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School of Electronic and Information Engineering
Simulations of nanophotonic waveguides and devices using COMSOL Multiphysics
Zheng Zheng
School of Electronic and Information Engineering
Beihang University 37 Xueyuan Road, Beijing 100191, China
Presented at the COMSOL Conference 2010 China
School of Electronic and Information Engineering
Acknowledgement Yusheng Bian Lin An Xin Zhao Muddassir Iqbal Ya Liu Wei Li Tao Zhou (NJIT) Jiangtao Cheng (Penn State Univ.) …
School of Electronic and Information Engineering
Simulation of dielectric waveguides and optic fibers using COMSOL
Simulation of surface plasmon
polariton (SPP) waveguides and devices using COMSOL
School of Electronic and Information Engineering
Simulation of dielectric waveguides and optic fibers using COMSOL
Simulation of surface plasmon
polariton (SPP) waveguides and devices using COMSOL
School of Electronic and Information Engineering
Development of Integrated Circuits
Moore's law
Conventional photonic device
Substrate
Low-index contrast waveguide
High-contrast planar waveguide Photonic crystal fiber and waveguide
Motivation - Nanophotonics
~ Diffraction limit Channel waveguide Slot waveguide
School of Electronic and Information Engineering
Dielectric slot waveguides and applications
Optical manipulation Optical modulator
Slot waveguide
Field distribution
Ring resonator Optical biosensing
*V. R. Almeida et. al, Optics Letters 29, 1209-1211 (2004).
School of Electronic and Information Engineering
Dispersion analysis of dielectric slot waveguides
COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition
Group velocity dispersion (GVD)
Sellmeier’s equation for silicon and silica refractive indices
*Z. Zheng, M. Iqbal, Optics Communications 281, 5151-5155 (2008).
School of Electronic and Information Engineering
Dispersion analysis of dielectric slot waveguides
Slot waveguide: In the normal dispersion regime near the 1550 nm wavelengths Channel silicon waveguide: In the abnormal dispersion regime GVD ( slot ) > GVD ( channel ) Higher order dispersion behavior depending strongly on the geometric parameters
of the slot waveguides (e.g. slot & slab width, material filled in the slot region)
*Z. Zheng, M. Iqbal, Optics Communications 281, 5151-5155 (2008).
School of Electronic and Information Engineering
Photonic Crystal Fibers (PCF)
A: Standard optical fiber (Total external reflection) B: Index-guiding photonic crystal fiber (Total internal reflection) C: Hollow core photonic bandgap fiber (Photonic bandgap)
A B C
Various kinds of PCF Lower transmission loss than conventional fibers Substantially higher damage thresholds than
conventional fibers Promising for various linear and nonlinear optical
processes
Merits and Potential of PCFs
*J. C. Knight, Nature 424, 847-851 (2003).
School of Electronic and Information Engineering
Design of ultrahigh birefringent, ultralow loss PCF
d
L
a
b
L1
L2
x
y
*L. An, Z. Zheng. Journal of Lightwave Technology 27, 3175-3180 (2009)
COMSOL settings Perpendicular waves of RF module- mode analysis PML boundary condition
A core region with a rectangular array of four
air holes (to provide the birefringence) A conventional circular-air-hole cladding (to
reduce the confinement loss).
x-polarization y-polarization
Intensity distributions with different elliptic ratio of the air hole
PCF structure
School of Electronic and Information Engineering
Ultrahigh single-mode birefringence (~10-2) Ultralow confinement losses (<0.002 dB/km) Relatively flat dispersion Easy to fabricate
Design of ultrahigh birefringent, ultralow loss PCF
PCF with circular air holes PCF with elliptical air holes Intensity distribution
1.48 1.50 1.52 1.54 1.56 1.58 1.60
-330
-300
-270
-240
-210
-180
-150
-120
GVD
(ps/
(nm
*km
))Wavelength (m)
x polarization y polarization
x-polarization y-polarization x-polarization y-polarization
*L. An, Z. Zheng. Journal of Lightwave Technology 27, 3175-3180 (2009)
School of Electronic and Information Engineering
Design of single-polarization, single-mode PCF
*L. An, Z. Zheng, Optics Communications 282, 3266-3269 (2009)
Single-mode and single-polarization propagation can be realized by tuning geometry of the air holes, with low confinement loss and small mode area
y-polarization
Intensity distribution PCF geometry
School of Electronic and Information Engineering
Design of single-polarization, single-mode PCF
*L. An, Z. Zheng, Optics Communications 282, 3266-3269 (2009)
Intensity distribution Dispersion optimization
COMSOL settings Perpendicular waves of RF module- mode analysis PML boundary condition
GVD
Dispersion & confinement loss GVD
Near-zero, dispersion-flattened
Low confinement loss(<0.25 dB/km)
Small mode area Ultra-wide band (0.3–1.84 μm)
School of Electronic and Information Engineering
Highly nonlinear holey fiber with a high index slot core
*L. An, Z. Zheng, Journal of Optics, 115502 (2010).
