Lumerical Solutions, Inc.

Basic Waveguide Properties

1. Basic waveguide properties Propagation constant, loss

TE vs TM

2. Waveguide cut off condition

3. Understanding dispersion

4. Evaluating loss

Learning Objectives

MODE Solutions introductory video:

https://www.lumerical.com/support/courses/mode_introductory_webinar_video.html

Getting started examples:

http://docs.lumerical.com/en/mode/getting_started.html

Pre-lesson preparation

BASIC WAVEGUIDE PROPERTIES

Basic waveguide properties

Open waveguide.lms

SOI strip waveguide

500nm x 220nm

Click

Brings up solver window

Wavelength = 1.55um

Click “Calculate modes”

Basic waveguide properties

MODE list provides basic waveguide properties

neff, loss, TE fraction

Mode profiles

Basic waveguide properties

Plot the different field components for the fundamental TE and TM mode.

How many modes does this waveguide support?

How do we know if a mode is bound?

Questions

Basic waveguide properties

BASIC WAVEGUIDE PROPERTIES

Waveguide cutoff conditions

In waveguide.lms, go to the “Optimizations and Sweeps”

Open the edit window for “waveguide_width”

• sweep will track neff of each mode as a function of the waveguide width

Click “run sweep”

Go to the “Result View” window, select all results and “Visualize”

Waveguide cutoff conditions

run sweepedit sweep

Open and run waveguide.lsf in the “Script File Editor” window to plot the sweep results in normalized units

Waveguide cutoff conditions

At what waveguide width does each mode cutoff?

When does the waveguide become single mode?

If we want the waveguide to operate with a single TE mode, what waveguide width should we use?

Questions

Waveguide cutoff conditions

Instead of running the parameter sweep, run waveguide2.lsf in the script file edtor

This script will track each mode

individually (instead of only tracking

the largest effective indices)

Notice mode crossing at 0.65um

Look at the polarization for the modes right before and after the mode crossing. Verify that the mode with the 2nd highest neff changes from TE to TM

Additional exercise

Waveguide cutoff conditions

BASIC WAVEGUIDE PROPERTIES

Understanding dispersion

Refractive index of material is dependent on wavelength

Open waveguide.lms, click on in the tool bar

Click on “Fit and plot” to see

material dispersion for silicon

Squares show actual Palik data

Line shows what is actually

used in simulation

Material dispersion

Understanding dispersion

Calculate modes in Eigenmode solver

Go to “Frequency analysis” tab

Select mode(s) to track

Ex. fundamental TE

Set wavelength range

Click “frequency sweep”

Understanding dispersion

plot results

Modal dispersion: neff()

Includes both material and

waveguide dispersion

Modal Group velocity: vg = d/d

Group velocity dispersion: D = d(1/vg)/d

Understanding dispersion

Understanding dispersion

Additional exercise

Remove the effect of material dispersion by changing the waveguide material from silicon to dielectric

Re-run the frequency sweep. Does the material dispersion of silicon have a strong effect on the overall modal dispersion?

Change the waveguide width, re-run the frequency sweep and observe how the dispersion is affected

BASIC WAVEGUIDE PROPERTIES

Evaluating loss

Open waveguide.lms, click on in the tool bar

Change wavelength range to go from 0.2um to 1um

Click on “Fit and plot” to see material dispersion for silicon Im(index) > 0 indicates material loss

Silicon highly lossy at wavelengths < 0.5um

Loss ~ 0 for wavelengths > 1um

Material loss

Evaluating loss

Open waveguide_bend.lms, calculate modes Record loss for the fundamental TE and TM mode

Right-click on each and select “add selected modes to global deck”

Select “bent waveguide”, set bend radius to 5um and re-calculate

Compare radiative loss between the straight and bent waveguide

Radiative loss for bent waveguides

Evaluating loss

Straight waveguide Bent waveguide

TE ~0 dB/cm* ~0 dB/cm*

TM ~0 dB/cm 2778 dB/cm

* ~0 since imag(neff) ~ 10e-6 ~ numerical error

Go to the “Overlap analysis” tab

Select the fundamental TE mode in the mode list

Select “global_mode1” in the DECK

Click “Calculate”• Power coupling gives the amount of power that can couple from one mode

to another (ie. coupling efficiency)

Repeat for the fundamental TM mode and “global_mode2”

Mode-mismatch loss for bent waveguides

Evaluating loss

TE power coupling TM power coupling

0.999 0.800

TE:

TM:

Mode-mismatch loss for bent waveguides

Evaluating loss

Calculate total loss in a 90 degree bend

Radiative loss

Overlap loss

Total loss for a 90 degree bend:

𝑙𝑜𝑠𝑠 𝑓𝑟𝑜𝑚 2 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 + 𝑙𝑜𝑠𝑠 𝑓𝑟𝑜𝑚 90 𝑑𝑒𝑔𝑟𝑒𝑒 𝑏𝑒𝑛𝑑

= −2 × 10 log 𝑐𝑜𝑢𝑝𝑙𝑖𝑛𝑔 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 + 𝑟𝑎𝑑𝑖𝑢𝑠 ×𝜋

2× 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑣𝑒 𝑙𝑜𝑠𝑠

TE = 0.0087 dB + 0 dB = 0.0087 dB

TM = 1.938 dB + 2.182 dB = 4.12 dB

Total loss for bent waveguides

Evaluating loss

In this lesson plan, we covered:

1. Basic waveguide properties • Propagation constant, loss

• TE vs TM

2. Waveguide cut off condition

3. Understanding dispersion

4. Evaluating loss

Summary

We would like to thank Professor Lukas Chrostowski from the University of British Columbia (Vancouver, Canada) for contributing to the contents of this module

http://www.ece.ubc.ca/faculty/lukas-chrostowski

Acknowledgement