集成光电子器件及设计 - 新型耦合器件与原理II：器件与结构

第5章

新型耦合器件与原理II：器件与结构集成光电子器件及设计2Outline

Structures

and

devices

for

coupling

Butt‐coupling;

Vertical

coupling;

Evanescent

coupling;

Mode

coupling/conversion;

31.

Butt‐coupling

Butt‐coupler

between

a

fiber

and

a

SOI

nanowire

Multimode

interference

(MMI)

couplers.

Vertical

direction

(μm)Vertical

direction

(μm)4Horizontal

direction

(μm)标准光纤和波导在端面耦合时模式失配损耗是插入损耗的主要因素；利用光纤和波导模场的重叠积分可以得到两者耦合时的损耗；改变波导的几何尺寸，从而改变波导的模场分布，可以使波导的模场和光纤的模场达到较好的耦合。f

(x,=∫∫Er(x,y)

⋅Enor*y)dxdyf

f

(x,f

(x,

∫∫Er(x,y)

⋅Enor*y)dxdy∫∫Enor(x,y)

⋅Enor*y)dxdyc0

=

wco=500nm,

hco=300nm,

hcl=2μm

Horizontal

direction

(μm)wco=6μm,

hco=6μm,Δ≈0.7%1.1

Butt‐coupler

between

a

fiber

and

a

SOI

nanowire

Coupling

coefficient5Butt‐coupling:

mode

converters

Lateral

Tapers;

Vertical

Tapers;

Combined

vertical

&

lateral

taper.

Lots

of

work

has

been

done

for

III‐V

PICs!6Lateral

TapersIEEE

JSTQE,

3(6):

1308‐1320,

19977Vertical

TapersIEEE

JSTQE,

3(6):

1308‐1320,

19978Combined

vertical

&

lateral

taperIEEE

JSTQE,

3(6):

1308‐1320,

19979Taper

fabrication

methods

based

on

dry

etching(c)

Shadow

masked

RIE.(a)

Oxide

shadow

technique.

(b)

Direct

shadow

etching10Mode

converters

in

silicon

photonics

for

the

fiber‐coupling

Dual

grating-assisted

directional

coupler.G.Z.

Masanovic,

et

al.

IEE

Proc.-Optoelectron.,

152(1),

2005.

NTT

Microsystem

Integration

Lab.IEEE

J

Select.

Top.

Qutant.

Electron.

11(1),

2005hLtopLbtwrHwcohcowtpxyzSilicon

NanotaperVilson

R.

Almeida,

Roberto

R.

Panepucci,

and

Michal

Lipson,

"Nanotaper

for

compact

mode

conversion,"

Opt.

Lett.

28,

1112hwSipolymerSiO2

h=250nmw=100nm

h=

350nmw=100nm

h=500nmw=100nmw=50nmw=50nmw=50nmInverse

taperNarrow

tip

is

needed.13Ultra‐low‐loss

inverted

taper

coupler

w=450

nm

<

15

nm

(a

thermal

oxidation

process)IL

of

each

inverted

taper

coupler：(1)

~0.36

dB

(TM);

(2)

~

0.66

dB

(TE)

M.

Pu,

et

al.

Optics

Communications,

283(19):

3678–3682,

2010.

y

(μm)y

(μm)y

(μm)y

(μm)y

(μm)y

(μm)Daoxin

Dai,

et

al.

JLT,

24(6):

2428‐2433,

2006.14x

(μm)z=0x

(μm)z=200μmx

(μm)z=400μmminor

peakx

(μm)z=800μmx

(μm)z=600μmx

(μm)y=–(H–h)hLtopLbtwrHBi‐level

mode

converter

wco

hcowtpxyz151.2.

MMI

couplers

由输入/输出波导、多模干涉区组成；

与方向耦合器、Y分支、星型耦合器等相比，具有结构紧凑、易于制作、损耗小、制作容差性好、偏振相关性小等优点；

已经在功分器、光开关、上下路器、波分复用器件、环形激光器等器件中得到了广泛应用。z]v(v+2)π

3LπE(x,z)

=∑cνϕν

(x)exp[−

j

νLucas

B.

Soldano

and

Erik

C.

M.

Pennings.

Optical

multi‐mode

interference

devices

based

on

self‐imaging:

principles

and

applications.

J.

