Optical Applications using CST MICROWAVE … University of Technology Institute of Optical and Electronic Materials, Eich Optical Applications using CST MICROWAVE STUDIO® Micro rings

Hamburg University of Technology Institute of Optical and Electronic Materials, Eich

Optical Applications using

CST MICROWAVE STUDIO®

Micro rings & slow light photonic crystals

High Q cavities in SOI & taper design

Photonic crystals in low index materials








Ring like structure provides resonant behaviour

SILICON-ON-INSULATOR MICRO RING RESONATOR

Input

Output

resonance peaks

At resonance :

Energy is stored in the ring

Signal is suppressed in the through port

Model volume: 10 million meshcells

Simulation time: 30 hours

(2 x Xeon 5130 dual core)

mλnr2π L effeff

r

198 199 200 201 202-40

-30

-20

-10

0

Input

Output

Tra

nsm

issio

n [

dB

]

Frequency [THz]


Silicon-On-Insulator (SOI) enables high scalability

MATERIAL PARAMETERS

SOI layer

Buried oxide (BOX) layer as insulator

Silicon handle wafer for mechanical stability

SiO2

Si

Si

SOI substrate:

SOI is widely used in CMOS:

• relatively inexpensive

• high quality available

SOI exhibits a high refractive index contrast:

•

• strong mode confinement

• bending radii below 5 µm possible

• propagation losses below 5 dB/cm

1.45n;3.5n2SiOSi

Default optical SOI Substrate:

• SOI layer thickness: 220 nm

• BOX layer thickness: 2 µm

• Silicon handle wafer: ca. 700 µm


SOI strip waveguides modes possess evanescent

componentsTYPICAL MODE PROFILE

TE like mode TM like mode

• dispersive mode

• relatively srong evanescent field

• open boundaries not PEC

• inhomogeneous condition at

waveguide port

SiO2

low index cladding

Si

SiO2

low index cladding

Si

xE

yE


Race track shape allows more efficient design of coupling

RACE TRACK MODEL EXAMPLE

Lc

r

dcgap

Radius r has influence on:

• effective coupling length Lc

• losses due to both bending and

coupling

Introducing straight part of length

Lc helps tailoring the coupling

condition

r = 10 µm

gap = 400 nm

Lc = 1 – 10 µm


Nanophotonic models may need non standard CST MWS

building blocksMODEL EVOLUTION

• 90° curve model

• 10 µm radius

• default number of

segments

• partly trimed cylinder

More than 3 million meshcells and

more than 1 hour simulation time on a Pentium 4 (3 GHz) CPU

Input

Output

• 1500 segments per

360° turn

• E-field pattern is as

expected


Investigation of coupling demands large models

MODEL FOR DIRECTIONAL COUPLING

50 µm

• almost 30 million meshcells

• 16 hours simulation time

• distributed computing on a 2 x dual core XEON 5130 (8 GB RAM)

Model design:

• 90° bend necessary for absorption reasons (third port)

• field monitors needed


Intensity modulation employs a shift in effective refractive

indexMODULATION EXAMPLE AND PARAMETER

m

nL eff

res

)(

on

res

off

res

• signal wavelength equals

• no shift (red line): full intensity output

• with shift (black line): strong intensity

attenuation due to resonance

off

res

1,485 1,488 1,491 1,494 1,497 1,500 1,503 1,506 1,509 1,512 1,515

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Tra

nsm

issio

n [d

B]

Wavelength [µm]

neff1

neff2


Two different conditions have been considered

MODELS FOR OPTIMIZING

SiO2

polymer

SiO2

polymer

active zone

silicon strip waveguide

silicon slot waveguide

• quasi TE mode

• both silicon rails act as electrode

• strong evanescent field

enhancement in slot

• quasi TM mode

• silicon strip acts as lower electrode

• upper electrode on top of polymer

optE

optE

External n is transferred

to neff via evanescent field


CST MWS “2D Port Mode Calculation” has been used

MODEL FOR 2D CALCULATION

SiO2

Polymer

Si

active zone

model

length

• models are very short (500 nm)

• length limitation due to port definition

• parameter sweep over geometry and

dielectric constant in actice zone

• user defined result watch (e.g. beta)