COMSOL settings Perpendicular waves of RF module- mode analysis PML boundary condition
Proposed structure
School of Electronic and Information Engineering
Highly nonlinear holey fiber with a high index slot core
1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70-6500
-6000
-5500
-5000
-4500
-4000
-3500
-3000
Gro
up v
eloc
ity d
ispe
rsio
n (p
s/nm
/km
)
Wavelength (m)
Fiber with a slot core
Intensity distribution Modal behavior Group velocity dispersion
Quasi-TE mode well confined in the slot region Single-mode propagation with ultra-small mode area ( < 0.3 μm2 )
A large negative GVD and large GVD slope
GVD
*L. An, Z. Zheng, Journal of Optics, 115502 (2010).
School of Electronic and Information Engineering
Highly nonlinear holey fiber with a high index slot core
1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64
-3200
-3100
-3000
-2900
-2800
Telecom C-Band
d/L = 0.66
d/L = 0.64
d/L = 0.62
d/L = 0.6
d/L = 0.58
Gro
up v
eloc
ity d
ispe
rsio
n (p
s/nm
/km
)
Wavelength (m)
1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68
-2050
-2000
-1950
-1900
-1850
-1800
-1750
-1700
Gro
up v
eloc
ity d
ispe
rsio
n (p
s/nm
/km
)
Wavelength (m)
Fiber with a slot core and a two-air-hole cladding
Fiber with a slot core and a four-air-hole cladding
Modification of GVD Much lower GVD than that
without air-hole Different dispersion slope at
various air-hole parameters Enhancement of the field
confinement
GVD
GVD
Even lower absolute GVD
values Further enhancement of the
field confinement
*L. An, Z. Zheng, Journal of Optics, 115502 (2010).
School of Electronic and Information Engineering
Simulation of dielectric waveguides and optic fibers using COMSOL
Simulation of surface plasmon
polariton (SPP) waveguides and devices using COMSOL
School of Electronic and Information Engineering
Sensing
Surface plasmons (SPs) Light guiding
Diffraction
limit
Nanolithography
Lasing
Introduction-Surface Plasmons
*W. L. Barnes, Nature 424, 824-830 (2003).
Coherent electron oscillations at
the metal/dielectric interface Field decays exponentially into
both neighboring media
School of Electronic and Information Engineering
Surface plasmon polariton (SPP) waveguide
Loss Confinement
Wm
hmnmMetal
y
xz
ndDielectric
Tradeoff
Introduction-SPP waveguides
Advantages Low propagation loss (a few dB/cm)
Disadvantages Weak confinement (mode size~λ)
Advantages Tight field confinement (subwavelength scale)
Insulator/Metal/Insulator (IMI) Metal/Insulator/Metal (MIM)
CPP waveguides metal slot waveguide Long-range SPP waveguide
Disadvantages Huge loss (propagation length ~ several μm)
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Hybrid plasmonic waveguide
Subwavelength mode confinement λ2/400 ~λ2/40 Long-range propagation distance 40 ~ 150 μm
*R. F. Oulton, Nature Photonics, 2008. 2(8): p. 496-500.
School of Electronic and Information Engineering
Wd
Wm
hm
hdnd
nmMetal
Slab
hg
ndSlab
y
xz
Cladding nb
Substrate nb
Design of symmetric hybrid plasmonic waveguide
*Y. S. Bian, Z. Zheng, Optics Express 17, 21320-21325 (2009).
