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

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

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…

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

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

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

Comsol Implementation Draw the geometry

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

Comsol Implementation Set the Boundary conditions Incident field

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

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

Comsol Implementation Set the sub domain settings

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