Dispersion management is critical in many optical applications, whether to reduce impairments in fiber optic communication or chirp pulse amplification, or to create time stretch instruments for single-shot continuous recording of fast phenomena. The most common solutions for achieving large dispersion with low loss include dispersion compensation fiber, fiber Bragg grating, and diffraction grating pairs. Such dispersive elements have finite operational bandwidth, limited total dispersion, or insufficient power handling. In this Letter, we demonstrate a new, to the best of our knowledge, implementation of the chromo-modal dispersion device based on a silicon waveguide slab that addresses these limitations. The device provides extremely large dispersion with a widely tunable spectrum. We also propose a new time-stretch spectrometer where the absorption cell simultaneously provides spectrum-to-time mapping for fast single-shot spectroscopy.