CST MWS 3D Eigenmode Solver is used for photonic

band calculationsMODELS FOR BANDDIAGRAM CALCULATION

3D Eigenmode solver:

• single unit cell models

• parameter sweep over phase shift

(defines k) at periodic boundary

• user defined result watch

• quasi 2D model is one mesh cell

in height

quasi 2D model

3D model


Certain photonic crystal (PhC) line defects exhibit “slow

light” regionBANDDIAGRAM AND FIELD DISTRIBUTION

dK

Kdvg

)(

a30,7W0.7a3W1

XZ

a

a aH


W0.7 waveguide allows low group velocity over wide

spectral rangeW0.7 GROUP VELOCITY SPECTRUM

ff 3105

band width in W0.7

g

gn

v1

21

21

gg

gg

nn

nnr

Benefits of slow light:

• pulses are delayed: delay lines

become shorter

• power increases since pulses

become compressed:

- sensors more effective

- nonlinear effects easier available

causes high coupling losses due to reflection at interfaces to

standard waveguides

coupling design is an important issue


Index distribution at the end of PhC influences coupling

W0.7

0

1

W0.7

CUTTING FACTOR AND SURFACE MODE

X

Z

2,07,0

X

Z

H-field

distribution of a

surface mode

at

• defines position of the cut through PhC lattice constant at

the strip to PhC defect waveguide interface

• different cuts lead to different refractive index distributions

along the interface (x)

• confined modes (evanescent in z) also along the interface

in x direction

and


XZ

Y

Quasi 2D models under investigation have symmetric

conditions at the input and output port

MODEL FOR COUPLING OPTIMIZATION

large models for transient simulations:

• to ensure settled mode transformation

• symmetric conditions for the ports

• reasonable TE mode is selected via magnetic boundaries in y direction and

electric field symmetry along z








HighQ photonic crystal (PhC) nanocavity has potential

application for slowing light

STATE OF THE ART OF PHC NANOCAVITY

1. Experimental loaded Q is 1.2 million 1

2. FIT TD method is used to simulate high Q cavity, with theoretical intrinsic Q

of 7x107 obtained

1. Notomi, etc., Nature Photonics, 2007


CST MWS can be applied to simulate loaded high Q structures

SIMULATION GEOMETRY

probe

Tools used in this simulation:

• Probes: detect resonant frequency of the cavity

• Monitor: record the coupling mechanism from PhC waveguide to nanocavity

X,Y,Z: open boundary condition

symmetry plane: XZ magnetic


Q calculation energy decay method is reliable

SIMULATION RESULTS FREQUENCY VS ENERGY DATA

Experiment: Q = 1.2*106

Simulation: Q = 2.2*106 (energy decay)

1 mio mesh cells

df/f: 6*10-3

simulation time ≈ 74 h

simulated time ≈ 163 ps

191,0 191,2 191,4 191,6 191,8 192,00,0

5,0x107

1,0x108

1,5x108

2,0x108

2,5x108

3,0x108

3,5x108

4,0x108

191,60445

Ma

gnitud

e (

V/m

)

Frequency (THz)

QFreq

=43000

After AR-filter:

QAR

=90000

0 20 40 60 80 100 120 140 160-80

-60

-40

-20

0

En

erg

y (

dB

)

Time (ps)

QEnergy

=2.20X106


Here is amplitude decay rate, where E(t)=E0*exp(-t/ )

Energy decay per unit (here ps) t1-t2=1ps:

Q factor can be easily calculated from energy decay rateDERIVATION OF Q FROM ENERGY DECAY

)/2exp()/2exp(

)/2exp(

)(

)(

20

10

2

1

tW

tW

tW

tW

)10ln(

)/2(10)]/2lg[exp(10

ps

dB

dt

dW

10

)10ln(/2

ps

dB

dt

dW

][)10ln(

100

psdB

dtdW

Q

dtdW

WQ 0

/2

/

0

0

dtQ

WdW

)/2exp(0 tWW

dtWdW )/2(

0 2 4 6 8 10 12-80

-60

-40

-20

0

Ene

rgy (

dB

)

Time (ps)


