A wide range of transformation media designed with conformal mapping are currently being studied extensively due to their favorable properties: isotropy, moderate index requirements, low loss and broad bandwidth. For optical frequency operation, the transformation media are commonly fabricated on high index semiconductor thin films. These 2D implementations, however, inevitably introduces waveguide dispersion, which affects the bandwidth and loss behavior. In this paper, for carpet cloaks implemented by a silicon nanorod array, we have confirmed that waveguide dispersion limits the bandwidth of the transformation medium by direct visualizing the cut-off conditions with near-field scanning optical microscopy (NSOM). Furthermore, we have experimentally demonstrated the extension of cut-off wavelength by depositing a conformal dielectric layer. This study illustrates the constraints on the 2D transformation media imposed by the waveguide dispersion and suggests a general technique to tune and modify their optical properties.