||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 1
COMSOL ® Design Tool:Simulations of Optical ComponentsWeek 6: Waveguides and Propagation 3 – S ParametersShadi Nashashibi, Raphael Schwanninger & Yannik Horst
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 2
Revision wave propagation Waveguide Confinement Modes
S-parameters Theory
COMSOL examples Taper Waveguide bend
Projects Outline Short overview projects
Content
Part of the Theory Recording
Part of the Tutorial Recording
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 3
Dielectric slab waveguide What we want Propagation in core Decay (exponential) in sub/superstrate High confinement
What we don’t want Propagation in sub/superstrate Low confinement (except in certain application - e.g. couplers)
Revision Wave Propagation
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 4
Confinement
Revision Wave Propagation
𝑛𝑛cladding
𝑛𝑛cladding
𝑛𝑛core
𝑦𝑦
𝑥𝑥
Strongly confinedWave mostly in the core
𝐸𝐸𝑧𝑧 𝑦𝑦
𝑛𝑛cladding
𝑛𝑛cladding
𝑛𝑛core 𝐸𝐸𝑧𝑧 𝑦𝑦
𝑦𝑦
𝑥𝑥
Weakly confinedWave leaks into cladding
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 5
Revision Wave PropagationOut-of-plane
Mode analysis
In-plane
Propagation
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 6
We have 1W at the input of our waveguide It’s straight We have lossless material
Now, the output 𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜 will bea) 0.333… Wb) 0.5 Wc) 1 Wd) Nah, who cares!
Revision Wave Propagation: Quiz
𝑃𝑃𝑖𝑖𝑖𝑖= 1W
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 7
Multimode silicon ridge waveguide
Revision Wave Propagation: Ridge Waveguide
Given:• 𝜆𝜆 = 1550 nm• 𝑛𝑛Si = 3.47
• SiHeight = 220 nm
• SiWidth = 350,1000 nm
Output:• E-field (guided modes)• Effective refractive index 𝑛𝑛eff
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 8
Single-mode ridge Solution 1: neff = 2.2719
Solution 2: neff = 1.5422
Multi-mode ridge (increased geometry) Fundamental mode
Higher order mode
Revision Wave Propagation: Ridge Waveguide𝑛𝑛Si = 3.4757𝑛𝑛SiO2 = 1.44𝑛𝑛air = 1
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 9
Revision Wave Propagation: Optical Fiber
2effn n<For a confined mode, no energy flow in the radial direction:
1 2effn n n< <Wave cannot be evanescent in the core region:
n2 n1
• Core• r = 8um• n = 1.4457
• Cladding• r = 40um• n = 1.4378
𝑚𝑚 = 1𝑛𝑛 = 1
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 10
Revision Wave Propagation: Optical Fiber
HE11 TE01 TM01
LP11LP01
E-Field
Intensity distribution of E𝑥𝑥
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 11
S-parameters Theory
Content
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 12
What happens with systems for multiple inputs and multiple outputs (MIMO)? How can it be described mathematically?
We use the S-matrix
S-Parameters: Motivation
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 13
How to characterize our photonics system as whole? Scattering matrix (so called S-matrix)
S-Parameters for Photonics
Superposition:
𝑏𝑏𝑖𝑖 = �𝑗𝑗=1..𝑖𝑖
𝑆𝑆𝑖𝑖𝑗𝑗𝑎𝑎𝑗𝑗
𝑏𝑏1𝑏𝑏2⋮𝑏𝑏𝑖𝑖
=𝑆𝑆11 … 𝑆𝑆1𝑖𝑖⋮ ⋱ ⋮𝑆𝑆𝑖𝑖1 … 𝑆𝑆𝑖𝑖𝑖𝑖
𝑎𝑎1𝑎𝑎2⋮𝑎𝑎𝑖𝑖
inputoutput
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 14
How to characterize our photonics system as whole? S-matrix Unitary in lossless systems Diagonal 𝑆𝑆𝑖𝑖𝑖𝑖 terms are complex valued amplitude reflection coefficients
S-Parameters for Photonics
Superposition:
𝑏𝑏𝑖𝑖 = �𝑗𝑗=1..𝑖𝑖
𝑆𝑆𝑖𝑖𝑗𝑗𝑎𝑎𝑗𝑗
𝑏𝑏1𝑏𝑏2⋮𝑏𝑏𝑖𝑖
=𝑆𝑆11 … 𝑆𝑆1𝑖𝑖⋮ ⋱ ⋮𝑆𝑆𝑖𝑖1 … 𝑆𝑆𝑖𝑖𝑖𝑖
𝑎𝑎1𝑎𝑎2⋮𝑎𝑎𝑖𝑖
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 15
How to characterize our photonics system as whole? S-matrix Unitary in lossless systems Diagonal 𝑆𝑆𝑖𝑖𝑖𝑖 terms are complex valued amplitude reflection coefficients
S-Parameters for Photonics
Two input/output ports:
𝑏𝑏1𝑏𝑏2
= 𝑆𝑆11 𝑆𝑆12𝑆𝑆21 𝑆𝑆22
𝑎𝑎1𝑎𝑎2
𝑎𝑎2
𝑏𝑏1
𝑎𝑎1
𝑏𝑏2
T
𝑻𝑻 =𝑹𝑹 =
R
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 16
How to characterize our photonics system as whole? S-matrix Unitary in lossless systems Diagonal 𝑆𝑆𝑖𝑖𝑖𝑖 terms are complex valued amplitude reflection coefficients
S-Parameters for Photonics
Two input/output ports:
𝑏𝑏1𝑏𝑏2
= 𝑆𝑆11 𝑆𝑆12𝑆𝑆21 𝑆𝑆22
𝑎𝑎1𝑎𝑎2
𝑎𝑎2
𝑏𝑏1
𝑎𝑎1
𝑏𝑏2
T
R𝑻𝑻 = 𝑆𝑆21 2
𝑹𝑹 = 𝑆𝑆11 2
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 17
Can COMSOL help? S-matrix Luckily, COMSOL has built-in calculation of these!
