FDTD is a time-domain method. Therefore the excitation in most cases is always a pulse. A pulse will create a braodband spectrum, thus you see the significant spectrum bandwidth.
The pulse is the most efficient source for FDTD. If you want to have a quasi-monochromatic light, you will need a transient part with half the pulse, then a sinusoidal signal, which must extends much longer time in order to reach the steady state, and use time domain monitor to get the result. Frequency-domain monitors are designed for pulse signal, which uses Fourier transform to get the steady-state result from the time signal. It is rarely used though. Here is an example https://optics.ansys.com/hc/en-us/articles/360042192813-1D-cavity-laser-using-4-level-2-electron-material