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

StepAction
1Start Waveguide Layout Designer.
2To create a new project, select File > New.

The Initial Properties dialog box appears.

3Click Profiles and Materials.

The Profile Designer window appears.

4Under the Materials folder, right-click the FDTD-Nonlinear folder and select New.

A new FDTDNonlinear1 material dialog box appears.

5Select 2nd order.

The 2nd order tab appears in the dialog box.

6Select/type the following:

Name: NL 2nd

Relative Linear Permittivity εL : 2.7225

2nd Susceptibility x( 2 )  m ⁄ V : 1.0e-6

7To save the material, click Store.

FDTD - Figure 8 FDTDNonlinear1 material definition dialog box

Figure 8: FDTDNonlinear1 material definition dialog box

8Under the Materials folder, right-click the Dielectric folder and select New.

A new FDTDDielectric1 material dialog box appears.

9Select/type the following information:

Name: Dielectric_1.65

Const Ref. Idx

N Re: 1.65

10To save the material, click Store.

Dielectric_1.65 appears in the Dielectric folder in the directory and in the dialog box title bar.

To define the channel profile, perform the following procedure.

StepAction
1Under the Profiles folder, right-click the Channel folder and select New.

The ChannelPro1 dialog box appears.

2Create the following channel profile: Profile name: NL 2nd_1 2D profile definition

Material: NL  2nd

3Click Store.
4Create a second profile:

Profile name: Dielectric 1.65_1

2D profile definition

Material: Dielectric 1.65

5Click Store.
6Close the Profile Designer.

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

StepAction
1In the Initial Properties dialog box, type/select the following:

Waveguide Properties

Width [μm]: 1.0

Profile: NL 2nd_1

Wafer Dimensions

Length [μm]: 10.0

Width [μm]: 5.0

2D Wafer Properties

Material: Air

2Click OK.

The Initial Properties dialog box closes and the layout window appears.

To create the waveguide, perform the following procedure.

StepAction
1From the Draw menu, select Linear Waveguide.
2In the layout window, drag the linear waveguide from the start point to the end point.

A linear waveguide appears in the layout window.

3To adjust the position and the shape of the waveguide, in the layout window, double-click the Linear Waveguide.

The Linear Waveguide Properties dialog box appears.

4Click the Start tab.
5Under Offset, type the following values:

Horizontal: 3

Vertical: 0

6Click the End tab.
7Under Offset, type the following values:

Horizontal (µm): 10.0

Vertical (µm): 0.0

8In Channel Thickness Tapering, select Use Default (Channel:None).
9Type/select the following:

Width (µm): 1.0

Depth (µm): 0.0

Label: Linear2

Profile: NL 2nd_1

10Repeat steps [1] through [9] to create another linear waveguide in the layout.
StepAction
1In Start > Offset, type the following values.

Horizontal: 0

Vertical: 0

2In End > Offset, type the following values: Horizontal: 3

Vertical: 0

3Type/select the following:

Width (µm): 1.0

Depth (µm): 0.0

Label: Linear1

Profile: Dielectric 1.65_1

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).

FDTD - Figure 9 Waveguides in layout

Figure 9: Waveguides in layout

Inserting the input plane

To insert the input plane, perform the following procedure.

StepAction
1From the Draw menu, select Vertical Input Plane.
2To insert the input plane, click in the layout window where you want it placed.

The input plane appears in the layout.

3To edit the input plane, double-click on the input plane in the layout.

The Input Plane Properties dialog box appears.

4Select Continuous Wave.
5Set Wavelength to 1.5 μm.
6On the General tab, type/select the following:

Input Field Transverse: Modal

Plane Geometry

Z Position [μm]: 1.25

Positive direction

7On the 2D Transverse tab, click Find Modes.

The Mode Solver 2D dialog box appears.

8On the Waveguides tab, select Linear1.
9Click Calculate Mode.

The Modes tab is activated.

10On the Modes tab, select the mode.
11Click Apply Data.

The Mode Solver 2D closes.

12On the 2D Transverse tab, select the Power radio button, and type the following:

Power [W/m]: 16.0

13Click OK.

The Input Field Properties dialog box closes.

Setting up the Observation Point

StepAction
1From the Draw menu, select Observation Point.
2Place the Observation Point in the desired position in the layout.
3Double-click the observation point.

The Observation Properties — Point dialog box appears.

