We discuss, with illustrations drawn from the simple example of a dielectric grating under total internal reflection illumination, the use of electric field, energy density and Poynting vector as tools for understanding phenomena associated with dielectric gratings. The electric field has greatest direct observational interest and exhibits patterns of nodes and antinodes that are both expected and intuitive. The energy density, although not directly linked with photoelectric response, has readily understood global patterns. The Poynting vector has more elaborate structure, involving patterns of curls, but the patterns are sensitive to small changes in illumination angle or groove depth. Plots of Poynting vectors may not be as useful for dielectric structures as they are for metals.