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We present a design of a one dimensional dielectric waveguide that can trap abroad band light pulse with different frequency component stored at differentpositions, effectively forming a "trapped rainbow"[1]. The spectrum of therainbow covers the whole visible range. To do this, we first show that thedispersion of a $\text{SiO}_2$ waveguide with a Si grating placed on top can beengineered by the design parameter of the grating. Specifically, guided modeswith zero group velocity(frozen modes) can be realized. Negative Goos-H\"anchenshift along the surface of the grating is responsible for such a dispersioncontrol. The frequency of the frozen mode is tuned by changing the lateralfeature parameters (period and duty cycle) of the grating. By tuning thegrating feature point by point along the waveguide, a light pulse can betrapped with different frequency components frozen at different positions, sothat a "rainbow" is formed. The device is expected to have extremely low ohmicloss because only dielectric materials are used. A planar geometry alsopromises much reduced fabrication difficulty.

Realization of "Trapped Rainbow" in 1D slab waveguide with Surface Dispersion Engineering