Lightwave

Technol.

13(4):

615‐627,

1995

(cited

1171

times).

M.

Bachmann,

P.

A.

Besse,

and

H.

Melchior,

"General

self‐imaging

properties

in

N

×

N

multimode

interference

couplers

16

MMI耦合器‐自成像原理

•

对于输入场E(x)，可将其分解成多模区所有模场的加权和(正交完备基

函数)

E(x,0)

=∑cνϕν

(x)

ν加权系数

cν

=

2

传播

常数

则在多模区传输距离z

后的场可表示为173Lπ

将模场分为两部分：奇模与偶模

Ei(x)

=

Ee(x)+

Eo(x)(a)

当

L=3Lπ时

各个模式的相位:

Φ3Lπ

={0,π,0,π,L}E3Lπ

(x)

=

Ee(x)−

Eo(x)

=

Ee(−x)+

Eo(−x)

=

Ein(−x)6LπE6Lπ

(x)

=

Ee(x)+

Eo(x)

=

Ein(x)•

(b)

当

L=6Lπ时

各个模式的相位:

Φ6Lπ

={0,0,0,0,L}镜像自成像z]v(v+2)π

3LπE(x,z)

=∑cνϕν

(x)exp[−

j

νE32(x)

=

Ee

o(x)

=Ei(x)e−

j

4π

+

Ei(−x)e

j

4π18{}1

11

2(x)−

jE3/2Lc1×2

splitterMMI耦合器‐Mode

Propagation

Analysis

(MPA)

•

(c)

当

L=3/2Lπ时

⎧

3

3

⎫

2

⎩

2

2

⎭19Self‐imaging

in

an

MMI

section20

三种输入方式(a)

一般干涉模式(General

Interference);(b)

限制干涉模式(Restricted

Interference);(c)

对称干涉模式(Symmetric

Interference);x

=±WMMI

/6x

=0(a)(b)(c)21Summary

for

the

self‐imaging

at

MMI

sections22Tapered

MMI

couplers

2×2

optical

coupler:

for

the

coupling

between

microring

and

the

access

optical

waveguides,

also

for

Mach-Zehnder

Interferometer

(MZI)

filter.zxw1w2L

θGw(z)zxw1LGTapering

the

MMI

section

small

MMI

coupler23How

to

design

of

2×2

tapered

MMI

couplersθzxw1w2LGw(z)To

find

the

exact

MMI

length

L

for

good

self-imaging,

one

usually

hasto

implement

a

series

of

numerical

simulations

(e.g.,

BPM

simulations)in

which

the

length

L

is

scanned.

Time-consumed.The

effective

index∆φ(L)w1=1.4μm24Our

design

method

for

Tapered

MMI

coupler

L

Δϕ(L)

=ϕ0

−ϕ1

=∫{neff0[w(z')]−neff1[w(z')]}k0dz'

0where

n0eff(w)=∑aiwi,

n1eff(w)=∑biwi.02682.33.1

32.92.82.72.62.52.4

4wMMI

(μm)Find

the

solution

of

∆φ(L)=∆φ0L.e.g.,

∆φ0=3π/N

for

a

GI-type

N-fold

selfimaging.

Daoxin

Dai,

Sailing

He.

Appl.

Opt.,

47(1):

38‐44,

2008.

4610122

2765438TE

8L

(μm)

w2=1.0μm∆φ0=3π/2w2=1.2μm

w2=2.0μmneff0

neff1

Obtained

by

the

FDM

mode‐solver

w20(μm)L

MMI(μm)25Realization

of

polarization‐sensitivity

by

tapering

MMI

sectionDaoxin

Dai,

and

Sailing

He.

IEEE

Photon.

Technol.