Simulation results of low Q PhC nanocavity using CST

MWS are reasonableSIMULATION RESULTS COMPARED WITH EXPERIMENT

7 layers

outs

ide t

he c

avity

Experimental loaded Q ≈ 2600 @ λ≈1567nm

Simulated intrinsic Q ≈ 4100 @ λ= 1563.4nm

x

z


symmetry plane:

• XZ magnetic

• YZ electric

• XY magnetic

0 2 4 6 8 10 12

-100

-80

-60

-40

-20

0

Energ

y (

dB

)

Time (ps)

H7A00 n=3.4

Simulation: Q=4100

Experiment: Q=2600


f=152.706THz

Q=2.84x108

f=152.715THz

Q=9.79x106

Quasi 2D simulation can be used to find out optimal

coupling from PhC waveguide to nanocavity

EXAMPLES AND RESULTS

70 000 mesh cells

4h

Boundary condition:

X, Z: open

Y: magnetic

x

z

152,2 152,4 152,6 152,8 153,0 153,2 153,40,0

2,0x107

4,0x107

6,0x107

8,0x107

3,7x108

3,8x108

3,8x108

Am

plit

ud

e

Frequency (THz)

s0 probe @ inside cavity

s0 probe @ output

s5 probe @ inside cavity

s5 probe @ output


Polymer cladded inverse taper structure optimizes fiber

to chip couplingSIMULATION STRUCTURE

Si taper tip

8million mesh cells

df 30THz

18h (to 4.7ps)polymer

waveguide

air

z x

y


symmetry plane: YZ electricSi taper end


Polymer waveguide covering taper is used to increase

the tolerance of cleavingSIMULATION RESULTS

1,8x1014

1,9x1014

1,9x1014

2,0x1014

2,0x1014

2,0x1014

2,1x1014

-1,4

-1,3

-1,2

-1,1

-1,0

-0,9

-0,8

-0,7

-0,6

-0,5

Frequency (Hz)

Tra

nsm

issio

n (

dB

)

dis 10µm

dis 30µm

1,8x1014

1,9x1014

1,9x1014

2,0x1014

2,0x1014

2,0x1014

2,1x1014

-60

-50

-40

-30

-20

-10

Reflectio

n (

dB

)

Frequency (Hz)

dis 10µm

dis 30µm


Transmission properties are stable above 2 µm taper

length

TRANSMISSION AND REFLECTION

taper length

silicaair


symmetry plane: YZ electric2µm: 58000 mesh cells, (10 min)

50µm: 520000 mesh cells, (5 h)

z x

y

1,8x1014

1,9x1014

1,9x1014

2,0x1014

2,0x1014

2,0x1014

2,1x1014

-0,68

-0,66

-0,64

-0,62

-0,60

-0,58

-0,56

-0,54

-0,52

Tra

nsm

issio

n th

rou

gh

po

rt 2

(d

B)

Frequency (Hz)

2 m

8 m

50 m


Absorbing unconsidered mode fields for inhomogeneous

ports better applies for taper structure

COMPARISON BETWEEN ABSORB AND NO ABSORB

2 µm

silicaair

1,8x1014

1,9x1014

1,9x1014

2,0x1014

2,0x1014

2,0x1014

2,1x1014

-0,6

-0,4

-0,2

0,0

0,2

0,4

absorb unconsidered mode fileds

option deselected

Tra

nsm

issio

n (

dB

)

Frequency (Hz)

1,8x1014

1,9x1014

1,9x1014

2,0x1014

2,0x1014

2,0x1014

2,1x1014

-45

-42

-39

-36

-33

-30

-27

-24

-21

-18

-15

-12

Reflection (

dB

)

Frequency (Hz)

absorb unconsidered mode fileds

option deselected


No absorbing unconsidered mode fields for

inhomogeneous ports better applies for PhC structureCOMPARISON BETWEEN ABSORB AND NO ABSORB

0 20 40 60 80 100 120 140 160-160

-140

-120

-100

-80

-60

-40

-20

0

En

erg

y (

dB

)

Time (ps)

3d simulation of Notomi's model

option deselected

absorb unconsidered mode fields

191,0 191,2 191,4 191,6 191,8 192,0

0,0

5,0x107

1,0x108

1,5x108

2,0x108

2,5x108

3,0x108

3,5x108

4,0x108

191,60445

3d simulation of Notomi's model

option deselected

absorb unconsidered mode fields

Ma

gn

itu

de

(V

/m)

