OptiFDTD provides two dimension nonlinearity and multiple input wave simulations, thereby enabling you to simulate the Four Wave Mixing (FWM) effect. The following lesson outlines how OptiFDTD performs a FWM simulation.

To create the Four Wave Mixing layout, perform the following procedures.

Designing a four-wave mixing layout

To design the four-wave mixing materials, perform the following procedures.

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

The Initial Properties dialog box appears.

3 Click Profiles and Materials.

The Profile Designer window appears.

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

A new FDTDDielectric1 material dialog box appears.

5 Select/type the following information:

Name: FDTD_1.65

Const Ref. Idx

N Re: 1.65

6 To save the material, click Store.

FDTD_1.65 appears in the Dielectric folder in the directory and in the dialog box title bar.

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

A new FDTDNonlinear1 material dialog box appears.

8 Select Kerr.

The Kerr tab appears in the dialog box.

9 Select/type the following:

Name: FDTD_NL_Kerr

Relative Linear Permittivity: 2.7225

Response Time: 2.0e-15

Permittivity: 2.0e-18

10 To save the material, click Store.

FDTD - Figure 19 FDTD_NL_Kerr material

Figure 19: FDTD_NL_Kerr material

To define the channel profile, perform the following procedure.

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

The ChannelPro1 dialog box appears.

2 Create the following channel profile:

Profile name: NL_Kerr

2D profile definition

Material: FDTD_NL_Kerr

3 Click Store.
4 Create a second profile:

Profile name: Linear_WG

2D profile definition

Material: FDTD_1.65

5 Click Store.
6 Close the Profile Designer.

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

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

Waveguide Properties

Width [μm]: 1.0

Profile: NL_Kerr

Wafer Dimensions

Length [μm]: 15.0

Width [μm]: 10.0

2D Wafer Properties

Material: Air

2 Click OK.

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

To create the waveguide, perform the following procedure.

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

A linear waveguide appears in the layout window.

Note: Release the Linear Waveguide selection tool by clicking the Select tool after the Linear Waveguide is drawn in the layout.

3 To 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.

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

Horizontal: 4.0

Vertical: 0

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

Horizontal (µm): 13.00

Vertical (µm): 0.0

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

Width (µm): 8.0

Depth (µm): 0.0

Label: linear4

Profile: NL_Kerr

10 Click OK.
11 Repeat steps [1] through [3] to create three input linear waveguides in the layout.

Note: The input waveguide is used to input three different wavelength waves into the nonlinear material.

Input Waveguide 1 properties:

Step Action
1 In Start > Offset, type the following values.

Horizontal: 0

Vertical: 0

2 In End > Offset, type the following values:

Horizontal: 4

Vertical: 0

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

Width (µm): 1.0

Label: linear1

Depth (µm): 0.0

Profile: Linear_WG

5 Click OK.

Input Waveguide 2 properties:

Step Action
1 In Start > Offset, type the following values.

Horizontal: 0

Vertical: 1.2

2 In End > Offset, type the following values:

Horizontal: 4

Vertical: 1.2

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

Width (µm): 1.0

Depth (µm): 0.0

Label: linear2

Profile: Linear_WG

5 Click OK.

Input Waveguide 3 properties:

Step Action
1 In Start > Offset, type the following values.

Horizontal: 0

Vertical: -1.2

2 In End > Offset, type the following values:

Horizontal: 4

Vertical: -1.2

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

Width (µm): 1.0

Depth (µm): 0.0

Label: linear3

Profile: Linear_WG

5 Click OK.

FDTD - Figure 20 Input waveguides

Figure 20: Input waveguides

Setting the input wave

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

The input plane appears in the layout.

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

The Input Plane Properties dialog box appears.

4 On the General tab, type/select the following:

Continuous Wave

Wavelength [μm]: 1.4

Input Field Transverse: Modal

Plane Geometry:

Z Position [μm]: 1.0

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

The Mode Solver 2D dialog box appears.

6 On the Waveguides tab, select Linear1.
7 Click Calculate Mode.

The Modes tab is activated.

8 On the Modes tab, select the mode.
9 Click Apply Data.

The Mode Solver 2D closes.

