# Knowledge Base

 Source - BFAST

This page describes the Broadband Fixed Angle Source Technique (BFAST), which only applies to the following case: periodic structures illuminated with a broadband source at an angle. In this case, this technique will allow users to obtain broadband simulation results at angled illumination.

FDTD

### Associated files

bfast_stack.fsp

bfast_stack.lsf

Symmetric and anti-symmetric BCs

Grating order transmission

Blaze grating

Plasmonic application

White paper - BFAST

### Related publications

B. Liang et al, Wideband Analysis of Periodic Structures at Oblique Incidence by Material Independent FDTD Algorithm, IEEE Trans. Antennas & Propagation, Vol.62 ,No.1, PP. 354 - 360.

## Broadband Fixed Angle Source Technique (BFAST)

When studying periodic systems, periodic Boundary Conditions (BC) allows you to calculate the response of the entire system by only simulating one unit cell, as mentioned in Periodic boundary conditions article. When a broadband plane wave is injected into a structure at an angle, special treatment will be required. One way is to use Bloch boundary condition. However, the actual injection angles for broadband illumination change with frequency, discussed in Plane waves - Angled injection. One way to solve this problem, the wavelength or frequency can be swept, or a number of incident angles are simulated and interpolation is required (refer this page, for advanced user only). Oftentimes, sweeping can take much more simulation time.

Another method to avoid the sweeping is to reformulate the FDTD algorithm. A simplified description of this method can be briefly described here:

A plane wave angled in xz plane (traveling along z axis) can be expressed as

$$\vec{E}(\vec{r})=e^{i k_{x} x} \vec{E}_{0}$$

To remove the angular dependence from the field, a set of new variables is used, such as:

$$\vec{Q}(\vec{r}) = e^{-ik_{x} x} \vec{E}(\vec{r})$$

and then the split field method (eg., split x component to xy and xz) is used to reformulate the FDTD update equations. Therefore, by reformulating the FDTD update equations, a new algorithm can be developed by removing this angle dependence. More details can be found in Liang's paper. Therefore, no Bloch BCs are required. It will have its own built-in boundaries conditions transverse to the propagation direction.

 When to use BFAST
 How to use BFAST
 Example
 Angle sweep
 Limitations
 Numerical stability
 Summary and Tips

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