In this example, we will demonstrate simple 1D soliton propagation using a linear dispersive Lorentz material and a nonlinear Raman and Kerr Chi3 material model. See the next page for another Soliton example in an SOI waveguide.
In order to support soliton propagation, the linear dispersive, nonlinear instantaneous and nonlinear dispersive contributions need to be tuned accordingly. In this example, we will use the values provided from reference , with a linear Lorentz material model and nonlinear Raman Kerr chi3 material model. The left figure below shows the linear dispersion of the Lorentz model as a function of wavelength. Note that we have selected this Lorentz model as the base material for the "Chi3 Raman Kerr" model, this will allow us to incorporate the effect of linear material dispersion on top of the nonlinear effects.
For this example, we will set up an effective 1D FDTD simulation with MODE' 2.5D FDTD Propagator (using periodic boundaries at y min/y max and z min/z max). It is important to make sure that the "broadband" option is selected for the simulation bandwidth (so that dispersive materials can be used), and verify that the material fit for the linear dispersion is adequate (using the Material Explorer).
A mesh override region is used to specify a reasonably fine uniform mesh, and to ensure that the amount of grid dispersion is kept at a minimum. The source is a plane wave source, and the soliton_custom_time_signal.lsf file is used to specify a Gaussian shaped pulse centered at 137.016 THz with Δt = 14.6fs. A 1D Linear X time monitor has been set up across the simulation region to observe the shape of the pulse as it propagates along the x direction. To reduce the amount of simulation memory, the 1D Linear X time monitor is set to only record the Ey fields, and spatial downsampling is also used.
To run the same simulation without the nonlinear effects, simply switch the material from "Raman Kerr" to "Lorentz".
To observe the shape of the pulse as a function of time, one can visualize the line monitor results in the Visualizer (select 1D line plot, and use the "t" slider to choose the time step to display the results). In the figure below, we compare the shape of the pulse at different time steps with and without the nonlinear contributions. One can see that the simulation that includes the nonlinear effects yields a soliton that retains its shape much better than the simulation where only linear dispersion is present.
- P. Goorjian, A. Taflove, Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons, Optics Letters, Vol. 17, Issue 3, pp. 180-182 (1992)
nonlinear Raman and Kerr Chi3 material model