Wave Source & Observation

中文/English

【波源與觀測(Wave & Observation.)】

1. Select Incident wave type, mode profile:

TFSF-RCS, TFSF-RCS-Substrate

To calculate : Radar-Cross-Section, Extinction-Scattering-Absorption

The incident mode profile : plane wave

TFSF-Line

To calculate :Transmission-Reflection

The incident mode profile : plane wave, Gaussian beam, Customize

Soft-Source

Point Source or other shape

Hard-Source

Point Source or other shape

2. Define the incident wave direction (Linear Polarization, Elliptical Polarization, Circular Polarization)

3. Define the observation range, (DFT : Discrete Fourier Transform)



Detailed Instructions:




Incident Source

Extinction = Scattering + Absorption

TFSF-RCS


TFSF-RCS-Substrate



TFSF-RCS(Total Field Scatter Field - Radar Cross Section)


TFSF-RCS(Total Field Scatter Field - Radar Cross Section) , this is a method to calculate scattering & absorption spectrum. The figure shows below, green region means PML for absorbing boundary condition (or called open space boundary condition). In the figure, the deep blue line means the incident wave, bright blue line means absorption Poynting observation position, the yellow line means scattering poynting observation position. (For detail of TFSF can refer to any FDTD book)

Attention, the simulation geometries can't exceed or touched the observation line. The distance larger than ten grids is better (for visible light region, as the simulation material is metal, there might exist strong evanescence wave on the metal surface. then the distance need to larger to this evanescence length)

There are four kinds of TFSF

TFSF-RCS (Typically)


The left figure of below shows Ex, Ez, Hy fields without any geometry inside. The incident wave from left bottom with theta = 65 degrees.

The right figure of below shows Ex, Ez, Hy fields with metal cylinder inside.

Without geometry -TFSF-RCS

With metal cylinder TFSF-RCS


TFSF-RCS-Substrate

This technological is design for the TFSF with substrate condition. In experiment, the structure under test not always levitate in the air. For example, if we'd like to measure a sphere scattering effect, it might put on the substrate. However, if the substrate exist in the simulation space which show in the left figure below. The TFSF technological will encounter error which show in the right side figure below.

This will lead to a wrong simulation result. The incident wave error is from 1D look up table source don't give the substrate (refer to the FDTD book).

In GUI parameters, the substrate position means that we need set the top position in 2D or 3D simulation. The substrate can be made of dielectric, metal, or other dispersion material. As there isn't any geometry inside (free space), we can see if setup correct the wave will excite perfect and without any diffraction to outer side.

in this example, X can set at any position, but the Z position need to set at position = 50, it's the same to the substrate top side of simulation structure.

(Also can refer to Lumerical commercial software, it's the same theory in the TFSF wave incident with substrate.)



對照引用 Comparison & Reference:
Lumerical FDTD Solutions
Multi-layer stack with gap 
http://docs.lumerical.com/en/index.html?ref_sim_obj_tfsf_sources_examples.html

wave excited success

And here show the wrong example, the substrate position isn't set correct to the "1D look up table " in FonSinEM.




TFSF-Line

Choice this if the source is a plane wave incident, and obtain the "Transmission" and "Reflection" results.

Be attention : this incident only in normal incident in FDTD algorithm. In oblique incident case, please choice the Split-Field Method (SFM) algorithm.



★A plane wave in oblique incident in time-domain algorithm (FDTD), there are encounter the optical path length problem ( phase different between right and left side). To solve this problem, there are several algorithm were developed, Angle-Updated, Sine-Cosine Method, Field Transform Method (Split Filed Method), Spectrum FDTD Method. Field Transform Method (Split Filed Method :SFM) is used in FonSinEM.



對照引用 Comparison & Reference:
Lumerical FDTD Solutions
Sources - Plane wave and Beam
http://docs.lumerical.com/en/index.html?ref_sim_obj_sources_plane_waves_and_beam.html
在Lumerical裡,TFSF-Line是定義為Plane wave,風行裡是稱作TFSF-Line,這兩者是一樣的。因為前面所提TFSF-RCS亦是激發平面波入射,且兩者都是使用TFSF的技術,想了想、最後還是使用線(Line)這個詞。因為若加上模態形狀,也不一定是激發平面波。另外也可參考其平面波-角度入射的應用。
Plane waves - Angled injection
http://docs.lumerical.com/en/index.html?ref_sim_obj_plane_waves_-_angled_injection.html
在Lumerical裡,TFSF-Line在有角度入射時,使用Bloch 邊界條件,且需要輸入正確的波向量k (wave vector)來激發正確的斜向入射
通常市售軟體或一些免費的FDTD軟體是使用此方法,好處是使用原本的疊代方程、穩定條件。缺點是要對波向量作正確的計算。
而風行是使用Field Transform (Split Field Method)方法,詳細可參考FDTD書本皆有討論,而目前使用SFM方法來處理斜向入射的軟體如
LFSIM
http://www.ece.ncsu.edu/oleg/wiki/WOLFSIM



Comparison of TFSF-RCS and TFSF-Line

TFSF-RCS*

●Obtain Scattering/Absorption/Extinction Spectrum.

