Masters Thesis

Non-linear waves in left-handed transmission lattice

During recent years, metamaterials, which are engineered structures with unique electromagnetic properties that can not be observed in natural material, have been subjected to special interest. One of the unique aspects of these engineered structures is that they can have negative permittivity and negative permeability at the same time, therefore, metamaterials are called left-handed oppose to natural materials which are called right-handed. Having this interesting feature, metamaterials have the ability to have electromagnetic waves travels in opposite direction which creates backward propagating waves. As a result, left-handed metamaterials would have negative refraction when it comes to microwaves or optical frequencies. In this paper, we study a two dimensional LC lattice that mimics a left-handed material and explore soliton solutions for our model. In our model we use voltage dependent and symmetric capacitance capacitors. For the given carrier wave, we will derive a non-linear Schrodinger equation by using a multiple scales expansion. At the end, we will explore the effect of the wave-number of the carrier wave to see either focusing or defocusing effect in our model.

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