Second Order Nonlinearity

OptiFDTD provides four types of nonlinear materials.

• 2nd Order
• 3rd Order
• Kerr-effect
• Raman-effect

All of these nonlinearities can be combined with the Lorentz dispersive model, which leads to dispersive nonlinear properties. To simulate the nonlinear material correctly, we recommend that you read the FDTD Basics.

Note:

• Because the nonlinear material may have a high frequency response, a finer mesh size for the simulation may be required.
• Set a suitable power level in the input plane. If the input power is too low, the material may not be excited to nonlinear levels. If the power is too high, the output will be an unstable modulated wave.
• Nonlinear material parameters must have physical meanings.

The following examples explain how to design, simulate, and analyze the nonlinear materials.

2nd Order nonlinear material simulation

Creating the layout

Figure 8: FDTDNonlinear1 material definition dialog box

To define the channel profile, perform the following procedure.

To define the wafer and waveguide properties, perform the following procedure.

To create the waveguide, perform the following procedure.

The two waveguides appear in the layout. The one on the left is the linear waveguide,
and the one on the right is the nonlinear waveguide (see Figure 9).

Figure 9: Waveguides in layout

Inserting the input plane

To insert the input plane, perform the following procedure.

Setting up the Observation Point

Setting the observation area

Setting the observation line

The observation line is only used for 2D simulations. It is used to show:

• field distribution along the line for the user input wavelength
• calculate the outgoing power in the line for user input wavelength
• calculate the absolute power spectrum and normalized transmittance power spectrum (to the input power)

The observation components of the project can be seen in Figure 10.

Figure 10: Observation components of project

Setting the 2D simulation parameters

Figure 11: Simulation Parameters dialog box

Observing the simulation results in OptiFDTD Simulator

Key things to observe:

• Field propagation pattern in OptiFDTD Simulator (see Figure 12)

Select View > Observation Point to observe the dynamic time domain and frequency domain response (see Figure 13).

Figure 12: Field propagation pattern

Figure 13: Observation point

Performing data analysis

When the simulation ends, a message appears and prompts you to open
OptiFDTD_Analyzer (see Figure 23).

Figure 14: Message box

Action

• To open OptiFDTD_Analyzer and view the simulated results, click Yes.

Note: When the simulation ends in OptiFDTD_Simulator, the results are saved automatically as a file with same name, but with a different file extension (*.fda).

Observe the layout, refractive index, Poynting vector, and field propagation pattern (DFT results) for the input wavelength (see Figure 15 for Poynting vector in z-direction).

Figure 15: Poynting vector in z-direction

• Select Tools > Crosscut Viewer. The X-Z Cut Visualizer dialog box appears.

You can do the mode analysis, mode overlap integral calculation, slice power calculation, and far field transformation (see Figure 16).

Figure 16: X-Z Cut Visualizer

• Select Tools > Observation Area Analysis. The Observation Area Analysis dialog box appears (see Figure 17).

Figure 17: Observation Area Analysis dialog box

• Click the Observation Line tab to start the observation line analysis. The field pattern and the corresponding power for the user input wavelength in the observation line appear in the dialog box (see Figure 18).

Figure 18: Observation field pattern and power in observation line

You can also follow the same procedure to perform another nonlinear material simulation.

See the following sample files:

• Sample12_2D_TE_3rd_Order_Nonlinear.fdt
• Sample13_2D_TE_Kerr_Nonlinear.fdt

In general, the Kerr effect and Raman effect belong to the 3rd-order nonlinearity. However, the Kerr effect uses a special model to consider photonic response time, while the Raman model considers both the response time and the oscillating frequency.