We propose deep-subwavelength optical waveguides based on metal-dielectricmultilayer indefinite metamaterials with ultrahigh effective refractiveindices. Waveguide modes with different mode orders are systematically analyzedwith numerical simulations based on both metal-dielectric multilayer structuresand the effective medium approach. The dependences of waveguide mode indices,propagation lengths and mode areas on different mode orders, free spacewavelengths and sizes of waveguide cross sections are studied. Furthermore,waveguide modes are also illustrated with iso-frequency contours in the wavevector space in order to investigate the mechanism of waveguide mode cutoff forhigh order modes. The deep-subwavelength optical waveguide with a size smallerthan {\lambda}0/50 and a mode area in the order of 10-4 {\lambda}02 isrealized, and an ultrahigh effective refractive index up to 62.0 is achieved atthe telecommunication wavelength. This new type of metamaterial opticalwaveguide opens up opportunities for various applications in enhancedlight-matter interactions.
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