COMSOL 6.4 - Modeling a Scatterer Near an Optical Waveguide

Modeling a Scatterer Near an Optical Waveguide

The dielectric slab waveguide is one of the conceptual building blocks in photonic structure design. Although most real structures are more complex than just a two-dimensional dielectric slab, a two-dimensional model permits to simplify the analysis. This model simulates the case of a small lossy scatterer in the proximity of an optical waveguide, shows how it interacts with the fields, and calculates reflection and transmission along the waveguide, as well as losses and scattering.

Model Definition

The schematic of the structure is shown in Figure 1. A dielectric slab waveguide has a small circular metallic object located nearby. The scatterer interacts with the fields, thus leading to some losses within the material, and causing scattering of light into all directions. In the absence of the nearby object, this example would reduce to a perfect dielectric slab waveguide (see the Application Library model Dielectric Slab Waveguide).

Figure 1: Schematic of a 2D dielectric slab waveguide with a lossy material in proximity to the core.

Imagine a waveguide that is wide enough to support multiple modes. For the sake of simplicity, this model restricts the analysis to just the example of the electric field polarized out of the modeling plane. Assume that either the electric or magnetic field is polarized purely out of plane and that there is no coupling between these two as long as all materials are isotropic.

Figure 2: The incident light guided along the waveguide can be reflected, transmitted, absorbed, and scattered.

The reflection and transmission along the waveguide, as well as absorption and scattering mechanisms are shown in Figure 2. Here, light propagates along the waveguide toward the scatterer (from left to right), and this incident light is the first or fundamental mode. Due to the presence of the scatterer, some fraction of the incident light will be

transmitted forward and of the same fundamental mode,

transmitted forward, but converted into the second mode,

reflected backward and of the same fundamental mode,

reflected backward, and converted into the second mode,

absorbed by the lossy metallic inclusion, and

scattered into other directions.

Computation of transmission into the four possible guided modes of the waveguide (items 1–6) requires four different numerical ports into the model, two on each side. As already discussed in Ref. 1, it is possible to introduce multiple interior slit port boundary conditions at boundaries within the modeling space. Modeling the absorption into the lossy material simply involves integrating the loss within the metallic object.

In summary, this model simulates a dielectric slab waveguide with a lossy scatterer nearby to analyze the guided light, reflection, transmission, absorption, and scattering mechanisms in 2D using the Electromagnetic Waves, Frequency Domain (ewfd) interface. Numeric ports are used and perfectly matched layers are employed to absorb most of the outgoing radiation. A Frequency Domain and four Boundary Mode Analysis study steps are applied to solve the domain fields.

Results and Discussion

Figure 3 shows the electric field norm from the simulation. The numeric port boundary condition at the left excites a fundamental mode that propagates in the tangential direction.

Figure 3: The Electric field norm.

Figure 4 shows the total resistive losses within the scatterer. Here, the loss distribution is not uniform within the material. Maximum losses are observed at the bottom part of the scatterer which is closer to the waveguide.

Figure 4: Resistive losses in the lossy scatterer.

For further details, see the blog post in Ref. 2.

References

1. Walter Frei, “Modeling Waveguides that Support Multiple Modes,” COMSOL Blog, Aug. 12, 2020; www.comsol.com/blogs/modeling-waveguides-that-support-multiple-modes/.

2. Walter Frei, “Modeling a Scatterer Near an Optical Waveguide,” COMSOL Blog, Aug. 25, 2020; www.comsol.com/blogs/modeling-a-scatterer-near-an-optical-waveguide/.

Wave_Optics_Module/Waveguides/waveguide_with_scatterer

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
lda0	1550[nm]	1.55E-6 m	Wavelength
n_core	1.5	1.5	Refractive index, core
n_cladding	1	1	Refractive index, cladding
h_core	1.25[um]	1.25E-6 m	Thickness, core, section A
h_cladding	8[um]	8E-6 m	Thickness, cladding
L_core	8[um]	8E-6 m	Core length
f0	c_const/lda0	1.9341E14 1/s	Frequency
t_PML	0.5[um]	5E-7 m	PML thickness
Pin	1[W/m]	1 W/m	Power in

Geometry 1

The geometry consists of a slab waveguide, with a scatterer on top, embedded in a cladding material.