10 On the 2D Transverse tab, select the Amplitude radio button and type the following:

Amplitude [V/m]: 2.0e09

11 Click OK.

The Input Field Properties dialog box closes.

12 Repeat steps [1] through [10] to create a second vertical input plane with the following data:

Vertical Input Plane 2 properties:

Step Action
1 In the Input Field Properties dialog box, select/type the following:

Continuous Wave

Wavelength [μm]: 1.55

2 On the General tab, type/select the following:

Input Field Transverse: Modal

Plane Geometry:

Z Position [μm]: 1.0

3 Click Find Modes.

The Mode Solver 2D dialog box appears.

4 On the Waveguides tab, select Linear2.
5 Click Calculate Mode.

The Modes tab is activated.

6 On the Modes tab, select the mode.
7 Click Apply Data.

The Mode Solver 2D closes.

8 On the 2D Transverse tab, select the Amplitude radio button and type the following:

Amplitude [V/m]: 2.0e09

9 Click OK.

The Input Field Properties dialog box closes.

Vertical Input Plane 3 properties:

Step Action
1 In the Input Field Properties dialog box, select/type the following:

Continuous Wave

Wavelength [μm]: 1.60

2 On the General tab, type/select the following:

Input Field Transverse: Modal

Plane Geometry:

Z Position [μm]: 1.0

3 Click Find Modes.

The Mode Solver 2D dialog box appears.

4 On the Waveguides tab, select Linear3.
5 Click Calculate Mode.

The Modes tab is activated.

6 On the Modes tab, select the mode.
7 Click Apply Data.

The Mode Solver 2D closes.

8 On the 2D Transverse tab, select the Amplitude radio button and type the following:

Amplitude [V/m]: 2.0e09

9 Click OK.

The Input Field Properties dialog box closes.

Setting up the Observation Point

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

The Observation Properties — Point dialog box appears.

4 On the General tab:

In Center, Offset, type/select the following: Horizontal: 6.0μm

Vertical: 0.0μm

Center depth: 0.0 μm

Label: Observation Point1

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

The Observation Properties — Point dialog box closes.

7 Repeat steps 1 to 5 and create another Observation Point with the following information.
8 On the General tab:

In Center, Offset, type/select the following: Horizontal: 6.0μm

Vertical: 1.2μm

Center depth: 0.0 μm

Label: Observation Point2

Click OK.

9 Repeat steps 1 to 5 and create another Observation Point with the following information.
10 On the General tab:

In Center, Offset, type/select the following: Horizontal: 6.0μm

Vertical: -1.2μm

Center depth: 0.0 μm

Label: Observation Point3

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

Setting the 2D simulation parameters

Step Action
1 From the Simulation menu, select 2D Simulation Parameters.

The Simulation Parameters dialog box appears.

2 Type/select the following information:

Polarization: TE

Mesh Delta X [μm]: 0.1

Mesh Delta Y [μm]: 0.1

3 Click Advanced….

The Boundary Conditions dialog box appears.

4 Type/select the following information:

-X: Anisotropic PML

+X: Anisotropic PML

-Z: Anisotropic PML

+Z: Anisotropic PML

Anisotropic PML Calculation Parameters

Number of Anisotropic PML Layers: 10

Theoretical Reflection Coefficient: 1.0e-12

Real Anisotropic PML Tensor Parameters: 5.0

Power of Grading Polynomial: 3.5

5 In Time Parameters, click Calculate.

The default time step size is calculated.

6 Select Run for 3000 Time Steps (Results Finalized).
7 Select Key Input Information: Input Plane1 and wavelength:1.4.

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

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

Note: Save your layout before starting the simulation.

Observing the simulation results

Key things to observe:

  • wave propagation pattern in time domain (see Figure 21)
  • field response in time domain and frequency domain for observation point (select View > Observation Point to see the dynamic time domain and frequency domain response (see Figure 22).

FDTD - Figure 21 OptiFDTD Simulator—wave propagation pattern in time domain

Figure 21: OptiFDTD Simulator—wave propagation pattern in time domain

FDTD - Figure 22 OptiFDTD Simulator—time domain and frequency domain for observation point

Figure 22: OptiFDTD Simulator—time domain and frequency domain for observation point