Lett.,

20(8):

599‐601,

2008.

zxw1w2L

θGw(z)11.41.82.211.5233.54

2.5w

1(μm)8.59.510.511.5To

make

LMMI_TE=LMMI_TM(a)(b)26MMI应用‐功分器1xN

power

splitter2x2

couplerRing

resonatorx(

μ

m)Output

power

from

two

ports

(dB)Output

power

from

two

ports

(dB)x(

μ

m)1310nm1550nmWMMIPort1zxPort21310nmPort31550nm通过选取合适的MMI宽度与长度实现1310nm与1550nm信道的分离。

LMMI

=

n⋅Lπ

(1310)

=

(n+1)⋅Lπ

(1550)MMI应用：1310/1550

nm

波分复用器

结构示意图0300400-10

-5050100300400

10-10

-50510

200z

(μm)

(c)

LMMITE偏振,

@1310nm

100

200

z

(μm)

(a)TE偏振,

@1550nm1330-30

1290-25-15-20-10-501300

1310

1320

Wavelength

(nm)

(a)1575-30

1525-25-15-20-10-501537

1550

1567

Wavelength

(nm)

(b)

27Port3Port2Port2Port3TETMTETMx

(μm)

x

(μm)28z

(μm)

(b)

TE2000

1000

0

(a)

TMwMMI1

MMI

#1

wMMI2

MMI

#2TE/TMTMTE

MMI应用：偏振分束器（PBS）传统方法：通过选取合适的MMI宽度与长度实现TE与TM的分离。

新方法：A

compact

design

with

cascaded

MMI

sectionsYuqing

Jiao,

et

al.

IEEE

Photonics

Technology

Letters,

,

21(20):

1538‐1540,

2009.

292.

Vertical

coupling

(with

grating

couplers)W.

Bogaerts,

et

al.

J.

Lightwave

Technol.

23(1),

2005Polarization-dependent,

wavelength-sensitive30Principle

of

grating

couplersBragg

condition31How

to

improve

the

coupling

efficiency?32D.

Vermeulen,

et

al,

"High‐efficiency

fiber‐to‐chip

grating

couplers

realized

using

an

advanced

CMOS‐compatible

Silicon‐On‐Insulator

platform,"

Opt.

Express

18,

18278‐18283

(2010)

Improved

designs

for

grating

couplers

using

a

poly‐silicon

overlay

−1.6dB

and

a

3dB

bandwidth

of

80nmChirped

grating

coupler

higher

efficiencyY.

Tang,

et

al.

Opt.

Lett.,

35(8):1290‐1292,

2010.

3334Directionality

D

~

tbufw=200nm,

t=260nm,

d=90nm,

Λ=629nm,

n1

=

n3

=

1.46,

n2

=

3.4835Reduce

the

mode

matching

loss.

With

Bragg

grating

underneath

to

reduce

the

leakage

to

the

substrate.

Chirp

grating

coupler

+

Bragg

grating36http://www.iph.rwth‐aachen.de/?page_id=40Ultra‐compact

curved

grating

coupler37

2D

grating

coupler

for

coupling,

polarization‐splitting/rotatingW.

Bogaerts,

et

al.

Optics

Express,

15(4):

1567‐1578,

2007.

38Application

of

2D

grating

couplersW.

Bogaerts,

et

al.

Optics

Express,

15(4):

1567‐1578,

2007.

39

High

coupling

efficiency,

short

coupling

length;

Mode

converter;

Q

Li,

et

al.

Opt.

Lett.

35,

3153‐3155

(2010)

3.

Evanescent

coupling:

asymmetrical

directional

coupler

Efficient

coupling

between

different

types

of

optical

waveguides

SHP

waveguides

and

SOI

nanowires40Evanescent

coupling:

directional

coupler

Symmetrical

directional

coupler;

Asymmetrical

directional

coupler;

Input

Section

Output

Section

1234A0A

Coupling

region

BB0sD

Input

Section

Output

Section

1234A0A

Coupling

region

BB0sD

Phase

matching

condition!41w1hco1wgw2WG

IWG

IIhco2TM0Input

Asymmetricalcoupling

systemThruCrossTE0SiO2

TE0,TM0APBS3.1

Application

of

asymmetrical

couplers

II

PBSs:

one

polarization

is

coupled

while

the

other

one

does

not.

42TETM

Lcupl=2*Lπ_TE=1*Lπ_TMDrawback:

Small

fabrication

tolerance,

Might

be

pretty

long.

Basic

principle

for

DC‐based

PBSLcupl=p*LπTE=q*LπTM,

where

p,

q

are

integers,

and

p=q+k,

k=±1,

3,

5,

…

Improved

design:

Idea

coupling

system

for

PBS:TMpolarizationhasstrongcoupling,whilenocouplingforTE.Lcupl=1*Lπ_TM

≈0*Lπ_TE!