●Plane wave incident,

●Any incident angle

●Traditional FDTD.

TFSF-Line

●Obtain Transmission/Reflection Spectrum

●can use any incident wave profile (Plane wave, Gaussian beam, etc.)

●Traditional FDTD for normal incident, SFM for oblique incident.


Traditional FDTD

SFM (Split-Field Method) for oblique incident, from top or bottom

(TFSF-Line) (Load Mode Profile)

In TFSF-Line, if you'd like to excite a Gaussian beam, you can use the built-in function in FonSinEM. the Gaussian beam equation is


GaussianProfile=exp(-(x^2+y^2)/beamsize^2)

refer to Wiki

http://zh.wikipedia.org/wiki/%E9%AB%98%E6%96%AF%E5%85%89%E6%9D%9F


Gaussian beam 2D exmaple

======== Parameters setup:2D =============

Total Grids

X = 200

Z = 200

delta = 5 nm


Boundary condition

X: PML

Z: PML

Wave

CW, 100nm

TFSF-line

Source Position

X = 50

Z = 30

Mode Profile

GaussianBeam, Beam-Size : 100e-9


Polarization 1

Amp : 1

theta : 30

phase : 0


Cal. Time Step

2000

========================

(Time domain for temp-field) wave propagate

(Frequency domain for steady-state field ) |E|

Gaussian beam 3D exmaple

======== parameters setup:3D =============


Total Grids

X = 50

Y = 50

Z = 120

delta = 10 nm


Boundary condition

X: PML

Y: PML

Z: PML


Wave

CW, 100nm



TFSF-line

Source Position

X = 25

Y = 25

Z = 11


Mode Profile

GaussianBeam, Beam-Size : 100e-9


Polarization 1

Amp : 1

theta : 0

phi: 0

psi: 0

phase : 0


Cal. Time Step

1000


==================================

(Time domain for temp-field) wave propagate

(Frequency domain for steady-state field ) |E|

SoftSource


Source can use for point, line or any other shape, but only one electric or magnetic can choice in a simulation.

2D TM (Ex Ez Hy) can choice Ex, Ez, Hy

2D TE (Hx Hz Ey) can choice Hx, Hz, Ey

3D (Ex Ez Hy) can choice Ex, Ey, Ez, Hx, Hy, Hz


Softsource means set a source on the choices position,for example : Ex

Ex = Ex + Js

if a reflection wave pass through the softsource position, the field will superposition.

The below figure means 2D TM, Hy point source (x=60:60,z=60:60), source is at center position, we can see the point source divergence (Huygens priciple).

reference :惠更斯原理(Huygens Principle) point source divergence

HardSource

Source can use for point, line or any other shape, but only one electric or magnetic can choice in a simulation.

2D TM (Ex Ez Hy) can choice Ex, Ez, Hy

2D TE (Hx Hz Ey) can choice Hx, Hz, Ey

3D (Ex Ez Hy) can choice Ex, Ey, Ez, Hx, Hy, Hz


Softsource means set a source on the choices position,for example : Ex

Ex = Js

if a reflection wave pass through the Hardsource position, the hardsource behavior like a perfect electric/magnetic wall.


Hardsource has another parameter N-Stop, if the calculate time step larger than N-Stop, the hardsource will remove. This can avoid there is always a electric/magnetic wall in the position.



SoftSource/Hardsource (Load File)

checked the "Load File" can customize the source position, range and shape.

Data_LoadSource.csv


For example : U shape source, use the input pannel


LoadSource(isrc-20,jb,ksrc-20:ksrc+20)=1;
LoadSource(isrc+20,jb,ksrc-20:ksrc+20)=1;
LoadSource(isrc-20:isrc+20,jb,ksrc-20)=1;

Example : U shape source


Perfect electric conductor wavegudie mode excite example



【Input pannel】


m=1;
d=(ib-1)*gdx;
for i=2:ib-1 
LoadSource(i,jcenter,kcenter)=cos(m*pi/d*(i-2)*gdx); 
end

Perfect electric conductor wavegudie mode, m=1

自訂觀測範圍 (Customize Observation Range)


For example : ☑X-,☑X+,☑Y-,☑Y+,☑Z-, ☑Z+


The figure shows


Boundary condition : X-:PML, Z+:PML。X: 16 grids, Z: 30 grids


Transmission Spectrum:☑X+, ☑Z+ , X:30=>183, Z:130:180


Reflection Spectrum:☑X-, ☑Z+ ,☑Z- , X:50=>80, Z:70:100


And we can obtain the result below, the green region means PML, only in X- and Z+


Transmission Spectrum only observe in ☑X+, ☑Z+ direction

☑X+ (x=183,z=130:180)

☑Z+ (x=30:183,z=180)