In this example, we will use the nonlinear Chi2 material model to model harmonic generation.
Simulation setup
The simulation model in harmonic.fsp consists of a plane wave source incident on a slab of nonlinear \( \chi^{(2)} \) medium (with the Chi(2) term set to 3e-10). Since the \( \chi^{(2)}\) term is a second harmonic term, we expect to see a transmission spectrum that not only has a resonance peak at the source frequency f1 = 200 THz, but also at the second harmonic frequencies.
To show this, we place a time monitor on top the nonlinear medium so that we can look at the spectrum (i.e. the FFT of the time signal). Also, since we cannot use the default frequency domain normalization for nonlinear simulations, we have to define the source pulse in time (instead of simply using the default auto-generated pulse).
Results
Below is the transmission response for the \( \chi^{(2)} \) medium. This figure was obtained by right-clicking on the time monitor, and selecting Visualize - Spectrum (log10).
As expected, we see a peak at the source frequency 200 THz, as well as at 400, 600, 800 THz. The reason we are able to see nice higher order harmonics is because we are simply using a dielectric as the base material (with index ~2.12). FDTD also supports base materials that are dispersive. In the same simulation file, switch the material from "chi2" to "chi2_Si", and repeat the simulation. The new spectrum will look like the following figure, and we can see the effect of the material dispersion from the Si base material.
See also
Four wave mixing, Kerr effect, nonlinear Chi2 material model