Artificial composite materials that focus on electromagnetic waves are known as metamaterials. Metamaterials are artificial materials engineered by human technology, possessing a geometric structure built from microscopic, engineerable materials. The goal is for the new material to be able to direct light, sound, and waves, making it useful. Metamaterials are known as left-handed materials (LHMs), but the concept of metamaterials is broader than LHM. The purpose of this research is to solve the transverse electric (TE) and transverse magnetic (TM) electromagnetic wave equations in left-handed materials (LHMs) using the Nikiforov-Uvarov approach and to analyze the results of the energy spectrum equation from the solution of the transverse electric (TE) and transverse magnetic (TM) electromagnetic wave equations in left-handed medium (LHM). This research was conducted using Matlab software. The material being studied is the positive-negative gradient profile in an LHM medium thru variations in dielectric permittivity and/or magnetic permeability. Energy and wave equations were obtained with their visualization.
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