S-Parameters for Photonics: COMSOL
Two input/output ports:
𝑏𝑏1𝑏𝑏2
= 𝑆𝑆11 𝑆𝑆12𝑆𝑆21 𝑆𝑆22
𝑎𝑎1𝑎𝑎2
𝑎𝑎2
𝑏𝑏1
𝑎𝑎1
𝑏𝑏2
T
R𝑻𝑻 = 𝑆𝑆21 2
𝑹𝑹 = 𝑆𝑆11 2
These are the ports we define in COMSOL!
COMSOL calculates this matrix!
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 18
COMSOL examples Taper Waveguide bend
Content
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 20
“Tapering” Sometimes, photonics design requires that waveguide also changes its width… Example is Multi – Mode – Interference coupler (one of the projects)
COMSOL Examples: Taper
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 21
Tasks: Plot transmission curve for different taper lengths (Note: you can add trapezoid or polygon in COMSOL) Ltaper greater then 100 nm…
COMSOL Examples: Taper
clad: SiO2
core: Si
wg1_widthLtaper
wg_length
wg_length
wg2_width
domain_y
domain_x
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 22
COMSOL Examples: Taper
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 23
Waveguide bending
Tapers
5 mm
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 24
S-Parameters for Photonics: COMSOL Waveguide Bend
Port 1
Port
2
Bending radiusbend_r
SiO2
Si
WG bend with a circular segment with
a radius bend_r
bend_r goes to the center of the WG
We collect the power at port 2
We calculate the transmission
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 25
COMSOL Examples: Waveguide Bend
Goals:1. Get S21(dB) parameter for 1 simulation,
check correct mode excitation2. Parametric sweep bend radius bend_r3. Parametric sweep lam0 = 1450:?:1550 nm
for bend_r = [1.5,10] um
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 28
Projects Outline Short overview projects
Content
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 29
Date ContentOct 26th Short description of all projectsNov 2nd Detailed project description, grouping, starting on the projectsNov 9th Individual work on projectsNov 16th Individual work on projectsNov 23rd Individual work on projects / How to do presentationsNov 30th Individual work on projectsDec 7th Start preparing your report / presentationsDec 14th Presentations
Projects – Outline
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 30
Directional coupler 2 students Goal Fix power ratio (to 50/50 and 90/10) Minimize bending losses
Ring resonator 2 - 3 students Goal Find the resonant behavior at 1550 nm Maximize Q factor and minimize losses Cascaded ring resonators
Projects Overview
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 31
Delay interferometer 3 students Goal Find delay line for a 𝜋𝜋 phase shift
Bragg mirror 2 - 3 students Goal Incoming wave should be 99% reflected
Projects Overview
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 32
Multimode interferometer 2 - 3 students Goal Find geometry such that output ratio is
50/50 and also 10/90
Waveguide to waveguide coupling 2 students Goal Design the taper as shown below for
defined power transmission
Projects Overview
Silicon Dioxide
Silicon Nitride
Silicongap
taper length
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 33
Waveguide Crossings 2 - 3 students Goal Minimize transmission losses
Projects Overview Waveguide to Fiber Coupling 3 students Goal Maximize transmission
Air (𝑛𝑛 = 1)
Silicon dioxide (𝑛𝑛 = 1.44)Silicon (𝑛𝑛 = 3.4777)
Core
Clad
Clad
taper length
dielectric length
dielectricw
idthwgwidth co
re
diam
eter fiber
diameter
gap
||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]
Shadi Nashashibi – [email protected] Schwanninger – [email protected]
26.10.2020 34
Your own ideas
They are WELCOME!
Please put together your ideas and make a small sketch by next week and let’s have a look together
Projects Overview