Lorentz dispersive material currently can only be simulated in 2D. This lesson describes how to create, run, and analyze a Lorentz dispersive material simulation.

The corresponding layout file is available in the sample folder of OptiFDTD:

Sample06_2D_TE_Multi-Lorentz_Dispersion_Multi-Input.FDT.

The corresponding results file is available on the OptiFDTD setup CD:

Sample06_2D_TE_Multi-Lorentz_Dispersion_Multi-Input.FDA.

Creating a layout

Step Action
1 Open Waveguide Layout Designer.
2 To create a new project, from the File menu, select New.

The Initial Properties dialog box appears.

3 To open the Profile Designer and set up the material and profile, click

Profiles And Materials.

The Profile Designer opens.

4 In the directory under OptiFDTD_Designer1, under the Material folder, right- click the FDTD-Dispersive folder.

A context menu appears.

5 Select New.

The FDTDDielectric1 material definition dialog box appears.

6 In the FDTDDielectric1 material definition dialog box, click Lorentz Dispersive.

The Lorentz Dispersive dialog box appears (see Figure 1).

FDTD - Figure 1 Lorentz Dispersive

Figure 1: Lorentz Dispersive

7 Select Lorenz Dispersive, and define the following parameters:

Name: FDTD_Lorentz_res3

ε∞  (F/m): 1.630130e00

ε0  (F/m): 2.630130e00

Resonance number: 3

8 Click Sellmeier Equation and input the corresponding values in the Sellmeier Equation table shown in Figure 1.
9 Click Transform To Lorentz Model, then click Lorentz Model radio button.

The Lorentz model resonant frequency, damping factor, and strength are shown in Figure 2.

FDTD - Figure 2 Frequency, damping factor, and strength

Figure 2: Frequency, damping factor, and strength

10 Click Store to save the material.
11 Repeat Step 4 to design a linear material with refractive index equal to 2.1 and the material with the name FDTDDielectric2.1, and click Store.
12 In the directory under Profile Designer, under the Profile folder, right-click the Channel folder.

A context menu appears.

13 Select New.

The ChannelPro1 dialog box appears.

14 In ChannelPro1 dialog box, set the Profile Name as Lorentz_res3 and the 2D profile material as FDTD_Lorentz_res3.
15 Save the profile.
16 Repeat Steps 12 to 14 design another 2D channel profile with the name Linear2.1 and the material as FDTDDielectric2.1.
17 Click Store to save the defined profile.
18 Close the Profile Designer.
19 In the Initial Properties dialog box, set the following parameters:

Waveguide Properties

Width: 1.0

Profile: Lorentz_res3

Wafer dimension

Length: 10

Width: 8

2D Wafer Material: Air

20 Click OK to start the layout designer.

The Designer window appears.

21 In the Waveguide Layout Designer window, from the Draw menu, select Linear Waveguide.
22 Draw the waveguide in the layout at the desired position.

The waveguide appears in the layout.

23 To edit the waveguide position and properties, double-click the waveguide in the layout.

The Linear Waveguide Properties dialog box appears.

24 Type the following parameters:

Waveguide start position

Horizontal: 0

Vertical:    2

Waveguide end position

Horizontal: 10

Vertical:    2

Select the Use Default checkbox. Width: 1.0

Depth: 0

Profile: Linear2.1

25 Repeat Steps 21 to 23 design another linear waveguide with following properties:

Waveguide start position

Horizontal: 0

Vertical:    –2

Waveguide end position

Horizontal: 10

Vertical:    –2

Select the Use Default checkbox. Width: 1.0

Depth: 0

Profile: Lorentz_res3

The two waveguides appear in the layout. The upper one is the Linear waveguide, and the lower one is the Lorentz Dispersive waveguide (see Figure 3).

FDTD - Figure 3 Linear and Lorentz Dispersive waveguides

Figure 3: Linear and Lorentz Dispersive waveguides

Setting the Input Plane

Step Action
1 From the Draw menu, select Vertical Input Plane.
2 Click in the layout to place the Input Plane in the desired position.

