We present a bilayer fractal structure for the realization of multiband left-handed metamaterial at terahertz frequencies. The structure is composed of metallic H-fractal pairs separated by a dielectric layer. The electromagnetic properties of periodic H-fractal pairs have been investigated by numerical simulation. The period in the propagation direction is extremely small as compared to the wavelength at the operational frequency. Under the electromagnetic wave normal incidence, the material exhibits negative refraction simultaneously around the frequencies of 0.10 and 0.15 THz for parallel polarization, and around the frequencies of 0.19 and 0.38 THz for perpendicular polarization. The design provides a left-handed metamaterial suitable for multiband and compact devices at terahertz frequencies.
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