comsol ® design tool: simulations of optical components

||Institute of Electromagnetic Fields (IEF)Yannik Horst – [email protected]

Shadi Nashashibi – [email protected] Schwanninger – [email protected]

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COMSOL ® Design Tool:Simulations of Optical ComponentsWeek 6: Waveguides and Propagation 3 – S ParametersShadi Nashashibi, Raphael Schwanninger & Yannik Horst



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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



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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



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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



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Revision Wave PropagationOut-of-plane

Mode analysis

In-plane

Propagation



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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



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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



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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



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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



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Revision Wave Propagation: Optical Fiber

HE11 TE01 TM01

LP11LP01

E-Field

Intensity distribution of E𝑥𝑥



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S-parameters Theory

Content



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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



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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



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How to characterize our photonics system as whole? S-matrix Unitary in lossless systems Diagonal 𝑆𝑆𝑖𝑖𝑖𝑖 terms are complex valued amplitude reflection coefficients


Superposition:

𝑏𝑏𝑖𝑖 = �𝑗𝑗=1..𝑖𝑖

𝑆𝑆𝑖𝑖𝑗𝑗𝑎𝑎𝑗𝑗

𝑏𝑏1𝑏𝑏2⋮𝑏𝑏𝑖𝑖

=𝑆𝑆11 … 𝑆𝑆1𝑖𝑖⋮ ⋱ ⋮𝑆𝑆𝑖𝑖1 … 𝑆𝑆𝑖𝑖𝑖𝑖

𝑎𝑎1𝑎𝑎2⋮𝑎𝑎𝑖𝑖



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Two input/output ports:

𝑏𝑏1𝑏𝑏2

= 𝑆𝑆11 𝑆𝑆12𝑆𝑆21 𝑆𝑆22

𝑎𝑎1𝑎𝑎2

𝑎𝑎2

𝑏𝑏1

𝑎𝑎1

𝑏𝑏2

T

𝑻𝑻 =𝑹𝑹 =

R



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𝑏𝑏1𝑏𝑏2


𝑎𝑎1𝑎𝑎2

𝑎𝑎2

𝑏𝑏1

𝑎𝑎1

𝑏𝑏2

T

R𝑻𝑻 = 𝑆𝑆21 2

𝑹𝑹 = 𝑆𝑆11 2



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Can COMSOL help? S-matrix Luckily, COMSOL has built-in calculation of these!

S-Parameters for Photonics: COMSOL


𝑏𝑏1𝑏𝑏2


𝑎𝑎1𝑎𝑎2

𝑎𝑎2

𝑏𝑏1

𝑎𝑎1

𝑏𝑏2

T

R𝑻𝑻 = 𝑆𝑆21 2

𝑹𝑹 = 𝑆𝑆11 2

These are the ports we define in COMSOL!

COMSOL calculates this matrix!



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COMSOL examples Taper Waveguide bend

Content



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“Tapering” Sometimes, photonics design requires that waveguide also changes its width… Example is Multi – Mode – Interference coupler (one of the projects)

COMSOL Examples: Taper



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Tasks: Plot transmission curve for different taper lengths (Note: you can add trapezoid or polygon in COMSOL) Ltaper greater then 100 nm…


clad: SiO2

core: Si

wg1_widthLtaper

wg_length

wg_length

wg2_width

domain_y

domain_x



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Waveguide bending

Tapers

5 mm



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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



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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



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Projects Outline Short overview projects

Content



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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



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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



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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



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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



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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



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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

comsol ® design tool: simulations of optical components

Documents