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