silicon integrated optics - university of colorado...

ECE 4006/5166 Guided Wave Optics

Robert R. McLeod, University of Colorado

Silicon integrated optics

• SOI wafers

• Si “wire” & ridge waveguides

– SM condition

– Mode structures

126

•Silicon photonics–Outline

http://photonics.intec.ugent.be/download/ocs75.pdf



Condensed view of

fabrication process

127

Original silicon on insulator

wafer.

Apply bottom anti-reflection coating

(BARC) and resist.

Photopatterning and solvent-wash of

resist.

Selective etching of resist, removal

of resist.

http://photonics.intec.ugent.be/download/pub_2397.pdf

•Silicon photonics–Intro



Rib waveguidesEIM analysis - setup

128

Step 1: Find effective index of slabs of height H and height h. Rather

than solve the transcendental equation, let’s use an approximate

expression (Pogossian, Opt & Quant Elec 25, 1993)

•Silicon photonics–Rib waveguides

( )

( )[ ] ( )[ ]( )

µm0845.0qµm936.0q

TMfor TE,for 1

1

TMTE

2

,,

2122

0

2122

0

2

2

0

22

==

=

−+−≡

+≡+

−≈

fscsc

sfscfc

eff

eff

fm

nn

nnknnkq

qhhmhk

nN

γ

γγ

π

Pogossian, JLT 16, Oct 1998

45.1,4788.3 µm,55.1 µm,12 0 ====clco

nna λ

Conclusion: Accurate for low-order modes.

For example, in Region II

For silicon, silicon dioxide and air at 1.55 microns.

Symmetric Si, SiO2 slab comparisonNote that polarization term is inverse to my definition



Rib waveguidesSingle mode condition, vertical

129

Step 2: Consider the possibility the first vertical mode beyond the

fundamental in the rib section.

Is this mode bound? In other

words, what is the proper

effective slab in the horizontal

direction?

( ) ( )

( ) ( )

2

1

1011

exteriorin ribin

2

2

0

22

2

0

2

2

0

2

1

>≡

+

−<+

−

<

eff

eff

eff

f

eff

f

H

hr

hkn

Hkn

NN

ππ


(Pogossian, JLT 16, Oct 1998)

Note that the classical condition is2

1>≡

H

hr (Soref, IEEE JQE 27, Aug 1991)

Consider the fundamental vertical mode in the region beyond the rib. Note

that it has good overlap with the lower lobe of the m=1 rib mode. Thus the

rib mode will couple strongly to the exterior mode. To be bound, the

effective index of the m=1 rib mode must be > the effective index of the

m=0 exterior mode. SM condition for vertical modes in rib is thus:



Rib waveguidesSingle mode condition, horizontal

130


Step 3: Require second horizontal mode be in cutoff.

( )

2

0

2

2

0

2

0

2

22

2

0

2

4

11

−<

′−

−

<+

′−

eff

f

effeff

f

II

eff

I

hkn

wkHkn

Nwk

N

πππ

π

INIIN IIN

w

[ ]22

02 IIIyeff NNkww −+≡′ γ

N of second mode < N of clad

Substitute approx expr

where

212 r

rt

−<

′

effeffeffeff HhrHwt ≡′≡′

Condition in the literature (Pogossian, JLT 16, Oct 1998) is

21 r

rt

−<

where

simplify

( )[ ]2122

02 cfceffeffeff nnkwwHwt −+=≡ γ

Or (Soref, IEEE JQE, 27, Aug 1991)

213.0

r

rt

−+< Hwt ≡

Soref, IEEE JQE, 27, Aug 1991,



Rib waveguidesSingle mode condition, verification

131

Pogossian, JLT 16, Oct 1998


213.0

r

rt

−+<

21 r

rt

−<

t,r defined in

terms of

effective

thicknesses

t,r defined in

terms of

actual

thicknesses

Conclusion: 0.3 factor is wrong.



SMC via numerical

mode solvers

132

( )

µm 5.1µm 0.1&5.03.0

1

25.094.005.0

2

<<<<

−

++≤

Hr

r

rH

H

W

Single-Mode and Polarization-Independent Silicon-on-Insulator Waveguides

With Small Cross Section, Chan, JOURNAL OF LIGHTWAVE

TECHNOLOGY 23, NO. 6, JUNE 2005 2103




Rib waveguidesComparison to FD mode-solver

133

w = .25 µm

h = .2 µm

H = .3 µm

r = 0.78 24.1

84.2/

88.0

21 r

r

t

t

−

′

w = .5 µm

h = .2 µm

H = .3 µm

r = 0.78 24.1

11.12/

43.1

21 r

r

t

t

−

′

w = .75 µm

h = .2 µm

H = .3 µm

r = 0.78 24.1

38.12/

99.1

21 r

r

t

t

−

′


Both models predict SM

Pogossian predicts MM,

Derived predicts SM

Both predict MM



Si “wire” waveguides

134

http://photonics.intec.ugent.be/download/pub_2451.pdf

0=≡H

hr

D. Van Thourhout, “Submicron Silicon Strip Waveguides,” Springer Series in Optical Sciences, 2006, number 119, pages 205-238

Air clad SiO2 clad

•Silicon photonics–Wire waveguides



Air-clad Si wire on SiO2H=220 nm.

135Submicron Silicon Strip Waveguides, D. Van Thourhout

Air clad


Silica clad

No modes for w

< 280 nm or V

= 1.89

54.543.532.52V

One mode in

two

polarizations

for w < 480 nm

or V < 3.1 ~ π.

Almost exactly

twice the

symmetric slab

case. Why?

Skew mode.

22

0

14788.32

280.289.1 −=

λ

π

22

0

45.14788.32

2−=

wV

λ

π



Air-clad Si wire on SiO2w=320 nm. 1 mode in one pol


N=1.7322

H=220 nm

xE00




Air-clad Si wire on SiO2w=500 nm. 1 mode in both pols

137

N=2.3976 N=1.5952x

E00

yE00




Air-clad Si wire on SiO2w=650 nm. 3 modes in various pols

138


N=2.5740 N=1.6058x

E00 N=1.7161? ?



SiO2 -clad Si wire on SiO2w=280 nm. 1 mode in both pols


N=1.7737x

E00

yE00


N=1.5860



SiO2 -clad Si wire on SiO2w=450 nm. 1 mode in both pols


N=2.3617 N=1.7465x

E00

yE00




SiO2 -clad Si wire on SiO2w=620 nm. 2 modes


N=2.585 N=1.8485x

E00

yE00 N=1.7450

xE10


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