This paper tackles the wave attenuation along with a cylindrical waveguides composed of a left Handed material (LHM), surrounded by a superconducting or metal wall. I used the transcendental equations for both TE and TM waves. I found out that the waveguide supports backward TE and backward TM waves since both permittivity and magnetic permeability of LHM are negative. I also illustrated the dependence of the TE and TM wave attenuation on the wave frequency and the reduced temperature of the superconducting wall (T/Tc). Attenuation constant increases by increasing the wave frequency and it shows higher values at higher T/Tc. Lowest wave attenuation and the best confinement are achieved for the thickest TE waveguide. LHM-superconductor waveguide shows lower wave attenuation than LHM-metal waveguide.
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