We propose and design a silicon-based long-range hybrid plasmonic slot (LRHPS) waveguide. The waveguide structure consists of a thin metal film (silver) inserted into a vertical low-index slot [filled with silicon nanocrystal (Si-nc)] between two high-index dielectrics (silicon), forming two nanoscale low-index Si-nc slot regions. The modes are confined within the two vertical regions. The designed LRHPS waveguide takes advantages of both traditional long-range surface plasmon polariton waveguide and hybrid plasmonic waveguide. The combined effects of long-range surface plasmon polaritons and discontinuity of electric field at the interface between two dielectrics with high-contrast refractive index enable a millimeter-scale propagation range together with a subwavelength mode confinement for potential high-density nanophotonic integration. The resultant quasi-TE mode properties of LRHPS waveguide, including long-range hybrid (LRH) mode and short-range hybrid (SRH) mode, are analyzed, showing a long propagation length up to 14.55 mm (corresponding to a low loss of
) with a slot size of 150 nm
200 nm. Normalized power and intensity are also calculated, indicating tight mode confinement within subwavelength low-index slot regions. Moreover, nonlinearity and chromatic dispersion are also studied. Due to the design freedom of double-slot structure, a high nonlinearity of
and a low chromatic dispersion of
28.29 ps/nm/km at 1550 nm are achieved, implying possible applications in efficient nonlinear optical signal processing.