We discuss, with illustrations drawn from the simple example of a diel
ectric grating under total internal reflection illumination, the use o
f electric field, energy density and Poynting vector as tools for unde
rstanding 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 ener
gy density, although not directly linked with photoelectric response,
has readily understood global patterns. The Poynting vector has more e
laborate structure, involving patterns of curls, but the patterns are
sensitive to small changes in illumination angle or groove depth. Plot
s of Poynting vectors may not be as useful for dielectric structures a
s they are for metals.