Frequency (THz)








Frequency data is used to calculate Q factor of

photonic crystal resonators in a low-n system

30.000 meshcells

Results of interest:

• Transmission spectrum

• Q and Tmax from frequency data

MODEL AND SPECTRUM OF LINE DEFECT RESONATOR


Field monitors are important to understand

mechanisms of the transmission spectrum

PC WAVEGUIDE TRANSMISSION FOR VARYING ETCHING DEPTHS

monochromatic at 1200nm

detch = 1.3µm

detch = 2.5µm

1000 1200 1400 1600 1800 20000,0

0,2

0,4

0,6

0,8

1,0 monochromatic 2D-BB, neff=1.50

3D-BB, etched:

2.5 µm

1.7 µm

1.5 µm

1.3 µm

Tra

nsm

issio

n

[nm]

Böttger, Eich et al., Appl. Phys. Lett. 81, 2517 (2002)


A shift of the hole position can be used to improve the

resonators performance

a1*a

a2*a

a3*a a3*a

a2*a

a1*a

MODEL AND DEFINITION OF PARAMETERS TO BE OPTIMIZED

To find optimal values for a1, a2 and a3

parameter sweep and optimizer were used


Parameter sweep and optimizer give similar results for

taper parameter values

Optimizer: a1=0.18; a2=0.154; a3=0.119

0 50 100 150 200 250 300 350

0

2000

4000

6000

8000

10000

220

225

230

235

240

a1=0.15a

1=0.1a

1=0.05a

1=0a

1=-0.05a

1=-0.1

Lo

ssy Q

[1

]

# run

a1=-0.15

a1=a

2=0.15

a3=0.1

re

s. fr

eq

. [T

Hz]

not optimized

optimized

FIELD PATTERNS OF OPTIMITZED AND STANDARD RESONATORS


Tapering of lattice parameters around the defect

improves resonator performance

3D SIMULATIONS OF REGULAR AND LATTICE ENGINEERED PC

aCa a

r=80nm...150nm

Three holes taper section

100 1000 10000

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Tm

ax [a

.u.]

Q [1]

untapered

radius taper

lattice taper

a1 a2 a3aC a1=472nm

a2=468nm

a3=427nm


Ridge waveguide defect resonators require larger

simulation volume

200.000 meshcells

RIDGE WAVEGUIDE DEFECT RESONATOR STRUCTURES

• Transmission spectrum

• Q from frequency data

• High Q and model volume require

long simulation time

• Geometry optimization very time

consuming


For bulk transmission behavior two transient solver

runs are necessary (ΓM and ΓK directions)

MODELS FOR TRANSMISSION OF BULK TRIANGULAR LATTICES

Same model file for both lattice directions.

Calculation by sweep of hole distances in x and z direction

ΓM

dx=a

dz=sqr(3)*a

ΓK

dx=sqr(3)*a

dz=a


Sim parameters:

a = 650 nm

r = 280 nm

CST MWS simulation and experimental results are in

excellent agreementSIMULATED AND EXPERIMENTAL SPECTRUM (BULK PHC)

1000 1100 1200 1300 1400 1500 1600

-60

-50

-40

-30

-20

-10

0

Tra

nsm

issio

n [dB

]

Wavelength [nm]

(sim)

(sim)

(exp)

(exp)#60 B/C 3b


CST MICROWAVE STUDIO® can be used for various

applications in photonics design

SUMMARY

• Micro ring resonator structures in SOI

– Transmission spectra, Q factor

– Mode profiles

– Bending and coupling losses

• Photonic crystals

– Slow light simulations (band diagram, coupling behavior)

