1. Periodic Boundary Conditions in Comsol
Example: Propagation of Plane Waves in Layered Media

2. Periodic Boundary condition
BCs that are used to model a large system by simulating a small part that is far away from the edges.
Ex1. Diffusion of particles in a large container
Ex2. Propagation of Plane Waves
Information obtained from one boundary is put as a boundary condition to the related boundary

3. Plane Waves Not found in nature
Infinitely large space + infinitely large source
Used to analyze antennas, small particles in nano photonics (structures work in the far-field).
Used to build up the physical sources mathematically:
Sommerfeld Integration
Fourier analysis in EM etc…

4. Plane Waves in Free Space
Solution of Homogenous Helmholtz equation:
Must have a magnetic part that obeys:
Propagating in +z direction
Propagating in -z direction
Directions: Right hand rule (E x H=direction of prop.)
Magnitudes: H=E/impedance

5. Plane Waves in Layered Media
In layered media reflection and transmission occur.
5: transmitted-3
The magnitudes and the angles of
plane waves in all the media can be
solved analytically.
Q: How to solve in FEM?
A: FEM needs some help!
(Use periodic BCs to truncate the system)
3: transmitted-1
4: transmitted-2
2: reflected
1: incident

6. Plane Waves in Layered Media by FEM
Idea: Get the information from right boundary
import it as a new boundary condition to the left
FEM BOX
Needed for FEM with Per. BCs:
The direction of propagation of
the waves other than the incident,
Analytically!! (Snell’s Law)
3: transmitted-1
2: reflected
1: incident

7. Comsol Implementation
Draw the geometry

8. Comsol Implementation
Initialize constants needed for the simulation
Options – Constants…

9. Comsol Implementation
Set the Boundary conditions
Incident field

10. Comsol Implementation
Set the boundary conditions - 2
The wave propagating outside

11. Comsol Implementation
Periodic Boundary conditions
Need to define different index for each set
Boundary Conditions - 3
The x and y component of wave number the field in medium 3

12. Comsol Implementation
Set the sub domain settings

13. Comsol Implementation
Set the frequency value to the value in constants:
In Physics – Scalar Variables…
Press Solve