-1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
Nor
mal
ized
Ey
y ( m )
-1.0 -0.5 0.0 0.5 1.0-1.0
-0.5
0.0
0.5
1.0
Nor
mal
ized
Ey
y ( m )
(a) (b)
Subwavelength confinement (1~2 orders of magnitude higher than insulator/metal/insulator waveguides)
Low loss ( propagation length~ hundreds of microns)
-1.0 -0.5 0.0 0.5 1.0
-0.5
0.0
0.5
-1.0 -0.5 0.0 0.5 1.0
-0.5
0.0
0.5
y (
m )
x ( m )
y (
m )
x ( m )-1.0 -0.5 0.0 0.5 1.0
-0.5
0.0
0.5
y (
m )
x ( m )0
1
-1.0 -0.5 0.0 0.5 1.0
-0.5
0.0
0.5y
( m
)
x ( m )MYMy
(a) (b) (c)
School of Electronic and Information Engineering
Design of symmetric hybrid plasmonic waveguide
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.40
2
4
6
8
10
12
Norm
alize
d co
uplin
g le
ngth
Sy
hg=10nm hg=30nm hg=50nm
Sy ( m )
2.2 2.4 2.6 2.8 3.0 3.2 3.40
2
4
6
8
10
12
Norm
alize
d co
uplin
g le
ngth
Sx
Sx ( m )
hg=10nm hg=30nm hg=50nm
(b)(a)
Sub-wavelength field confinement 1~2 orders of magnitude higher than long-range SPP waveguides
High-density 3D photonic integration( packing density increased by nearly 60 times over insulator/metal/insulator waveguides)
Finite dimensions in both directions, enabling multilayer, 3-dimensional (3D) integrated circuits
COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition
*Y. S. Bian, Z. Zheng, Optics Express 17, 21320-21325 (2009).
School of Electronic and Information Engineering
Dielectric-loaded SPP waveguides
Relatively tight confinement of light (subwavelength scale)
Relatively long propagation distance ( tens of microns)
Low-index DLSPP waveguides Low-index polymer (n~1.5) Low loss Relatively large geometry size (e.g.600nm×600nm)
Not suitable for high integration
High-index DLSPP waveguides
High-index dielectric (n~2 & n~3.5) Stronger confinement Compact, Si fab process
compatible, suitable for integration
Huge loss
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Design of DLSPP waveguide with a holey ridge
w
h
εm
εc
ha
wa
w
h
εm
εc εd
εd
(b)(a)
y
xz
0
1
Air
Si
(a)
SiO2SiO2 Si
Ag Ag
(c)
SiO2SiO2
Air
Si
(b)
*Y. S. Bian, Z. Zheng, Optics Express, To be published.
COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition
Strong field enhancement in the nanohole due to the slot effect
Geometry
Field distribution
School of Electronic and Information Engineering
Design of dielectric-loaded waveguide with a holey ridge
-0.2 0.0 0.2 0.4 0.60.0
0.5
1.0
E y
(m) y
-0.2 0.0 0.2 0.4 0.60.0
0.5
1.0
E y
(m)
y-0.2 0.0 0.2 0.4 0.6
0.0
0.5
1.0
(m)y
E y
-0.2 0.0 0.2 0.4 0.60.0
0.5
1.0
E y
(m)
y
-1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
(m)x
E y
-1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
(m)x
E y
-1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
E y
x (m)
-1.0 -0.5 0.0 0.5 1.00.0
0.5
1.0
E y
x (m)
(l)(k)(j)(i)
(h)(g)(f)(e)
1
0
(a) ha=10nm (c) ha=50nm (d) ha=100nm(b) ha=30nm
Even stronger field enhancement with a shallow and wide, low-index nanohole
*Y. S. Bian, Z. Zheng, Optics Express, to be published.
Field distributions at different nanohole widths
School of Electronic and Information Engineering
Design of dielectric-loaded waveguide with a holey ridge
High optical power and strong optical intensity in the nanohole
*Y. S. Bian, Z. Zheng, Optics Express, To be published.
0 30 60 90 120 1500.0
0.1
0.2
0.3
0.4
0.5 wa=10nm wa=30nm wa=50nm wa=100nm wa=150nm
ha (nm)
NOP
0 30 60 90 120 150
10-1
100
101
NAOI
ha (nm)
(a) (b)
0 30 60 90 120 15050
100
150
200
FOM
wa (nm)0 30 60 90 120 150
0.0
0.5
1.0 ha=10nm ha=30nm ha=50nm ha=100nm ha=150nm DLSPP
wa (nm)
A eff
/A0
0 30 60 90 120 150
1.6
2.0
2.4
2.8
Lp (m)
N eff
0
50
100
150
200
wa (nm)
(c)(a) (b)
High optical power and strong optical intensity in the nanohole Loss reduction achieved with small sacrifice in the mode area Improved figure of merit (FOM) with a shallow and wide air nanohole
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Nanolasers
The first laser (1960)
Nanotechology
Dielectric nanowire lasers [1]
~ diffraction limit
Plasmon nanolasers << diffraction limit
2D [2] 3D [3] Directional emissions
similar to the FP lasers High field confinement in
the gain media region Low-threshold operation
[1] Nature 421, 241-245 (2003).
