While it is certainly possible to formulate essentially any numerical technique as a scalar method, FDTD is by its nature a fully vectorial and fully rigorous method; aside from the approximation of fitting the fields to a discrete grid. In fact, I am not sure I have ever seen it implemented as a scalar method.
In my mind, FDTD has some important benefits and drawbacks you should consider. Here are only a few:
Benefits
1. FDTD is a fully vectorial and fully rigorous method!!!!
2. FDTD is a time-domain method so it is possible to characterize a device over an incredibly huge range of frequencies in a single simulation. Frequency-domain methods must repeat their computations for every frequency of interest.
3. FDTD is not based on linear algebra so if the problem size doubles, the number of computations only doubles. Methods based on linear algebra operations like matrix division or eigen-system computations scale exponentially.
Drawbacks
1. It is very difficult, but not impossible, to implement source waves at oblique angles of incidence.
2. FDTD must iterate for incredibly long periods of time when there are sharp or abrupt features in their spectral response.
3. It is very difficult in many situations to exploit longitudinal periodicity. For example, if you want to model transmission through a photonic crystal slab that is 100 periods thick, FDTD must store all of these periods in memory at once. Other methods based on scattering matrices (or similar approaches) can compute on unit cell, then stack that on itself 100 times to dramatically improve efficiency.
-Tip