Tapered Waveguide

In the tree, select .

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

These parameters define the geometry of the waveguide, the material properties for the different domains, and the wavelength and frequency used in the simulation.

Browse to the model’s Application Libraries folder and double-click the file tapered_waveguide_parameters.txt.

Part Libraries

In the toolbar, click

and choose .

In the window, select in the tree.

Geometry 1

Tapered Waveguide

In the window, under click .

In the window for , type Tapered Waveguide in the text field.

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


Name	Expression	Value	Description
input_core_width	w_core_1	3.1E-6 m	Input core width
input_cladding_width	w_clad_1	1.55E-4 m	Input cladding width
output_core_width	w_core_2	3.1E-7 m	Output core width
output_cladding_width	w_clad_2	1.55E-4 m	Output cladding width
element_length	d_taper	3.1E-4 m	Element length

Locate the section. In the text field, type -90.

Click to expand the section. Click .

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

In the window for , locate the section.

Click .

In the dialog box, type Non-PML in the text field.

In the window for , locate the section.

The selections above will be used for defining selections for materials and variables as well as in postprocessing.


Name	Keep	Physics	Contribute to
Core		√	Core
Cladding		√	None
All	√	√	Non-PML

Setting the value in the first row of the column to will make the domain selection contribute to a cumulative domain selection, representing all waveguide core domains.

Selecting the check box in the last table row makes domains in the available as a separate domain selection. Furthermore, by setting the last value in the column to , the domain selection will contribute to a cumulative domain selection representing all domains that are not part of a Perfectly Matched Layer (PML).

Click to expand the section. In the table, enter the following settings:


Name	Keep	Physics	Contribute to
Exterior		√	None
Port 1 core		√	None
Port 1 cladding		√	None
Port 1		√	None
Port 2 core		√	None
Port 2 cladding		√	None
Port 2		√	None
Transverse perimeter	√	√	None

The represents the top and the bottom exterior boundaries for this part. This selection will later be used when defining the mesh.

Part Libraries

In the toolbar, click

and choose .

In the window, click .

In the window, select in the tree.

Geometry 1

Input Waveguide

In the window, under click .

In the window for , type Input Waveguide in the text field.

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


Name	Expression	Value	Description
core_width	w_core_1	3.1E-6 m	Core width
cladding_width	w_clad_1	1.55E-4 m	Cladding width
element_length	lam0	1.55E-6 m	Element length

Click to select row number 3 in the table.

Locate the section. In the text field, type -lam0.

In the text field, type -90.

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


Name	Keep	Physics	Contribute to
Core		√	Core
Cladding		√	None
All	√	√	Non-PML

Locate the section. Click .

In the dialog box, type Straight Waveguide Transverse Perimeter in the text field.

In the window for , locate the section.


Name	Keep	Physics	Contribute to
Exterior		√	None
Port 1 core		√	None
Port 1 cladding		√	None
Port 1	√	√	None
Port 2 core		√	None
Port 2 cladding		√	None
Port 2		√	None
Transverse perimeter		√	Straight Waveguide Transverse Perimeter

The selection will be used as the selection for the input port in the model. The cumulative selection will be used when defining the mesh.

button in the toolbar.

Input PML

Right-click and choose .

In the window for , type Input PML in the text field.

Locate the section. In the text field, type -2*lam0.

Locate the section. Click .

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

In the window for , locate the section.


Name	Keep	Physics	Contribute to
Core		√	Core
Cladding		√	None
All	√	√	PML

The selection will be used for the Perfectly Matched Layer.

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


Name	Keep	Physics	Contribute to
Exterior		√	None
Port 1 core	√	√	None
Port 1 cladding	√	√	None
Port 1	√	√	None
Port 2 core		√	None
Port 2 cladding		√	None
Port 2		√	None
Transverse perimeter		√	Straight Waveguide Transverse Perimeter

The , , and selections will be used when defining the mesh.

button in the toolbar.

Output Waveguide

In the window, under right-click and choose .

In the window for , type Output Waveguide in the text field.

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


Name	Expression	Value	Description
core_width	w_core_2	3.1E-7 m	Core width
cladding_width	w_clad_2	1.55E-4 m	Cladding width

Locate the section. In the text field, type d_taper.

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


Name	Keep	Physics	Contribute to
Exterior		√	None
Port 1 core		√	None
Port 1 cladding		√	None
Port 1		√	None
Port 2 core		√	None
Port 2 cladding		√	None
Port 2	√	√	None
Transverse perimeter		√	Straight Waveguide Transverse Perimeter

The selection will be used for the output port.

button in the toolbar.

Output PML

In the window, under right-click and choose .

In the window for , type Output PML in the text field.

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


Name	Expression	Value	Description
core_width	w_core_2	3.1E-7 m	Core width
cladding_width	w_clad_2	1.55E-4 m	Cladding width

Locate the section. In the text field, type d_taper+lam0.