PBS

based

on

an

asymmetrical

DC.neff431.451.701.952.702.452.202.950.30.60.91.21.5

Waveguide

width

(μm)Daoxin

Dai,

JLT,

30(20):

3281‐3287

(2012).

TE0

TE1w2w1hco=220nmTM0TM1TE3w1wgw2TE0TM1TE0TM0TM1

PBS

based

on

an

asymmetrical

DC(a).

Asymmetrical

DC

consisting

of

two

WGs

with

different

widths.

Principle

TM0TMTE44w2w1

wgLc1

Lc2L0Lz1Lx1Lz2Lx2Daoxin

Dai,

Journal

of

Lightwave

Technology,

30(20):

3281‐3287

(2012).

PBS

based

on

a

three‐waveguides

coupling

system

StructureTM/TETETMTransmission

(dBm)Power

(dBm)1.53μm1.58μmTransmission

(dBm)Power

(dBm)0

1.45Wavelength

(nm)-25-10-15-20

0-51.65Thru

port(a)

Input:

TM0

1.5

1.55

Wavelength

(μm)‐35‐45‐15

‐25Thru

TM

input

(a)Results15101590

45

1530

1550

1570

Wavelength

(nm)

1590Thru

Cross

‐55‐15

1510

1530

1550

1570

TE

input

‐25‐35‐45‐55-30

-10

-20

-30

-40

-501.451.51.61.65

1.55Wavelength

(μm)

Cross

port

1.6Thru

portCross

port(b)

Input:

TE0SimulationMeasurement

CrossR2=20μm,R1=R2–0.7μmWG#22mismatchWG#1w1(b)TER2=20μm,R1=R2–0.7μmWG#2w2w1WG#1(a)TMOPLOPL46(b).

Asymmetrical

DC:

a

bending

coupler.

Due

to

the

birefringence,

the

phase‐matching

condition

is

satisfied

for

only

one

polarization

(e.g.,

TM)

in

this

structure.

Therefore,

TM

polarization

will

be

coupled

from

one

waveguide

R1R2w1wgw2

148

146

144

142

140

138

136

1340.440.460.580.60.48

0.5

0.52

0.54

0.56

Waveguide

width

(μm)0.440.460.580.60.48

0.5

0.52

0.54

0.56

Waveguide

width

(μm)

to

the

other

one

while

TE

polarization

won’t.

Then

these

two

polarizations

are

separated.

Because

the

TM

polarization

has

very

strong

coupling,

an

ultra‐compact

PBS

is

expected.

The

phase

matching

condition:

OPL≡β2R2θ=

β1R1θ.

208

204

200

196

192

188

184

18047Phase‐matching

conditionw1opt=0.55um;

w1

wg

w2R2=20um,

R1=R2-0.7um,

w2=0.46umR1R248TMTESiO2TE/TMw1hcowgw2SiSiTMTETE/TMw1w2wgapR3LxLzR=20μmS-bendL<10umTMTESiO2

~0.983~0.97~0.02<0.001The

PBS

design

SiPower

(dB)Power

(dB)Extinction

ratio

(dB)495020151025145016501500

1550

1600

Wavelength

(nm)

TE

TM(c)

Calculated

‐20‐25

‐5‐10/p>

1550

1600

Wavelength

(nm)CrossThru(b)

TM

inputCalculated

The

fabricated

PBS

and

the

characterization

TE

TMTM

TE‐20‐25

‐5‐10/p>

14501500

1550

1600

Wavelength

(nm)ThruCrossCalculated(a)

TE

inputneff50(c)

Asymmetrical

DC

with

two

different

types

of

WGsTETMSiO2SiTE/TMwcohcwg

wS

wslotSiO2SiSiSiAirUse

the

coupling

betweenSOI

nanowire

and

nano-slot

waveguide.Daoxin

Dai,

Zhi

Wang,

and

John

E

Bowers,

Optics

Letters,

36(13),

2590-2592

(2011).

