This chapter introduces the concept of low-dimensional optical waves and wavenumber surface. It discusses the origin of diffraction limit in geometrical approach in wavenumber space. The chapter describe principles to confine and guide optical waves in nanostructures beyond the diffraction limit using low-dimensional optical waves. It presents structures and calculated transmission properties in various types of negative dielectric waveguides. Dielectric optical waveguides are the basic elements for transmission of light. In dielectric optical waveguides, optical waves are confined and guided by total internal reflection at a dielectric interface. An important potential application of one dimensional optical waveguides in the near future could be a high-efficiency optical probe with high spatial resolution. Low-dimensional optical waveguides could play a crucial role in constructing nano-optical integrated circuits: they could serve as a bridge linking the subwavelength world to a truly nanometer world.