Plane Wave Simulation Based on the Periodic Cell of PhC

Compatibility:

Most of the photonic crystal has the periodic lattice. In some cases, you may want to know the band gap effect for such a lattice. As discussed in the OptiFDTD Technical Background, this task can be simplified in an FDTD simulation using plane wave excitation and PEC/PMC boundary conditions.

For example, Figure 100 shows a 2D square lattice going to infinity in both x- and z directions.

FDTD - 2D square lattice

Figure 100: 2D square lattice

You can simulate the structure shown in Figure 100 by taking a domain-reduced
region (shown in Figure 101) with a plane wave and PMC boundary conditions for 2DTE
wave.

FDTD - Figure 101 Domain reduced region

Figure 101: Domain reduced region

Designing a PBG structure

To design a PBG structure, 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 of OptiFDTD Designer1, right-click the Dielectric folder and select New.

A new Dielectric material dialog box appears.

5 Type the following information:

Name: PBG_atom 

Refractive index (Re:): 3.1

6 To save the material, click Store.

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

To define the channel profile, perform the following procedure.

Step Action
1 Under the Profiles folder of OptiFDTD Designer1, right-click the Channel folder and select New.

The ChannelPro1 dialog box appears.

2 Create the following channel profile:

Profile name: Profile_PBG

2D profile definition

Material: PBG_atom

3D profile definition

Layer name: layer_01

Width:  1.0

Thickness: 1.0

Offset: 0.0

Material: PBG_atom

3 Click Store.
4 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: Profile_PBG

Wafer Dimensions

Length [μm]: 10.0

Width [μm]: 1.0

2D Wafer Properties

Material: Air

2 Click OK.

The Initial Properties dialog box closes.

3 In the Layout Designer, from the Draw menu, select PBG Crystal Structure.
4 In the layout window, drag the cursor from a designated starting point and release, to create the PBG area.

The PBG Crystal Structure appears in the layout window.

5 To edit the crystal structure, double-click on the PBG structure in the layout.

The Crystal Lattice Properties dialog box appears (see Figure 86 as a reference).

6 In Origin, Offset, type/select the following:

Horizontal: 2.0

Vertical: -0.5

7 Click Evaluate.
8 Type/select the following:

Depth: 0.0

Azimuth [deg]: 0.0

9 In Lattice Properties, select 2D Rectangular.
10 In Lattice Dimensions, type/select the following:

Scale: 1.0

#A: 1

#C: 6

Note: When a 2D lattice is selected, the Y-direction cell #B is set to the default value of 1.

11 In Label, type PBGCrystalStruct1.

Note: Do NOT close the Crystal Lattice Properties dialog box.

Setting the atom properties

To set the atom properties, perform the following procedure in the Crystal Lattice Properties dialog box.

Step Action
1 In Atom Waveguide in Unit Cell, Add New, select Elliptic Waveguide from the drop-down menu and click New.

The Elliptic Waveguide Properties dialog box appears (see Figure 87 as a reference).

2 In Center, Offset, type/select the following:

Horizontal: 0.5

Vertical: 0.5

3 Type/select the following:

Major radius: 0.2

Minor radius: 0.2

Orientation angle: 0.0

Channel thickness tapering: Use Default (Channel: None)

Depth: 0.0

Label: Atom

Profile: Profile_PBG.

4 Click OK to close the Elliptic Waveguide Properties dialog box.

Note: When you return to the Crystal Lattice Properties dialog box, you will see the defined elliptic waveguide listed in Atom Waveguide in Unit Cell.

5 Click OK to close the Crystal Lattice Properties dialog box.

The defined PBG structure appears in the layout window (see Figure 102).

FDTD - Figure 102 Defined PBG structure in layout window

Figure 102: Defined PBG structure in layout window

Inserting the input plane

To insert the input plane, perform the following procedure.

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 Set Wavelength to 1.9 mm
5 Select Gaussian Modulated Continuous Wave.
6 On the Gaussian Modulated CW tab, type/select the following: Time Offset [Sec]: 6.0e-14

Half Width [Sec]: 1.0e-14

7 On the General tab, select Input Field Transverse: Rectangular.
8 On the 2D Transverse tab, type/select the following:

Center Position [μm]: 0.0

Halfwidth [μm]: 2.0

Tilting Angle [deg]: 0.0

Effective Refractive Index: Local

Amplitude [V/m]: 1.0

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

Plane Geometry

Z Position [μm]: 0.5

Positive direction

10 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: 0.25μm

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: 8.5μm

Vertical: 0.0μm

Center depth: 0.0 μm

Label: Observation Point2

9 On the Data Components tab, ensure that 2D TE: Ey is selected (default).
10 Repeat steps 1 to 5 and create another Observation Point with the following information.
11 On the General tab:

In Center, Offset, type/select the following:

Horizontal: 9.5μm

Vertical: 0.0μm

Center depth: 0.0 μm

Label: Observation Point3

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

Note: Observation Point1 is used to calculate the reflection, while Observation Point2 and Observation Point3 are used to calculate the transmittance.

Setting the 2D TE FDTD 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]: 0.05

Mesh Delta Y [μm]: 0.05

3 Click Advanced….

The Boundary Conditions dialog box appears.

4 Type/select the following information (see Figure 103):

-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

FDTD - Figure 103 2D simulation parameters

Figure 103: 2D simulation parameters

Note: The rectangular beam with PMC boundaries on the edge realizes the TE plane wave simulation for the periodic structure.

5 In Time Parameters, click Calculate.
The default time step size is calculated.
6  Select Run for 12000 Time Steps (Results Finalized).
7  Select Key Input Information: Input Plane1 and wavelength:1.9.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: Before running the simulation, save the project to a file.

Observing the simulation results in OptiFDTD Simulator

Key things to observe:

  • Refractive index distribution
  • Observe the wave propagation in OptiFDTD Simulator (see Figure 104).
  • Select View > Observation Point to see the dynamic time domain and frequency domain response (see Figure 105).

FDTD - Figure 104 OptiFDTD Simulator—Wave propagation

Figure 104: OptiFDTD Simulator—Wave propagation

FDTD - Figure 105 OptiFDTD Simulator—Dynamic time domain and frequency domain response

Figure 105: OptiFDTD Simulator—Dynamic time domain and frequency domain response

Performing data analysis

In OptiFDTD_Analyzer, perform the following procedure.

Step Action
1 To start the observation point analysis, from the Tools menu, select Observation Area Analysis.

The Observation Area Analysis dialog box appears (see Figure 99).

2 Select ObservationPoint1, ObservationPoint2, and ObservationPoint3.

The simulation results from the observation points displays in the graph window.

3 Type/select the following:

Frequency DFT Min. λ /f : 1.5μm

Max. λ /f : 2.3μm

Sample Point: 1000

Normalize With

InputPlane1

4 Click Update Graph to view the transmittance and reflection curves (see Figure 106).

FDTD - Figure 106 Observation Area Analysis dialog box

Figure 106: Observation Area Analysis dialog box