[3] Nature 460, 1110-1112 (2009). [2] Nature 461, 629-632 (2009).
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2D plasmon nanolasers
Hybrid plasmonic waveguides Plasmon nanolaser
Low loss propagation Subwavelength
confinement
A lower index buffer (e.g. air) helps to further enhance the field enhancement in that region
An air gap is impossible to fabricate
r
h
rCdS
Ag n=-9.2+0.3i n=1.4 n=2.4
MgF2
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r r
MgF2
Ag tm h rCdS
y
xz
Design of coplanar plasmon nanolaser
Based on an edge-coupled hybrid plasmonic waveguide Strong field enhancement and low loss caused by the air gap Easy to fabricate Edge plasmonic mode Low pump threshold
λ=490nm, tm=2r, h:2~30nm
Air gap
0
1
*Y. S. Bian, Z. Zheng, 2010 Frontiers in Optics
0 5 10 15 20 25 30
100
101
h (nm)
Th
res
ho
ld (
m)
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h rrctm
1
0
Round corner effect for the plasmon laser
*Y. S. Bian, Z. Zheng, 2010 Frontiers in Optics
COMSOL settings Perpendicular waves of RF module- mode analysis Scattering boundary condition
A strong field enhancement occurs in the gap region The enhancement is further strengthened in the center of the gap The pump threshold shows a monotonical reduction with increased radius Compared to the case with sharp corners, the threshold could be lowered by 50% at
appropriate corner radius
0 10 20 30 40 50 600.5
1.0
1.5
2.0
2.5
3.0
rc (nm)
Thre
shol
d (
m)
School of Electronic and Information Engineering
Integrated plasmonic sensors w/ nanostructure
Conventional plasmonic sensing device
On-chip SPR sensor based on nanohole array and microfluidic
Nature Biotech 26, 417-426 (2008)
Target molecular diffusion rate <<Binding or reaction rate Target depletion zone
Mass transport limitation
Colinear optical detection Denser integration Smaller footprint Multiplexing biosensing High sensitivity
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Plasmonic lens
Appl. Phy. Lett. 91, 061124 (2007) Nano Lett. 9, 235-238 (2009)
Optical field gradient
Plasmonic microzone plate lens Plasmonic slits array lens
Trapping and manipulating targets
Subwavelength focusing High field intensity Large field gradient
Optical force
Focused beam or evanescent field
Large optical force
School of Electronic and Information Engineering
Proposed plasmonic nano-slit array
Optimized nano-slit structure for trapping in micro-fluidic
Divergent beam focused beam w1 = 250 nm w1 ,w2 = 50, 62 nm w1 ,w2, w3= 50, 62,160 nm
Hz of TM mode
Focal length f ~ 0.6 m
*X. Zhao, Z. Zheng, 2010 Frontiers in Optics
Optical field gradient
Trapping and manipulating targets Optical force
Focused beam or evanescent field
School of Electronic and Information Engineering
Optical gradient force of nano-slit lens
A
j
jtijti dSnTF
tjihtjihtij trHtrHtrEtrET ,,,, 00
' '
''0''0 ,,,,2
1
i itiihtiihij trHtrHtrEtrE
Maxwell stress tensor
Input power density=1.28mW/mm2
Time average optical force
Sensing object: nanorods with a diameter of 50 nm
When X=0, Y> f attractive force Y<f repulsive force
0.2 0.6 1.0 1.4 1.8 2.2-6.0x10-14
-4.0x10-14
-2.0x10-14
0.0
2.0x10-14
4.0x10-14
6.0x10-14
8.0x10-14
Opt
ical
forc
e (N
/m)
Y position of the nanorod (m)
x=0 x=0.3 x=0.6
attractive force
repulsive force
School of Electronic and Information Engineering
Impact and effect of slit in micro-fluidic
• Optical force could increase target concentration near focal point • More target molecular diffused to the sensing surface
Alleviate mass transport limit
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Conclusions
• Design and optimization of the nanophotonic devices are critical in realizing advanced photonic integrations in the future.
• Comsol can be used for simulating various types of nanophotonic devices involving different materials and dimensions.
• Increased functionalities of the nanophotonic devices also demand simulators capable of handling complex multiphysics simulations.
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Thank you!