Optimization of a Photonic Crystal for Demultiplexing

In the tree, select .

Create the geometry. To simplify this step, insert a prepared geometry sequence.

Geometry 1

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file photonic_crystal_demultiplexer_optimization_geom_sequence.mph.

In the toolbar, click

The pillars are made of Gallium arsenide (GaAs), which is available in the Optical Material Database. Follow the instructions below to add it to the model. Note that the refractive index of GaAs depends on the frequency.

button in the toolbar.

In the window, collapse the node.

Materials

Air

In the window, under right-click and choose .

In the window for , type Air in the text field.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Refractive index, real part	n_iso ; nii = n_iso, nij = 0	1	1	Refractive index

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

GaAs (Gallium arsenide) (Papatryfonos et al. 2021: n,k 0.260-1.88 um) (mat2)

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (ewfd)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Scattering Boundary Condition 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Scattering Boundary Condition 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Specify the E0 vector as


0	x
0	y
1	z

Mesh 1

In the window, under right-click and choose .

Definitions

Power Port 1

In the toolbar, click

and choose .

In the window for , type Power Port 1 in the text field.

In the text field, type obj1.

Locate the section. From the list, choose .

Click in the upper-right corner of the section. From the menu, choose .

Power Port 2

Right-click and choose .

In the window for , type Power Port 2 in the text field.

In the text field, type obj2.

Locate the section. From the list, choose .

Global Definitions

Wave Parameters

In the toolbar, click

and choose .

In the window for , type Wave Parameters in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Value	Description
meshsz	lambda2/9	1.2222E-7 m	Mesh size
minPower	0.25[nW/m]	2.5E-10 W/m	Pass band power
maxPower	minPower/5	5E-11 W/m	Minimum out-of-band power
lambda1	1[um]	1E-6 m	First wavelength
lambda3	0.96*lambda1	9.6E-7 m	Out-of-band wavelength (lower)
lambda4	1.055*lambda1	1.055E-6 m	Out-of-band wavelength (center)
lambda5	1.1175*lambda1	1.1175E-6 m	Out-of-band wavelength (higher)
lambda6	1.13*lambda1	1.13E-6 m	Out-of-band wavelength (highest)
dWaveN	3	3	Frequencies per pass band
dWaveN3	4	4	Frequencies for first out-of-band constraint
dWaveN4	7	7	Frequencies for middle out-of-band constraint
dWaveN5	6	6	Frequencies for third out-of-band constraint
dWaveN6	5	5	Frequencies for last out-of-band constraint
dWave	0.01*lambda1	1E-8 m	Bandwidth for pass band
dWave3	2*dWave	2E-8 m	Bandwidth for first out-of-band wavelengths
dWave4	2.5*dWave	2.5E-8 m	Bandwidth for middle out-of-band wavelengths
dWave5	dWave/1.5	6.6667E-9 m	Bandwidth for third out-of-band wavelengths
dWave6	1.5*dWave	1.5E-8 m	Bandwidth for last out-of-band wavelengths

Mesh 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Size

In the window, under click .

In the window for , locate the section.

In the text field, type meshsz.

In the text field, type meshsz/2.

In the text field, type Inf.

Size 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type meshsz/2.

In the text field, type meshsz/4.

Clear the check box.

Study 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type range(lambda1-50[nm],1[nm],lambda2+50[nm]).

Click to expand the section. From the list, choose .

In the window, click .

In the window for , type Initial Design in the text field.

In the toolbar, click

Component 1 (comp1)

Free Shape Domain 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the dialog box, type 2 in the text field.

Add also an empty study that will be edited and used later.

Transformation 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


	Lock	Lower bound (m)	Upper bound (m)
X		-5E-8	5E-8
Y		-5E-8	5E-8

Locate the section. From the list, choose .

Definitions

Objectives

In the window, under right-click and choose .

In the window for , type Objectives in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
objA	if(lambda0<(lambda1+lambda2)/2,-obj1/minPower,-obj2/minPower)		Pass band objective
objB	(obj1+obj2)/maxPower-2		Out-of-band objective
obj	if(min(abs(lambda0-lambda1),abs(lambda0-lambda2))<dWave/1.99,objA,objB)		Objective function

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Initial Design

Disable the shape optimization for the first study.

In the window, under click .

In the window for , locate the section.


Physics interface	Solve for	Equation form
Electromagnetic Waves, Frequency Domain (ewfd)	√	Automatic (Frequency domain)
Deformed geometry (Component 1)		Automatic

Study 2

This causes the solver to identify the frequency associated with the maximum objective function and prioritize this over the other frequencies (while still taking all frequencies into account).

In the window, under click .

In the window for , locate the section.

