PMC/PEC Boundary Conditions and Plane Wave Simulation (FDTD)

OptiFDTD now has options to use Perfect Electrical Conductor (PEC) and Perfect

Magnetic Conductor (PMC) boundary conditions. You can choose which boundaries

use the new conditions, and Anisotropic PML can be used for the remaining

boundaries. With this PEC/PMC/Anisotropic PML combination, the following

simulations may be obtained:

• Plane wave simulation
• Domain reduced simulation for symmetric, periodic, or photonic band gap structures

Image value of PEC/ PMC

The following graphs show the field set up in the PEC/PMC wall (zero thickness) and

its image value

Figure 8: Field in PMC and image area

(E_┴ is the vertical electric component in the PMC wall, and H_II is the parallel

magnetic component in the PMC wall.)

Figure 9: Field in PEC and image area

As we can see from Figure 8, PMC is a symmetric wall for the symmetric structure

with symmetric wave propagation. The following two cases details the results when

PMC occurs.

Figure 10: PMC wall in a symmetric waveguide—excited by symmetric TE waveguide mode

Figure 11: PMC wall in a periodic structure for TE plane wave propagation

PMC can be seen as the special case for Bloch’s boundary condition (periodic

boundary condition) where the k-vector is set to zero in the corresponding direction.

PEC line is the complement of PMC, so in Figure 10, and Figure 11, the PMC line will

become the PEC line if the wave polarization is changed to TM.

Plane wave realized in symmetric/periodic structure

Figure 12 shows how the plane wave simulation can be realized for a symmetric

structure. For a 2D TE simulation, the edge of transverse plane should be set to the

PMC boundary condition to realize the plane wave.

Figure 12: Plane wave in TE simulation

For a 2D TM simulation, the edge of transverse plane should set to the PEC boundary

condition to realize the plane wave.

Figure 13: Plane wave in TM simulation

For a 3D simulation, the plane wave realization depends on the wave polarization and

the boundary condition setup at different edges of the transverse plane. If the wave

goes in z-direction, and the input wave is in y-direction polarization, then the y plane

(x-z) edge should be set to the PEC and x-plane (y-z plane) edge set to the PMC

boundary.

Figure 14: Y-polarization plane wave (z-direction propagation) with boundary conditions

For 3D simulation, if the wave goes in z-direction, and the input wave is in x-direction

polarization, then the y plane (x-z) edge should be set to the PMC and x-plane

(y-z plane) edge set to the PEC boundary.

Figure 15: X-polarization plane wave (z-direction propagation) with boundary conditions

The plane wave shape can be set by setting the rectangular wave parameters in the

Input Wave Properties dialog box. Currently, plane wave does not support the tilting

angle. Currently, the plane wave simulation is only effective for symmetrical

structures.