Basic Waveguide Properties
Lumerical Solutions, Inc.
Learning Objectives
1. Basic waveguide properties
 Propagation constant, loss
 TE vs TM
2. Waveguide cut off condition
3. Understanding dispersion
4. Evaluating loss
Pre-lesson preparation
 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
Basic waveguide properties
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
Questions
 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?
Waveguide cutoff conditions
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”
edit sweep
run sweep
Waveguide cutoff conditions
 Open and run waveguide.lsf in the “Script File Editor”
window to plot the sweep results in normalized units
Waveguide cutoff conditions
Questions
 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?
Waveguide cutoff conditions
Additional exercise
 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
Understanding dispersion
BASIC WAVEGUIDE PROPERTIES
Understanding dispersion
Material 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
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”
plot results
Understanding dispersion
 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
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
Evaluating loss
BASIC WAVEGUIDE PROPERTIES
Evaluating loss
Material 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

Evaluating loss
Radiative loss for bent waveguides
 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
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
Evaluating loss
Mode-mismatch loss for bent waveguides
 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”
TE power coupling
TM power coupling
0.999
0.800
Evaluating loss
Mode-mismatch loss for bent waveguides
 TE:
 TM:
Evaluating loss
Total loss for bent waveguides
 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
𝜋
= −2 × 10 log 𝑐𝑜𝑢𝑝𝑙𝑖𝑛𝑔 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 + 𝑟𝑎𝑑𝑖𝑢𝑠 ×
× 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑣𝑒 𝑙𝑜𝑠𝑠
2
 TE = 0.0087 dB + 0 dB = 0.0087 dB
 TM = 1.938 dB + 2.182 dB = 4.12 dB
Summary
 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
Acknowledgement
 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