In the text field, type range(lambda3-dWave3/2,dWave/(dWaveN3-1),lambda3+dWave3/2) range(lambda1-dWave/2,dWave/(dWaveN-1),lambda1+dWave/2) range(lambda4-dWave4/2,dWave4/(dWaveN4-1),lambda4+dWave4/2) range(lambda2-dWave/2,dWave/(dWaveN-1),lambda2+dWave/2) range(lambda5-dWave5/2,dWave5/(dWaveN5-1),lambda5+dWave5/2) range(lambda6-dWave6/2,dWave6/(dWaveN6-1),lambda6+dWave6/2).

Locate the section. From the list, choose .

Shape Optimization

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 50.

Click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

Locate the section. From the list, choose .

In the window, click .

In the window for , type Shape Optimization in the text field.

In the toolbar, click

In the window, click .

In the window for , locate the section.

Select the check box.

From the list, choose .

Solver Configurations

It is easier to converge the problem using a Segregated solver.

In the window, expand the node.

Solution 2 (sol2)

In the window, expand the node, then click .

In the window for , click to expand the section.

From the list, choose .

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

From the list, choose , to reduce the computational time.

Right-click and choose .

In the window for , type Optimization in the text field.

Locate the section. In the list, select .

Under , click

In the window, under click .

In the window for , type Electric Fields in the text field.

Locate the section. Under , click

In the dialog box, in the list, choose and .

Shape Optimization/Solution 2 (sol2)

In the window for , click

Results

In the window, expand the node.

Right-click and choose .

Initial Design

In the window, under right-click and choose .

Study 3

In the window, right-click and choose .

In the window for , locate the section.

In the table, clear the check box for .

Click to expand the section. Find the subsection. From the list, choose .

From the list, choose .

Find the subsection. From the list, choose .

Under , click

In the dialog box, in the list, choose and .

In the window for , click to expand the section.


Component	Mesh
Component 1	Mesh 2

In the window, click .

In the window for , type Verification in the text field.

Locate the section. Clear the check box.

In the toolbar, click

Results

Electric Field (initial)

In the window, under click .

In the window for , type Electric Field (initial) in the text field.

Surface 1

In the window, expand the node, then click .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. Click

In the dialog box, select in the tree.

Streamline 1

In the window, right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

Locate the section. Find the subsection. From the list, choose .

Select the check box.

In the text field, type 3e-9.

Surface 1

In the window, click .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

In the dialog box, select in the tree.

Electric Field (optimized)

In the window, under click .

In the window for , type Electric Field (optimized) in the text field.

Locate the section. From the list, choose .

In the toolbar, click

button in the toolbar.

From the list, choose .

In the toolbar, click

Create a new plot for the spectrum.

Spectrum

In the toolbar, click

and choose .

In the window for , type Spectrum in the text field.

Locate the section. From the list, choose .

Click to expand the section. From the list, choose .

Locate the section.

Select the check box. In the associated text field, type P (nW/m).

Locate the section. From the list, choose .

Global 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Click in the upper-right corner of the section. From the menu, choose .

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
obj1	nW/m	Power port 1 (mesh2)
obj2	nW/m	Power port 2 (mesh2)

Locate the section. From the list, choose .

Click to expand the section. From the list, choose .

Global 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Find the subsection. From the list, choose .

Find the subsection. From the list, choose .

From the list, choose .

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
obj1	nW/m	Power port 1
obj2	nW/m	Power port 2

In the toolbar, click

button in the toolbar.

Shape Optimization

Finally, create a new for the thumbnail.

Thumbnail

In the window, right-click and choose .

In the window for , type Thumbnail in the text field.

Locate the section. Clear the check box.

Line 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the text field, type 5e-9.

Select the check box.

Line 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Deformation 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. In the text field, type -tsf1.dXg.

In the text field, type -tsf1.dYg.

Locate the section.

Select the check box. In the associated text field, type 1.

Color Expression 1

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type sqrt(material.dX^2+material.dY^2).

Click to expand the section. Clear the check box.

Filter 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type (abs(X)<1e-6)*(abs(Y)<1e-6).

Right-click and choose .

Filter 1

In the window, right-click and choose .

Filter 1

In the window, right-click and choose .

In the toolbar, click

button in the toolbar.

Geometry Modeling Instructions

button in the toolbar.

From the menu, choose .

New

In the window, click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.


Name	Expression	Value	Description
lambda2	1.1[um]	1.1E-6 m	Second wavelength
W	4.25*lambda2	4.675E-6 m	Design domain width
rHole	0.07*lambda2	7.7E-8 m	Hole radius
nCircles	6	6	Circles per channel
dPeriod	W/nCircles/2	3.8958E-7 m	Periodicity

Add Component

In the toolbar, click

and choose .

Geometry 1

Polygon 1 (pol1)

In the toolbar, click

In the window for , locate the section.