– High Q cavities in SOI

– Optimization of line defect resonators

in low index materials

• Taper design

专注于微波、射频、天线设计人才的培养易迪拓培训网址：http://www.edatop.com

C S T 视频培训课程推荐

CST 微波工作室(CST Microwave Studio)是 CST 工作室套装中最核心的一个子软件，主要用于三维

电磁问题的仿真分析，可计算任意结构任意材料电大宽带的电磁问题。广泛应用于高频/微波无源器件

的仿真设计、各种类型的天线设计、雷达散射截面分析、电磁兼容分析和信号完整性分析等各个方面。

易迪拓培训(www.edatop.com)推出的 CST 微波工作室视频培训课程由经验丰富的专家授课，旨在

帮助用户能够快速地学习掌握 CST 微波工作室的各项功能、使用操作和工程应用。购买 CST 教学视

频培训课程套装，还可超值赠送 3 个月免费在线学习答疑，让您学习无忧。

CST 学习培训课程套装

该培训套装由易迪拓培训联合微波 EDA 网共同推出，是最全面、系统、

专业的 CST 微波工作室培训课程套装，所有课程都由经验丰富的专家

授课，视频教学，可以帮助您从零开始，全面系统地学习 CST 微波工

作的各项功能及其在微波射频、天线设计等领域的设计应用。且购买该

套装，还可超值赠送 3 个月免费学习答疑…

课程网址：http://www.edatop.com/peixun/cst/24.html

HFSS 天线设计培训课程套装

套装共含 5 门视频培训课程，课程从基础讲起，内容由浅入深，理论

介绍和实际操作讲解相结合，全面系统的讲解了 CST 微波工作室天线

设计的全过程。是国内最全面、最专业的 CST 天线设计课程，可以帮

助您快速学习掌握如何使用 CST 设计天线，让天线设计不再难…

课程网址：http://www.edatop.com/peixun/cst/127.html

更多 CST 视频培训课程：

CST 微波工作室入门与应用详解 — 中文视频教程

CST 微波工作室初学者的最佳培训课程，由工程经验丰富的资深专家授课，全程中文讲解，高清

视频，直观易学。网址：http://www.edatop.com/peixun/cst/25.html

CST 微波工作室天线设计详解 — 中文视频培训教程

重点讲解天线设计相关知识和使用 CST 进行天线仿真设计的使用操作，是学习掌握使用 CST 微

波工作室进行天线设计的必备课程，网址：http://www.edatop.com/peixun/cst/26.html

CST 阵列天线仿真设计实例详解 —— 中文视频教程

阵列天线设计专业性要求很高，因此相关培训课程是少之又少，该门培训课程由易迪拓培训重金

聘请专家讲解；课程网址：http://www.edatop.com/peixun/cst/123.html

更多 CST 培训课程，敬请浏览：http://www.edatop.com/peixun/cst

`

专注于微波、射频、天线设计人才的培养易迪拓培训网址：http://www.edatop.com

关于易迪拓培训：

易迪拓培训(www.edatop.com)由数名来自于研发第一线的资深工程师发起成立，一直致力和专注

于微波、射频、天线设计研发人才的培养；后于 2006 年整合合并微波 EDA 网(www.mweda.com)，

现已发展成为国内最大的微波射频和天线设计人才培养基地，成功推出多套微波射频以及天线设计相

关培训课程和 ADS、HFSS 等专业软件使用培训课程，广受客户好评；并先后与人民邮电出版社、电

子工业出版社合作出版了多本专业图书，帮助数万名工程师提升了专业技术能力。客户遍布中兴通讯、

研通高频、埃威航电、国人通信等多家国内知名公司，以及台湾工业技术研究院、永业科技、全一电

子等多家台湾地区企业。

我们的课程优势：

※ 成立于 2004 年，10 多年丰富的行业经验

※ 一直专注于微波射频和天线设计工程师的培养，更了解该行业对人才的要求

※ 视频课程、既能达到现场培训的效果，又能免除您舟车劳顿的辛苦，学习工作两不误

※ 经验丰富的一线资深工程师讲授，结合实际工程案例，直观、实用、易学

联系我们：

※ 易迪拓培训官网：http://www.edatop.com

※ 微波 EDA 网：http://www.mweda.com

※ 官方淘宝店：http://shop36920890.taobao.com

专注于微波、射频、天线设计人才的培养

官方网址：http://www.edatop.com 易迪拓培训淘宝网店：http://shop36920890.taobao.com

Optical Applications using CST MICROWAVE … University of Technology Institute of Optical and Electronic Materials, Eich Optical Applications using CST MICROWAVE STUDIO® Micro rings

Documents