Substrate-based atom waveguide using guided two-color evanescent light fields

We propose a dipole-force linear waveguide which confines neutral atoms up to $\ensuremath{\lambda}/2$ above a microfabricated single-mode dielectric optical guide. The optical guide carries far blue-detuned light in the horizontally-polarized TE mode and far red-detuned light in the vertically-polarized TM mode, with both modes close to optical cut-off. A trapping minimum in the transverse plane is formed above the optical guide due to the differing evanescent decay lengths of the two modes. This design allows manufacture of mechanically stable atom-optical elements on a substrate. We calculate the full vector bound modes for an arbitrary guide shape using two-dimensional non-uniform finite elements in the frequency-domain, allowing us to optimize atom waveguide properties. We find that a rectangular optical guide of $0.8\ensuremath{\mu}\mathrm{m}$ by $0.2\ensuremath{\mu}\mathrm{m}$ carrying 6 mW of total laser power (detuning $\ifmmode\pm\else\textpm\fi{}15\mathrm{nm}$ about the $D2$ line) gives a trap depth of $200\ensuremath{\mu}\mathrm{K}$ for cesium atoms ${(m}_{F}=0),$ transverse oscillation frequencies of ${f}_{x}=40\mathrm{kHz}$ and ${f}_{y}=160\mathrm{kHz},$ collection area $\ensuremath{\sim}1\ensuremath{\mu}{\mathrm{m}}^{2}$ and coherence time of 9 ms. We discuss the effects of non-zero ${m}_{F},$ the $D1$ line, surface interactions, heating rate, the substrate refractive index, and the limits on waveguide bending radius.