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


Name	Keep	Physics	Contribute to
Exterior		√	None
Port 1 core		√	None
Port 1 cladding		√	None
Port 1		√	None
Port 2 core		√	None
Port 2 cladding		√	None
Port 2		√	None
Transverse perimeter		√	Straight Waveguide Transverse Perimeter

Perfectly Matched Layer 1 (pml1)

button in the toolbar.

Materials

Cladding

In the window, under right-click and choose .

In the window for , type Cladding 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	n_clad	1	Refractive index

Core

Right-click and choose .

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

Locate the section. From the list, choose .

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	n_core	1	Refractive index

Definitions

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the text field, type 2*pi/kx. The variable kx will be highlighted in orange to warn that it has not been defined yet.

Electromagnetic Waves, Beam Envelopes (ewbe)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

From the list, choose .

In the φ1 text field, type phi. The variable phi will also be displayed in orange, as it has not yet been defined.

Click to expand the section. Specify the k1 vector as


kx	x
0	y

It is necessary to manually define the wave vector to get the right phase and wave vector in the Perfectly Matched Layer (PML) domains. For more information, see the discussion in the Model Definition section.

Port 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Select the check box.

From the list, choose .

Click to make the arrows in the window point in the positive x direction (meaning that the power will flow into the tapered waveguide).

Port 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 .

Select the check box.

From the list, choose .

Click to make the arrows in the window point in the positive x direction (meaning that the power will flow out of the waveguide and into the backing PML).

This port will not absorb any radiation. Instead, all radiation reaching the port will be absorbed by the backing PML. The port, however, will make sure that the proper S-parameter and transmittance variables are defined.

Definitions

Next, define the missing phase and wave vector variables. Notice that the expressions below will make the phase variable phi continuous everywhere along the waveguide.

Input PML

In the window, under right-click and choose .

In the window for , type Input PML in the text field.

Locate the section. From the list, choose .

From the list, choose .

Now, define the mesh, using the selections defined when the geometry was created.

button in the toolbar.

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


Name	Expression	Unit	Description
kx	ewbe.beta_1	rad/m
phi	kx*pml1.x	rad/m

Above, the phase phi is defined using the complex scaled PML coordinate pml1.x. This will make the field in the PML attenuate. The wave vector in the x direction, kx, is defined by the propagation constant for the input port.

Input Waveguide

Right-click and choose .

In the window for , type Input Waveguide in the text field.

Locate the section. From the list, choose .

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


Name	Expression	Unit	Description
phi	kx*x	rad

Let the setting for kx remain unchanged.

Tapered Waveguide

Right-click and choose .

In the window for , type Tapered Waveguide in the text field.

Locate the section. From the list, choose .

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


Name	Expression	Unit	Description
kx	ewbe.beta_1+(ewbe.beta_2-ewbe.beta_1)*x/d_taper	rad/m
phi	(kx+ewbe.beta_1)*x/2	rad

The wave vector component kx changes value linearly from the propagation constant for the input port to that for the output port. Thereby, the phase phi will depend quadratically on the propagation coordinate, x.

Output Waveguide

Right-click and choose .

In the window for , type Output Waveguide in the text field.

Locate the section. From the list, choose .

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


Name	Expression	Unit	Description
kx	ewbe.beta_2	rad/m
phi	kx(x-d_taper)+(ewbe.beta_1+ewbe.beta_2)d_taper/2	rad

Output PML

Right-click and choose .

In the window for , type Output PML in the text field.

Locate the section. From the list, choose .

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


Name	Expression	Unit	Description
phi	kx(pml1.x-d_taper-lam0)+(ewbe.beta_1+ewbe.beta_2)d_taper/2+kx*lam0	rad

Here again, it is important to use the complex scaled x coordinate from the PML, pml1.x, when defining the phase. This will give the proper attenuation of the field in the PML.

Let the setting for kx remain unchanged.

Mesh 1

Edge 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Distribution 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 50.

Distribution 2

Right-click and choose .

In the window for , locate the section.

From the list, choose . This is the leftmost boundary adjacent to the core domain.

Locate the section. In the text field, type 10.

Mapped 1

In the toolbar, click

In the window for , click to expand the section.

Select the check box. This makes sure the PML mesh, especially on the input side, is not skewed.

Distribution 1

Right-click and choose .

In the window for , locate the section.

From the list, choose . The selected entities are the top and bottom boundaries adjacent to the straight (non-tapered) waveguide domains.

Locate the section. In the text field, type 10.

Distribution 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type max(10,n_taper/20).

The expression above will allow for a few more layers in the propagation direction for the longest taper lengths.

Study 1

Parametric Sweep

In the toolbar, click

In the window for , locate the section.


Parameter name	Parameter value list	Parameter unit
n_taper (Taper length in vacuum wavelengths)

In the dialog box, type -1 in the text field.

In the text field, type 1.

In the text field, type 4.

From the list, choose – .