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
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
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
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
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
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
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
•Silicon photonics–Rib waveguides
(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:
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
Rib waveguidesSingle mode condition, horizontal
130
•Silicon photonics–Rib waveguides
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,
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
Rib waveguidesSingle mode condition, verification
131
Pogossian, JLT 16, Oct 1998
•Silicon photonics–Rib waveguides
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.
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
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
•Silicon photonics–Rib waveguides
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
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
−
′
•Silicon photonics–Rib waveguides
Both models predict SM
Pogossian predicts MM,
Derived predicts SM
Both predict MM
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
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
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
Air-clad Si wire on SiO2H=220 nm.
135Submicron Silicon Strip Waveguides, D. Van Thourhout
Air clad
•Silicon photonics–Wire waveguides
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
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
Air-clad Si wire on SiO2w=320 nm. 1 mode in one pol
136Submicron Silicon Strip Waveguides, D. Van Thourhout
N=1.7322
H=220 nm
xE00
•Silicon photonics–Wire waveguides
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
Air-clad Si wire on SiO2w=500 nm. 1 mode in both pols
137
N=2.3976 N=1.5952x
E00
yE00
•Silicon photonics–Wire waveguides
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
Air-clad Si wire on SiO2w=650 nm. 3 modes in various pols
138
•Silicon photonics–Wire waveguides
N=2.5740 N=1.6058x
E00 N=1.7161? ?
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
SiO2 -clad Si wire on SiO2w=280 nm. 1 mode in both pols
139Submicron Silicon Strip Waveguides, D. Van Thourhout
N=1.7737x
E00
yE00
•Silicon photonics–Wire waveguides
N=1.5860
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
SiO2 -clad Si wire on SiO2w=450 nm. 1 mode in both pols
140Submicron Silicon Strip Waveguides, D. Van Thourhout
N=2.3617 N=1.7465x
E00
yE00
•Silicon photonics–Wire waveguides
ECE 4006/5166 Guided Wave Optics
Robert R. McLeod, University of Colorado
SiO2 -clad Si wire on SiO2w=620 nm. 2 modes
141Submicron Silicon Strip Waveguides, D. Van Thourhout
N=2.585 N=1.8485x
E00
yE00 N=1.7450
xE10
•Silicon photonics–Wire waveguides