Lcupl=1*Lπ_TM

=0*Lπ_TE!Phase-matching

for

TM

only.1.61.52.12.01.91.81.72.32.22.52.40.10.150.20.40.450.50.25

0.3

0.35

wSi,

wco

(μm)TEwcoTETMNano-slot

WG

wSi

wslot

Airhco

Si

SiO2

Nanowire

TM

Si

Air

Si

SiO2wslot=60nmwslot=80nmwslot=100nmhco=250nmTE

(Ex)

TE

(Ex)TM

(Ey)TM

(Ey)nano-slotwaveguideSOI

nanowire

(b)51Light

propagation

Length

<9

μ

m,

and

simple

structure;Daoxin

Dai,

Zhi

Wang,

and

John

E

Bowers,

Optics

Letters,

36(13),

2590-2592

(2011).Lc(a)

TE(b)

TM0.4μm0.4μm52Experimental

demonstrationShiyun

Lin,

et

al.

Appl.

Phys.

Lett.

98,

151101

2011Normalized

Power

(dB)P

(h

)P

(h

)1.451.5TE

Input1.65F.

Lou,

D.

Dai,

and

L.

Wosinski,

Opt.

Lett.

37,

3372

(2012)

531.551.6-15-20

-5-1001.551.61.65

-15

-20

1.45

1.5Wavelength

(μm)

-5-1002

d3

dTM

Input

Au

SiO2

SiSiO2w

=100nm

AgAir

SiSiO201.32×109D.

Dai,

et

al.

Opt.

Express,

17:

16646,

2009

(d)

Asymmetrical

DC

with

two

different

types

of

WGsUsing

the

coupling

between

an

SOI

nanowire

and

a

hybrid

plasmonics

waveguideneffTransmission

(dB)Transmission

(dB)LC

=

2.2

μm

1.3μmC54w2w1mismatchingEx(TE0@HPW)Ey(TM0@HPW)Ex(TE0@NW)Ey

(TM0@NW)TM0@HPWTE0@HPWTM0@NWTE0@NWBLcTE/TMRTMTE

BOXSi

substrateThruCrosshmhSiO2w1

wgap

w2hSiBOXThruCross1

0-1

width

(nm)Cross

Thru

TE

TMInput

Input

Length~3.7

μm

Total

Total

Cross

Cross

Thru

Thru

(a)

TE

(b)

TM

wavelength

(μm)

wavelength

(μm)X.

Guan,

et

al.

Opt.

Lett.

(to

be

published)(e)

Asymmetrical

DC

with

two

different

types

of

WGs

Using

the

coupling

between

an

SOI

nanowireand

a

hybrid

plasmonics

waveguide55Advanced

multiplexing

plays

an

important

role.Application

of

asymmetrical

couplers

II

to

realize

the

multi‐channel

mode

multiplexing

technology.

Any

multiplexing?56Space‐division‐multiplexing

(SDM)

Space‐division‐multiplexing:

Multiple

fibers

/

Multi‐core

fiber;Multimode/polarization

mode

multiplexing:

Mode

handling

(conversion

&

coupling)

is

difficult

to

control

for

optical

fibers,

It

is

convenient

for

planar

optical

circuits

(which

will

be

shown

below);

Photonic

network‐on‐chip

with

the

mode‐multiplexing

technology.

Active:

Laser

diode;

Optical

modulators;

Photodetectors;Passive:

Power

splitter;

Polarization

handling

devices;

Mode

(de)multiplexer.57

Optical

modulator

array

for

TE

LD1×2

Powersplitter

1×N

Powersplitter

1×NPowersplitter

Polarization

rotatorAdvantages:

Only

one

laser

source

is

needed

(convenient

to

use

an

off‐chip

laser);

All

the

optical

modulators

are

identical

(easy

chip

design).

Easy

management;

Low

cost;

Monolithical

integration

is

possible

with

the

Ge‐on‐Si

platform.

Mode

MUXer

ModeMUXer

ModedeMUXer

Mode

deMUXerPhotodetector

array

Multimode

waveguide

PolarizationPolarization

°°°°

Splitter

combiner

Multimode

waveguide58Mode

(de)multiplexer:

structure

and

designDesign

the

widths

(w1,

w2,

…

)

and

lengths

(Lc1,

Lc2,

…

)

for

the

coupling

region.°°°°

Mode

demultiplexer

Multiode

waveguide(a)

w1w2

w3Lc1

Lc2

Mode

multiplexerLc34‐channel10z

(μm)00010−10−10−1059−2−112

0x

(μm)−3

−2

−112

0x

(μm)1

23−3

−2

−1

0

x

(μm)01w3=2.35μm

Cw2=1.68μm

Bw1=1.02μm

A

Accesswaveguide

Accesswaveguide

AccesswaveguideI4

Configuration

of

the

proposed

mode

MUXersLc3I2

and

deMUXersawith

4

channels

60°°°Mode

deMUXer

Multiode

waveguide

w2w3The

designed

and

fabricated

MUXer/deMUXer

with

four

channels.