A red line that presents the input plane appears in the layout window.

3 To edit the Input Plane properties, in the layout, double-click the Input Plane.

The Input Field Properties dialog box appears.

4 Click Gaussian Modulated Continuous Wave.
5 Set the center wavelength to 1.35um
6 To edit the Input Pulse, click the Gaussian Modulated CW tab.
7 Type the following values:

Time offset (sec): 4.0e-14

Half width (sec):  1.5e-14

8 Click the General tab, and then click Modal.
9 Click the 2D Transverse tab to start solving the 2D TE fundamental mode for the lower waveguide, and then apply the solved mode as the input plane.
10 Repeat Steps 1-8 to design another vertical input plane in the same position as Input Plane1, and set the Mode input for the upper waveguide.

Setting up the Observation point

Step Action
1 From the Draw menu, select Observation Point.
2 Click in the layout to place the observation point in the desired position.
3 To edit the observation point properties, double-click the observation point in the layout.

The Observation Point Properties dialog box appears

4 Type the following values:

Center Position

Horizontal: 7.5um

Vertical: –2

Depth: 0

Data Components

2D TE: Ey (default)

5 Repeat Steps 1 to 4 to design another observation point with the following values:

Center Position

Horizontal: 7.5um

Vertical: 2

Depth: 0

Data Components

2D TE: Ey (default)

Setting up the 2D simulation parameters

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

The Simulation Parameters dialog box appears (see Figure 4).

FDTD - Figure 4 Simulation Parameters dialog box

Figure 4: Simulation Parameters dialog box

2 Click TE.
3 Type the following Mesh Delta X and Mesh Delta Z values: 0.05
4 To set the Anisotropic PML boundary condition parameters, click Advance.

The Boundary Conditions dialog box appears.

5 Type the following values:

Number of Anisotropic PML layer: 10

Theoretical Reflection Coefficient: 1.0e-12

Real Anisotropic PML Tensor Parameter: 5.0

Power of Grading Polynomial: 3.5

6 Click OK.
7 Click Calculate for time step size.
8 In the Run for Time Steps (Results Finalized) field, type 3000.
9 From the Key Input Plane drop-down list, select Input Plane1 and wavelength:1.35

Note: The Key Input Plane center wavelength is used for the DFT calculation.

10 To save the settings and start the 2D simulation, click Run.
11 After the simulation ends, open OptiFDTD_Analyzer.

Performing the simulation

Step Action
1 In OptiFDTD_Simulator, view the refractive index distribution and the wave propagation (see Figure 5).

FDTD - Figure 5 View simulation results in OptiFDTD_Analyzer

Figure 5: View simulation results in OptiFDTD_Analyzer

Note:

–    The two input waves have the same parameters.

–    The wave in the Dispersive waveguide is delayed because of the Dispersive effect.

2 To view the dynamic time domain and frequency domain response, from the View menu in the OptiFDTD_Simulator, select Observation Point Analysis.

The Observation Area Analysis dialog box opens (see Figure 6).

FDTD - Figure 6 Observation Area Analysis dialog box

Figure 6: Observation Area Analysis dialog box

Performing data analysis

Using this example, you can perform the following analysis in OptiFDTD_Analyzer.

Step Action
1 View the layout, refractive index, Poynting vector, and field propagation pattern (DFT results) for the center wavelength (see Figure 7).

FDTD - Figure 7 View simulation results for the center wavelength

Figure 7: View simulation results for the center wavelength

2 To view the Mode Analysis, from the Tools menu, select Crosscut Viewer.

The X-Z Cut Visualizer dialog box appears (see Figure 8).

FDTD - Figure 8 X-Z Cut Visualizer dialog box

Figure 8: X-Z Cut Visualizer dialog box

3 To start the observation point analysis, from the Tools menu, select Observation Area Analysis.

The Observation Area Analysis dialog box opens (see Figure 9).

FDTD - Figure 9 Observation Area Analysis dialog box

Figure 9: Observation Area Analysis dialog box