4On the General tab:

In Center, Offset, type/select the following:

Horizontal: 2.5μm

Vertical: 0.0μm

Center depth: 0.0μm

Label: ObservationPoint1

5On the Data Components tab, ensure that 2D TE: Ey is selected (default).
6Click OK.

The Observation Properties — Point dialog box closes.

Repeat steps 1 to 5 to create the following additional observation points with the following information:

On the General tab:

In Center, Offset, type/select the following:

Horizontal: 4.5μm

Vertical: 0.0μm

Center depth: 0.0μm

Label: ObservationPoint2

Click OK.

On the General tab:

In Center, Offset, type/select the following:

Horizontal: 6.0μm

Vertical: 0.0μm

Center depth: 0.0μm

Label: ObservationPoint3

Click OK.

On the General tab:

In Center, Offset, type/select the following:

Horizontal: 7.4μm

Vertical: 0.0μm

Center depth: 0.0μm

Label: ObservationPoint4

Click OK.

On the General tab:

In Center, Offset, type/select the following:

Horizontal: 9.0μm

Vertical: 0.0μm

Center depth: 0.0μm

Label: ObservationPoint5

Click OK.

On the General tab:

In Center, Offset, type/select the following:

Horizontal: 0.625μm

Vertical: 0.0μm

Center depth: 0.0μm

Label: ObservationPoint6

Click OK.

Setting the observation area

StepAction
1From the Draw menu, select Observation XZ.
2Place the Observation Area in the desired position in the layout.
3Double-click the observation area.

The Observation Properties — XZ Area dialog box appears.

4On the General tab:

In Center, Offset, type/select the following:

Horizontal: 3.0μm

Vertical: 0.0μm

Center depth: 0.0μm

Z length: + 1.5

X length: + 1.5

Label: ObservationArea1

5On the Data Components tab, select the following:

2D TE: Ey, Hx, Hz

6Click OK.

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)
StepAction
1From the Draw menu, select Observation Vertical Line.
2Place the Observation Line in the desired position in the layout.
3Double-click the observation line.

The Observation Properties — Vertical Line dialog box appears.

4On the General tab:

In Center, Offset, type/select the following: Horizontal: 9.5μm

Vertical: 0.0μm

X length: + 2.0

Label: ObservationLine1

5On the Data Components tab, select the following:

2D TE: Ey, Hx, Hz

6Click OK.

Repeat steps 1 to 5 to create an additional observation line with the following information:

7On the General tab:

In Center, Offset, type/select the following:

Horizontal: 6.5μm

Vertical: 0.0μm

X length: + 2.0

Label: ObservationLine2

8On the Data Components tab, select the following:

2D TE: Ey, Hx

9Click OK.

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

FDTD - Figure 10 Observation components of project

Figure 10: Observation components of project

Setting the 2D simulation parameters

StepAction
1From the Simulation menu, select 2D Simulation Parameters.

The Simulation Parameters dialog box appears (see Figure 11).

2Type/select the following information:

Polarization: TE

Mesh Delta X [μm]: 0.05

Mesh Delta Y [μm]: 0.05

FDTD - Figure 11 Simulation Parameters dialog box

Figure 11: Simulation Parameters dialog box

3Click Advanced….

The Boundary Conditions dialog box appears.

4Type/select the following information: Anisotropic PML Calculation Parameters

Number of Anisotropic PML Layers: 20

Theoretical Reflection Coefficient: 1.0e-12

Real Anisotropic PML Tensor Parameters: 5.0

Power of Grading Polynomial: 3.5

5In Time Parameters, click Calculate.

The default time step size is calculated

6Select Run for 2000 Time Steps (Results Finalized).
7Select Key Input Information: Input Plane1 and wavelength:1.5.

Note: The input plane’s center wavelength is used for DFT calculations.

8Click OK to close the Simulation Parameters dialog box without running the simulation, or click Run to start the OptiFDTD Simulator.

Note: Before running the simulation, save the project to a file.

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).

FDTD -Figure 12 Field propagation pattern

Figure 12: Field propagation pattern

FDTD -  Figure 13 Observation point

Figure 13: Observation point

Performing data analysis

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

FDTD - Figure 14 Message box

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).

FDTD - Figure 15 Poynting vector in z-direction

Figure 15: Poynting vector in z-direction

  • Select Tools > Crosscut ViewerThe 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).

FDTD - Figure 16 X-Z Cut Visualizer

Figure 16: X-Z Cut Visualizer

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

FDTD - Figure 17 Observation Area Analysis dialog box

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).

FDTD - Figure 18 Observation field pattern and power in observation line

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.