c1

Lc2Mode

MUXer

I1

I3

O1

O3

O4

O2

w1

wg

°°°MUXerdeMUXerI4

I2

I1

I3

O4

O2

O1

O3

Power

(dBm)Power

(dBm)Power

(dBm)Power

(dBm)61°°°I4

I2

I1

I3

O4

O2

O1

O3

O125dBO224dB

Wavelength

(nm)MUXer

O4

O2

O3

From

I1Wavelength

(nm)

O3

28.3dB

O2

O4

O1

From

I3Wavelength

(nm)

deMUXer

O3

O4

O1

From

I2Wavelength

(nm)

O4

23dB

O1

O3

O2

From

I4

AC

BDWDMPDMMultimode

SDMMulti‐core

SMDNch4~10022~81~10MUXerHybrid

multiplexing

technologyLDOptical

modulator

array1×2N

PSPR°°°°Mode

MUXerPhotodetector

ArrayPR

ModedeMUXerPS:

Power

SplitterPR:

Polarization

Rotator~1Terabit/s

using

a

single‐wavelength

carrier

(with

PDM

+

multimode

SDM);

~

100

Terabit/s

using

many

wavelengths

(with

WDM);

~

1Petabit/s

using

multiple

cores

(with

multi‐core

SDM);

Need

novel

PICs!

6263Devices

for

hybrid

multiplexing:

polarization

+

mode

MUXersTE

(4‐channels)

+

TM

(4‐channels)A

PBS

for

TE0

&

TM064Possibility

of

Tera‐bit/s

with

only

a

single

wavelength

carrier

[

8

ch

(TE)

+

8

ch

(TM)

]

*

70Gbps

>

1Tbps.

Y.

Tang,

J.

D.

Peters,

and

J.

E.

Bowers.

Optics

Express,20:11529

(2012)

65Nature

Photonics

1,

52

(2007)Opt.

Express

16,

4872‐4880

(2008)

4

Polarization

mode

conversion/rotationMotivation:

to

realize

the

polarization

diversity,

which

is

a

general

solution

for

polarization‐dependence

issue

Polarization

transparent

PICs.

Key

devices:

PS,

PR.

66An

approach

for

realizing

polarization

rotatorsExEySiTM(a)TEHSiO2:

n1=1.445

W

He

WeSi:

n2=3.48x

y

(b)Mode

hybridizationMode

#2:

neff=2.7086

ExEyMode

#1:

neff=2.6016

ExEy

(c)

Length

~8μm;

Simple

structure;

Easy

design

and

fabrication;Z.

Wang,

and

D.

Dai.

JOSA

B.

25(5):

747‐753,

2008

8μm67Experimental

demonstrationVermeulen,

et

al.

PTL,

2011.68Daoxin

Dai,

and

John

E.

Bowers,

Opt.Express,

19(11):

10940-10949

(2011).SiO2TM

SiTEPolarization

splitter

rotator

(PSR)

Structure

and

principle

TE

TETE0TE1TM0TM0TE2w=0.TE176μmSiNSiSiO2TE0TE1TE2TM0TM1SiO2SiSiO2TE0TE2TE1w0TM0AirTM0TE1SiSiO2The

effective

index

neffThe

effective

index

neffThe

effective

index

neffy

(μm)69Daoxin

Dai,

Yongbo

Tang,

and

John

E

Bowers,

Opt.

Express

20(12):

13425‐13439

(2012).

