來源： Reference from

Phys. Rev. Lett. 96, 233901 – Published 13 June 2006

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.233901

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In this paper Fig 1. & Fig 2., the material of the periodic rectangular waveguide is perfect electric metal (PEC)

the periodicity length d of X and Y axis are relate to the parameter a, the length, width and height of the waveguide are 0.9a, 0.2a and 0.2a, respectively.

And the observation frequency range are (c/a) [0.2-1.1].

Define Parameters

A.Main-Setup

1. Define total x, y, z length that equal to CAD, and then set a appropriate resolution.

2. Press【建立網格 Cad to Grids (Create)】button to create simulation grids.

The first example periodic length d=1.1a, and we define the a=500 nm (500e-9 meter)

d=550nm, (X, Y length)

B.Boundary Conditions

A. Define the boundary conditions

B. Press the【創建 (Create)】button => Create the total grid size (Include the boundary condition & add space)

C.Wave & Observation

The incident wave is linear polarization in y axis (pis=0) from bottom side(theta =0).

Reflection Spectrum observation : - Z direction

Transmission Spectrum observation : + Z direction

instruction webpage: DFT (Observation Range)

D. Probe & Lumped

None, press 【創建(Create)】 button

E. Geometries. Design

Checked out the simulation geometries, and then press 【輸出 Output】button to output the geometries files

Data_Materials.csv // (simulation index of structures)

In this example the "矩形孔洞 Square Hole" structure is using the built-in function.

instruction webpage: Built-in Function

%=================矩形孔洞 SquareHole===========================

lengthx=450e-9;  % 長0.9a

lengthy=100e-9;  % 寬0.2a

lengthz=100e-9;  % 高0.2a

nindex=1^2;

sigma=0;

choice='PEC'; %E_Iso,PEC,M_Iso,PMC,E_Model1,M_Model1,EM_Model1

gridtype=-1;    %

xposition=icenter*gdx;

yposition=jcenter*gdy;

zposition=kcenter*gdz;

Iso_SquareHole(choice,gridtype,nindex,sigma,xposition,yposition,zposition,lengthx,lengthy,lengthz)

%=================矩形孔洞 SquareHole===========================

F.Spectrum & Field Pattern

1. Set the Spectrum Analysis & Wavelength range

2. Check out the source

In this example the a=500nm (500e-9m)，

d=550nm, (X, Y length)

The observation frequency =speed of light / wavelength=3e8/550e-9 = 545THz

This frequency(c/a) is also the "Grating Effect" position

And then the observation frequencies range are around 0.2*545THz to 1.1*545 THz,

G.Calculation

1. Set the simulation time setp

2. Save parameters

3. Calculation

H.Result Analysis

★(Result Analysis)：

頻譜 (Spectrum) : Analysis the spectrum

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Compared results:

the periodic length d=1.2a, 1.0a are same to above，the figure at below is an example of d=1.2a =600 nm

Results of FonSinEM :

Reference paper:

Phys. Rev. Lett. 96, 233901 – Published 13 June 2006

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.233901

% ==== The Normalized method of this paper ===========

In the simulation, the maximum of the normalized transmission is 1,

However, In this paper the "Transmission" value is lager than 1. this is due to the transmission value is divide the cross-section value of the square hole.

For example :

d=1.0a

the normalized transmission/(area of the square hole)

= 0.9x0.2/(1.0*1.0)＝0.18

d=1.1a

=0.9*0.2/(1.1*1.1)=0.148760331

d=1.2a

=0.9*0.2/(1.2*1.2)=0.125

We can calculate these value in Excel, and then the normalized transmission will be same to paper

Field Pattern analysis

F.Spectrum & Field Pattern

1. Set the Spectrum Analysis & Wavelength range

2. Check out the source

The wavelength of resonance peak of the d=1.1a case is 911 nm.

If we want to observe the field pattern, back to here to setup the CW (continue wave) source

G.Calculation

1. Set the simulation time setp

2. Save parameters

3. Calculation

H.Result Analysis

★(Result Analysis)：

頻譜 (Spectrum) : Analysis the spectrum

instruction webpage: Near Field Pattern Analysis

Period Extend function (only in expression)

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For a period structure simulation, only need to simulate a single cell area for a infinity period structure.

If we'd like to see the more periodic structure in geometries or field pattern, here can use the period extend function to copy the geometries.

Menu :

select "其他 (Other)=>週期結構擴充 (Period Extend)" button

(example : *4 in X direction, *3 in Y direction)

the field pattern also can extend the image

Temporary Fields Analysis

if checked ☑暫態場輸出 ( Output Temp Fields)