Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.
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Transcript of Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.
![Page 1: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/1.jpg)
Periodic Boundary Conditions in Comsol
Example: Propagation of Plane Waves in Layered Media
![Page 2: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/2.jpg)
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
0 0.1 0.2
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
X (m.)
Z (
m.)
Real part of the solution
-1
-0.5
0
0.5
1
Ex2. Propagation of Plane Waves
Information obtained from one boundary is put as a boundary condition to the related boundary
![Page 3: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/3.jpg)
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…
![Page 4: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/4.jpg)
Plane Waves in Free Space
• Solution of Homogenous Helmholtz equation:
• Must have a magnetic part that obeys:
zjkzjkx
xx
eEeEE
EkE00
00
20
2 0
Propagating in +z direction Propagating in -z direction
zjky e
EH
HjE
0
0
0
Directions: Right hand rule (E x H=direction of prop.)Magnitudes: H=E/impedance
0
00
![Page 5: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/5.jpg)
Plane Waves in Layered Media
• In layered media reflection and transmission occur.
1: incident2: reflected
3: transmitted-14: transmitted-2
5: transmitted-3The 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)
![Page 6: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/6.jpg)
Plane Waves in Layered Media by FEM
1: incident
FEM BOX
Needed for FEM with Per. BCs:The direction of propagation of the waves other than the incident,Analytically!! (Snell’s Law)
2: reflected
3: transmitted-1
ri
ir
t
2
1
sin
sin
n
n
i
t
iririn ,,
Idea: Get the information from right boundaryimport it as a new boundary condition to the left
![Page 7: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/7.jpg)
Comsol Implementation
• Draw the geometry
![Page 8: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/8.jpg)
Comsol Implementation
• Initialize constants needed for the simulation– Options – Constants…
![Page 9: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/9.jpg)
Comsol Implementation
• Set the Boundary conditions
Incident field
![Page 10: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/10.jpg)
Comsol Implementation
• Set the boundary conditions - 2
The wave propagating outside
![Page 11: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/11.jpg)
Comsol Implementation
• Boundary Conditions - 3
Periodic Boundary conditions
Need to define different index for each set
The x and y component of wave number the field in medium 3
![Page 12: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/12.jpg)
Comsol Implementation
• Set the sub domain settings
![Page 13: Periodic Boundary Conditions in Comsol Example: Propagation of Plane Waves in Layered Media.](https://reader035.fdocuments.in/reader035/viewer/2022062322/56649ef45503460f94c0742c/html5/thumbnails/13.jpg)
Comsol Implementation
• Set the frequency value to the value in constants:– In Physics – Scalar Variables…
• Press Solve