1.452.702.452.201.951.700.31.5

0.6

0.9

1.2The

waveguide

width

wco

(μm)1.45Principle:

Mode

conversion

(TM0

2.95

2.70

2.45

2.20

1.95

1.700.31.5

0.6

0.9

1.2The

waveguide

width

wco

(μm)2.12.0TE1)

in

a

taper

structure

2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.20.31.5

0.5

0.7

0.9

1.1

1.3The

waveguide

width

wco

(μm)x

(μm)x

(μm)(a)

neff=2.25295(b)

neff=2.19855ExEyExEyMode

hybridizationLtp1=15,10,5,4,3,2,1μmTM0TE1TM0TM0Ltp1=15,10,5,4,3,2,1μmTE0TE1TM0TM0TE2w=0.76μmSSiiNTE1SiO2The

mode

conversion

efficiency

ηThe

effective

index

neff-1.5-1.5-1.0-0.50.00.50.50.0-0.5-1.0x/umx/um1.01.07005101520253035404550556065

z/um05101520253035404550556065

z/umDaoxin

Dai,

Yongbo

Tang,

and

John

E

Bowers,

Opt.

Express

20(12):

13425‐13439

(2012).

Principle:

Mode

conversion

(TM0

2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.2

2.1

2.00.31.5

0.5

0.7

0.9

1.1

1.3The

waveguide

width

wco

(μm)TM0TE1

(~100%)TE0TE00%

TE1)

in

a

taper

structure100%

90%

80%

70%

60%

50%

40%

30%

20%

10%0204060100120140160

80Ltp2

(μm)71TE0(a)

TE

inputTE0TE0(b)TaperCoupling(b)

TM

inputTM0TE1TE0Ltot=71μmLtp1Ltp2Ltp3LdcLtpoutw3w0w4woutwoutw2Daoxin

Dai,

and

John

E.

Bowers,

Opt.Express,

19(11):

10940-10949

(2011).

Adiabatic

taper•

Easy

to

fabricate.

No

additional

steps

needed.•

Standard

waveguide

geometry.

SOI

with

any

top

silicon

thickness.TMSiO2SiTEWith

the

help

of

an

asymmetrical

coupler:

TE1

TE

TEw1Polarization

splitter‐rotator

(PSR)

Ltot=71μm50μm72Shorter

taper

section

shorter

PSR17μmLtp1Ltp3LdcLtpoutw3w0w4woutwoutw1w2

Ltp2Adiabatic

taper73For

SOI

strip

waveguides,

one

can

introduce

a

SiO2

upper‐cladding

make

the

waveguide

symmetrical

in

the

vertical

direction

so

that

the

mode

conversion

can

be

depressed

when

needed.

However,

for

SOI

ridge

waveguides,

which

is

often

used,

what

happens?het

HCladding

wco

Core

Buffernclnco

nbf(b)It

is

still

asymmetrical

in

the

vertical

direction

even

with

the

same

material

for

the

upper‐

and

under‐cladding.74Mode

conversion

in

a

sub‐micron

SOI

ridge

waveguide

tapers

w2Regular

taper

Ltp

w1(a)Bufferhet

HCladding

wco

Corenclnconbf(b)het

HCladding

wco

Core

Buffer

wsidenconclnbf(b)Bi‐level

taper

(a)Daoxin

Dai,

Y.

Tang,

and

J.

E

Bowers,

Opt.

Express

20(12):

13425‐13439

(2012).

(a)het=0.4HTE0TE2TE1TE3TM0TM0CladdingwcoTE1nclhHetncoCoreTM0nbfBuffer(b)het=0.5HTE0TE1TE2TE3TM0TM0CladdingwconclhHetncoCoreTM0nbfBufferTE1(c)het=0.6HTE0TE1TE2TM0TM0TE3wcoTM0nclncoCoreCladdinghetHTE1nbfBufferThe

effective

index

neffThe

effective

index

neffThe

effective

index

neffy(μm)y(μm)y(μm)y(μm)752.83.02.93.23.10.531

1.5

2

2.5

The

waveguide

width

wco

(μm)2.83.02.90.531

1.5

2

2.5

The

waveguide

width

wco

(μm)2.72.83.02.93.23.10.531

1.5

2

2.5The

waveguide

width

wco

(μm)Mode

hybridization

in

SOI

ridge

waveguides

3.2

3.1

CoreBufferhet

HCladding

wconclnconbf(b)x

(μm)(a)

mode

#1:

neff=2.908029wco=1.0μmExEyx

(μm)(b)

mode

#2:

neff=2.877179wco=1.0μmExEyx

(μm)(a)

mode

#1:

neff=2.942011wco=2.45μmExEyx

(μm)(b)

mode

#2:

neff=2.947892wco=2.45μmExEyDaoxin

Dai,

Y.

Tang,

and

J.

E

Bowers,

Opt.

Expres