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type L_core.

In the text field, type h_core.

Locate the section. From the list, choose .

Click

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type L_core.

In the text field, type h_cladding.

Locate the section. From the list, choose .

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


Layer name	Thickness (µm)
Layer 1	t_PML

Select the checkbox.

Click

Click the

button in the toolbar.

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type h_core/10.

Locate the section. In the text field, type h_core*0.65.

Click

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_cladding	1	Refractive index

Core

Right-click and choose .

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

Select Domains 3, 8, and 13 only.

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

Add Material

Pick gold as the lossy scatterer from the Optical material library.

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > > > > .

Right-click and choose .

In the toolbar, click

to close the window.

Materials

Au (Gold) (Johnson and Christy 1972: n,k 0.188-1.937 um) (mat3)

Select Domain 16 only.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1–6 and 10–15 only.

Electromagnetic Waves, Frequency Domain (ewfd)

Define the incident port.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Port 1

In the toolbar, click

and choose .

Select Boundaries 14, 16, and 18 only.

In the window for , locate the section.

From the list, choose .

In the Pin text field, type Pin.

Select the checkbox.

Click .

Port 2

Define the transmission port for the first mode.

In the toolbar, click

and choose .

Select Boundaries 25, 27, and 29 only.

In the window for , locate the section.

From the list, choose .

Select the checkbox.

Port 3

Right-click and choose .

Define the port to capture the first and second reflected modes.

In the window for , locate the section.

Click

Select Boundaries 14, 16, and 18 only.

Locate the section. Click .

Port 4

Right-click and choose .

Define the transmission port for the second mode.

In the window for , locate the section.

Click

Select Boundaries 25, 27, and 29 only.

Locate the section. Click . These boundaries are same as Port 2.

Mesh 1

In the window, under click .

In the window for , locate the section.

Select the checkbox.

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type f0.

Step 2: Boundary Mode Analysis

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type f0.

In the text field, type n_core.

Step 3: Boundary Mode Analysis 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 2.

Step 4: Boundary Mode Analysis 2

Right-click and choose .

In the window for , locate the section.

In the text field, type 3.

Select the checkbox. In the associated text field, type 2.

Step 5: Boundary Mode Analysis 3

Right-click and choose .

In the window for , locate the section.

In the text field, type 4.

Step 1: Frequency Domain

In the window, click .

Drag and drop below .

In the toolbar, click

Results

Electric Field (ewfd)

In the toolbar, click

Click the

button in the toolbar.

Electric Mode Field, Port 1 (ewfd)

Plot the first mode at port 1.

In the window, click .

Electric Mode Field, Port 2 (ewfd)

Plot the first mode at port 2.

In the window, click .

Electric Mode Field, Port 3 (ewfd)

Plot the second mode at port 1.

In the window, click .

Electric Mode Field, Port 4 (ewfd)

Plot the second mode at port 2.

In the window, click .

Electric Field (ewfd)

Plot the resistive losses in the gold scatterer.

Losses

In the window, right-click and choose .

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

Click to expand the section. Click

Select Domain 16 only.

Surface 1

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type ewfd.Qrh.

Locate the section. From the list, choose .

Click the

button in the toolbar.

Reflectance, Transmittance, and Loss (ewfd)

As the total absorptance variable, ewfd.Atotal, only includes the loss due to absorption in the Gold domain, add a variable accounting for the loss due to power flowing into the top and bottom PML domains and for radiation not matching the port mode fields, ewfd.Lsca.

In the window, under click .

In the window for , type Reflectance, Transmittance, and Loss (ewfd) in the text field.

Reflectance, Transmittance, and Loss (ewfd)

In the window, expand the node, then click .

In the window for , type Reflectance, Transmittance, and Loss (ewfd) in the text field.

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

In the toolbar, click

Loss Calculation

Also add a separate node to separately calculate the absorptance, scattering, and total loss.

In the toolbar, click

In the window for , type Loss Calculation in the text field.

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
ewfd.Atotal+ewfd.Lsca	1	Total losses

Click