  We present a previously unexplored forward-mode differentiation method for
Maxwell's equations, with applications in the field of sensitivity analysis.
This approach yields exact gradients and is similar to the popular adjoint
variable method, but provides a significant improvement in both memory and
speed scaling for problems involving several output parameters, as we analyze
in the context of finite-difference time-domain (FDTD) simulations.
Furthermore, it provides an exact alternative to numerical derivative methods,
based on finite-difference approximations. To demonstrate the usefulness of the
method, we perform sensitivity analysis of two problems. First we compute how
the spatial near-field intensity distribution of a scatterer changes with
respect to its dielectric constant. Then, we compute how the spectral power and
coupling efficiency of a surface grating coupler changes with respect to its
fill factor.
