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.

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 of OptiFDTD Designer1, right-click the Dielectric folder and select New.

A new Dielectric material dialog box appears.

5Type the following information:

Name: PBG_atom 

Refractive index (Re:): 3.1

6To 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.

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

The ChannelPro1 dialog box appears.

2Create 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

3Click Store.
4Close 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: Profile_PBG

Wafer Dimensions

Length [μm]: 10.0

Width [μm]: 1.0

2D Wafer Properties

Material: Air

2Click OK.

The Initial Properties dialog box closes.

3In the Layout Designer, from the Draw menu, select PBG Crystal Structure.
4In 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.

5To 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).

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

Horizontal: 2.0

Vertical: -0.5

7Click Evaluate.
8Type/select the following:

Depth: 0.0

Azimuth [deg]: 0.0

9In Lattice Properties, select 2D Rectangular.
10In 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.

11In 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.

StepAction
1In 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).

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

Horizontal: 0.5

Vertical: 0.5

3Type/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.

4Click 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.

5Click 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.

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.

4Set Wavelength to 1.9 mm
5Select Gaussian Modulated Continuous Wave.
6On the Gaussian Modulated CW tab, type/select the following: Time Offset [Sec]: 6.0e-14

Half Width [Sec]: 1.0e-14

7On the General tab, select Input Field Transverse: Rectangular.
8On 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

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

Plane Geometry

Z Position [μm]: 0.5

Positive direction

10Click 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: 0.25μm

Vertical: 0.0μm

Center depth: 0.0 μm

Label: Observation Point1

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

The Observation Properties — Point dialog box closes.

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

In Center, Offset, type/select the following:

Horizontal: 8.5μm

Vertical: 0.0μm

Center depth: 0.0 μm

Label: Observation Point2

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

In Center, Offset, type/select the following:

Horizontal: 9.5μm

Vertical: 0.0μm

Center depth: 0.0 μm

Label: Observation Point3

12On 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

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

The Simulation Parameters dialog box appears.

2Type/select the following information:

Polarization: TE

Mesh Delta X [μm]: 0.05

Mesh Delta Y [μm]: 0.05

3Click Advanced….

The Boundary Conditions dialog box appears.

4Type/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.

5In 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.

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

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

2Select ObservationPoint1, ObservationPoint2, and ObservationPoint3.

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

3Type/select the following:

Frequency DFT Min. λ /f : 1.5μm

Max. λ /f : 2.3μm

Sample Point: 1000

Normalize With

InputPlane1

4Click 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