Wsb : Electromagnetic field simulator by BPM

Calculation principle

Wsb improves the calculation accuracy to the same level as FDTD, while maintaining the fast computing- performance of BPM. The calculation principle of wsb is based on the FFT-BPM (Beam Propagation Method) and it has a propagation process that applies the Babinet's principle as shown in (1) and (2) below.
(1)  Propagation in a homogeneous medium can be calculated by repeated FFT based on the Helmholtz’s equation (i.e., FFT-BPM), which is a rigorous wave equation in a homogeneous medium.


(2)  Light distribution is divided into regions of different refractive index media at refractive surfaces, and propagation is calculated for each forward and return path. Based on differences in characteristics in a frequency space, light incident on the refractive surfaces is classified into four types: transmitted light and evanescent light on the forward path, Fresnel reflection light and total reflection light on the return path, and each is combined to express the accurate propagation based on the Babinet's principle, where evanescent light is a decay component radiating total reflection light. Since Fresnel reflection is considered at the refractive surfaces, polarization can be handled. The process of synthesizing light distributions passing through complementary regions is the same as the Babinet‘s principle and it is a calculation method in which the energy change under the operation is very small (that is, energy conservation is nearly satisfied).


(Reference)  Babinet's principle
For diffraction due to complementary screens A' and A", the relationship of u_A'+u_A"=u_A holds where complexed amplitudes of diffractive light are u_A' and u_A".

Types of boundary conditions

 In the case of a periodic boundary condition (PBC).

 In the case of an absorbing boundary condition (ABC).

Calculation of transmitted light and reflected light

Transmitted light and reflected light (forward light and backward light) are calculated separately and merged.

 Forward path (dislayed in 1st of Wscnt).

 Backward path (displayed in 2nd of Wscnt).

 Marge of forward and backward paths (displayed in 3rd of Wscnt).

Polarization calculation

Wsb can handle polarized light at the refraction boundary.

 Light enters the refraction boundary at an angle.


 Angular dependence of reflectance for polarization.

Calculation for a far field

 Inclined light propagates from the top surface to the bottom surface.

 Far field pattern in the lower side.

 Far field pattern in the upper side.

Measurement of light amount

 The amount of light inflowing and outflowing to materials and the amount of light absorbed by each material can be measured individually.

 Measurement result for each material region.

Examples of cross-section for various structures

 In the case of internal definition.

 In the case of external definition using sub.dat.
The structure defined by the piled data of four points. A periodic pattern for these structures can be defined easily.

Calculation for lens focusing

 The lens shape is expressed by stacking the internally defined circular structure.

 The lens shape is expressed by stacking the externally defined circular structure.

Displaying the calculation results

 At runtime, the calculation results are displayed in real time by Wscnt.