*Article* **Identifying Near-Perfect Tunneling in Discrete Metamaterial Loaded Waveguides**

#### **Kimberley W. Eccleston \* and Ian G. Platt**

Lincoln Agritech Ltd., Canterbury 7640, New Zealand; ian.platt@lincolnagritech.co.nz **\*** Correspondence: kim.eccleston@lincolnagritech.co.nz; Tel.: +64-3-325-3741

Received: 25 October 2018; Accepted: 3 January 2019; Published: 11 January 2019

**Abstract:** Mu-negative and epsilon-negative loaded waveguides taken on their own are nominally cut-off. In ideal circumstances, and when paired in the correct proportions, tunneling will occur. However, due to losses and constraints imposed by finite-sized constituent elements, the ability to experimentally demonstrate tunneling may be hindered. A tunnel identification method has been developed and demonstrated to reveal tunneling behavior that is otherwise obscured. Using ABCD (voltage-current transmission) matrix formulation, the S-parameters of the mu-negative/epsilon-negative loaded waveguide junction is combined with S-parameters of an epsilon-negative loaded waveguide. The method yields symmetric scattering matrices, which allows the effect of losses to be removed to provide ye<sup>t</sup> clearer identification of tunneling.

**Keywords:** evanescent field tunneling; metamaterials; mu-negative material; epsilon-negative material; split-ring-resonators; waveguides
