oriented in opposite directions. Our results show that separation thickness plays a significant role for the oppositely oriented layers. The LC resonance disappears when the separation between layers is less a micron (~λ_res/1000) and the composite behaves as a closed ring resonator. However, the separation has a very minimum effect when splits on SRRs are oriented in same direction.