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We have investigated the dispersion relation of a novel metal-dielectric-gap optical waveguide. This structure confines the optical field strongly in the gap region between metals and dielectric materials, and its size can be reduced to less than the wavelength of the transmitted light. In addition, the propagation length of light extends much greater than that of the surface plasmon modes on metal surfaces. We show that this mode of propagation has a cut-off at zero wavenumber, and that it is hollow-waveguide-like for small wavenumbers, while it approaches a surface-plasmon-like mode for large wavenumbers. A typical propagation length at around the communication wavelength is 10-20 mum, and optical fields are confined into an approximately 100 times 200 nm2 cross section.