COMSOL 6.4 - Silicon on Insulator Optical Grating Coupler

Silicon on Insulator Optical Grating Coupler

Silicon photonics combine low-cost and high-performance functionalities into the state-of-the-art optical systems, while maintaining a compact footprint. The high packing density allows for the integration of different photonic components like lasers, waveguides, and detectors on a single chip. However, there is a challenge when interfacing the chip with external systems. This is because the large size mismatch between the on-chip and the off-chip optical modes (that is, a single-mode optical fiber) might cause problems with the coupling efficiency and the overall device footprint. One solution to this problem is the use of optical grating couplers, which offer compact footprints, flexible placement anywhere on the die, relaxed alignment and packaging, and straightforward wafer-level testing. These advantages are especially attractive in large-scale photonic integrated circuits.

This model analyzes the performance of an optical surface grating coupler on a silicon-on-insulator (SOI) platform operating at 1550 nm wavelength. The device consists of a one-dimensional periodic grating patterned on the top of a silicon layer. The coupling efficiency and the radiation losses for different incident angles of a free space laser beam, to couple into the guided mode of the waveguide, is evaluated to characterize the coupler.

Model Definition

Figure 1 shows the schematic of a grating coupler on a SOI platform. A one-dimensional grating is patterned on top of a silicon layer, along the x direction, and the silicon layer is supported by an SiO2 insulator substrate. A paraxial Gaussian beam is focused on the grating surface. The angle between the beam axis and the normal axis to the grating coupler is θ.

The fundamental operation of a grating coupler is based on the Bragg condition or the phase-matching condition. The gratings create a periodic variation of refractive index of the waveguide that enables to couple external light into the waveguide mode upon satisfying the phase-matching condition. For coupling between the incident light and the fundamental mode of the waveguide, the phase-matching condition is expressed as

(1)

In Equation 1, β is the propagation constant of the guided mode, k is the wavenumber in the incident medium, neff is the effective index of the guided mode, Λ is the periodicity of the gratings, and m is the grating diffraction order.

Figure 1: The modeled SOI grating coupler. The model considers a one-dimensional periodic grating patterned on top of a silicon layer that is supported by an SiO2 insulator.

To estimate the coupling efficiency, the power loss through the major channels should be considered. Firstly, some uncoupled power Ps will propagate downward and leak in to the insulator substrate. Secondly, some portion Pr will be reflected from the grating coupler surface back to the incident medium. Thirdly, some portion Pwl is coupled to the waveguide, but propagates in the opposite direction, especially when the incident beam axis is near the normal axis to the grating coupler surface. The final coupled power into the waveguide is expressed as

(2)

The performance of the grating coupler depends on the incident angle of the beam. This is because the incident angle determines how well the in-plane momentum of the incident wave matches the momentum of the guided mode.

Results and Discussion

Figure 2 shows the electric field norm of the total field for an incident angle θ = 12°. The incident beam is coupled as a fundamental mode into the waveguide through the grating coupler and propagates dominantly in the +x direction. Some of the incident waves are reflected back from the grating coupler while others are transmitted to the transmission side insulator domain.

Figure 2: Total electric field norm for incident angle θ = π/15.

Figure 3 and Figure 4 show the norm of the electric field of the fundamental guided mode at the cross sections of Port 1 and Port 2, respectively.

Figure 3: The norm of the electric mode field for Port 1.

Figure 4: The norm of the electric mode field for Port 2.

Figure 5 shows the calculated reflectance and transmittance for the Gaussian beam, as well as the power of the guided mode flowing through Port 1 and Port 2 versus the incident angles. Optimal coupling occurs for the incident angle θ = 12°, where the power of the fundamental mode flowing through Port 2 is at its maximum.

Figure 5: A plot of the reflectance, transmittance, and power outflow of the guided mode through Port 1 and Port 2 versus incident angles.

The radiation loss plot in Figure 6 shows that the loss is minimum for the incident angle

, where the coupling efficiency is maximum.

Figure 6: Radiation loss versus incident angles.

Notes About the COMSOL Implementation

The Electromagnetic Waves, Frequency Domain interface is used to perform full-wave simulation at the specified excitation wavelength of 1550 nm. Two Scattering Boundary Condition nodes and two Port nodes are used to handle the free space and the guided modes, and to analyze the coupling efficiency of the incident beam into both sides of the waveguide as well as the general reflection and the transmission characteristics.

The incident wave is an s-polarized free space paraxial Gaussian beam and is defined using a Scattering Boundary Condition (SBC) node. The Reference Point subnode of this SBC is used to ensure that the incident beam is focused on the center of the grating for all incident angles. Another Scattering Boundary Condition is used to absorb the wave transmitted through the waveguide in the transmission side. A numeric-type Port in combination with a Boundary Mode Analysis study step is used to compute the fundamental lowest-order mode of the waveguide. Since modes may exit at both sides of the waveguide, each side has its own numeric Port and associated Boundary Mode Analysis study steps. To ensure that any higher-order modes in the waveguide are not reflected by the Port conditions, they are backed by Perfectly Matched Layer domains with the slit condition being used. A Wavelength Domain study step with Auxiliary sweep is used to perform a sweep over the incident angle of the beam.

Wave_Optics_Module/Gratings_and_Metamaterials/grating_coupler

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

Create a list of parameters to define the wave properties.

Parameters: Wave Properties

In the window, under click .

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

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


Name	Expression	Value	Description
lda0	1.55[um]	1.55E-6 m	Vacuum wavelength
f0	c_const/lda0	1.9341E14 1/s	Frequency
E0	1[V/m]	1 V/m	Incoming wave field
alpha	30[deg]	0.5236 rad	Angle of incidence
beam_d	8[um]	8E-6 m	Beam waist diameter
P0	E0^2/Z0_const*beam_d/pi	6.7594E-9 W/m	Gaussian beam power

Parameters: Geometric Properties

Now, create a list of parameters that will be used to draw the geometry.

In the toolbar, click

and choose > .

In the window for , type Parameters: Geometric Properties in the text field.

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


Name	Expression	Value	Description
si_d	250[nm]	2.5E-7 m	Si layer thickness
a	600[nm]	6E-7 m	Grating constants
N	9	9	Number of ridges
ridge_d	si_d/2	1.25E-7 m	Ridge depth
ridge_w	a/2	3E-7 m	Ridge width
wg_top	lda0	1.55E-6 m	Waveguide top size
wg_bottom	lda0	1.55E-6 m	Waveguide bottom size
R	3*beam_d	2.4E-5 m	Simulation domain size
t_PML	2[um]	2E-6 m	Thickness PML