What is Floquet boundary conditions?

What is Floquet boundary conditions?

The most common method of determining the dispersion curves of a periodic waveguide is to use, what COMSOL Multiphysics software refers to as, Floquet boundary conditions (Floquet BC). These boundary conditions, and methods involving them, are called different things depending on the field of study and application.

What is Floquet theorem?

and defines the state of the stability of solutions. that transforms the periodic system to a traditional linear system with constant, real coefficients. When applied to physical systems with periodic potentials, such as crystals in condensed matter physics, the result is known as Bloch’s theorem.

What is Floquet stability analysis?

Floquet stability analysis is similar to linear stability analysis of steady base flows. Each eigenvalue of this operator shows the growth/decay rate of the perturbation over a period: these are the Floquet multipliers ( ). When , the flow is unstable and the perturbation grows each period. …

What are Floquet multipliers?

A Floquet exponent (sometimes called a characteristic exponent) is a complex \mu such that {e^{\mu T}} is a Floquet multiplier of the system. Notice that Floquet exponents are not unique since e^{(\mu+({2\pi ik}/T))T} = {e^{\mu T}}\ (where k is an integer), but Floquet multipliers are unique.

What is periodic condition in Comsol?

The periodic condition applies a constraint on the destination selection, constraining the solution at each destination point rdst to be equal to the solution at a corresponding source point rsrc.

How do you get a Floquet exponent?

(T(n)f)(x)=f(x+ωn),x∈R,n∈Z.

What is Floquet port in CST?

Floquet theorem is used for periodic structures. So, in Microwave interaction structure design we apply this theorem in CST microwave studio. Set electric and magnetic field according to structure. Use Eigen mode solver for your particular mode or for all mode.

How do you simulate a unit cell in CST?

When you open CST, Go to “MW & RF & Optical”, then you can go to “Periodic Structures”, then you can decide to have Unit Cell or Full Structure.

How do you plot a dispersion diagram?

Creating a dispersion graph

1. Step 1 – Vertical axis. Review the data and decide upon a scale. In this case, the highest value is 40 mm so the vertical scale will run from 0 to 45 at 5 mm intervals.
2. Step 2 – Horizontal axis. The horizontal axis has three entries, one for each site.
3. Step 3 – Plot. Plot the data on your graph.

What is primitive cell in solid state physics?

A primitive cell is a unit cell that contains exactly one lattice point. It is the smallest possible cell. If there is a lattice point at the edge of a cell and thus shared with another cell, it is only counted half.

How do you plot dispersion?

How is Floquet Bloch related to Schrodinger equation?

This wave function is a solution of the Schrödinger equation with a periodic potential and Bloch showed that it was the product of a simple plane wave multiplied by a periodic function with the same periodicity of the lattice. The mathematical description of these ideas, in the context of quantum mechanics, can be found in [ 3

How is Floquet-Bloch theory related to periodic structure?

Floquet-Bloch (hereafter F-B) theory provides a strategy to analyze the behavior of systems with a periodic structure. Floquet’s seminal paper dealt with the solution of 1D partial differential equations with periodic coefficients [ 1

How is the Floquet-Bloch strategy implemented in Finite Element Software?

The Floquet-Bloch strategy computes the solution on a unit cell, whose influence is studied here. It is implemented in commercially finite element software and increasing the number of layers of the system does not bring additional numerical difficulties.