Simulations of nanophotonic waveguides and devices using ...

School of Electronic and Information Engineering

Simulations of nanophotonic waveguides and devices using COMSOL Multiphysics

Zheng Zheng


Beihang University 37 Xueyuan Road, Beijing 100191, China

Presented at the COMSOL Conference 2010 China

http://www.comsol.com/conf_cd_2011_cn


Acknowledgement Yusheng Bian Lin An Xin Zhao Muddassir Iqbal Ya Liu Wei Li Tao Zhou (NJIT) Jiangtao Cheng (Penn State Univ.) …


Simulation of dielectric waveguides and optic fibers using COMSOL

Simulation of surface plasmon

polariton (SPP) waveguides and devices using COMSOL


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


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).


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).


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).


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).


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


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)


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


Design of single-polarization, single-mode PCF

*L. An, Z. Zheng, Optics Communications 282, 3266-3269 (2009)

Intensity distribution Dispersion optimization


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)


Highly nonlinear holey fiber with a high index slot core

*L. An, Z. Zheng, Journal of Optics, 115502 (2010).


Proposed structure



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




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



Simulation of dielectric waveguides and optic fibers using COMSOL

Simulation of surface plasmon

polariton (SPP) waveguides and devices using COMSOL


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


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)


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.


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)


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


*Y. S. Bian, Z. Zheng, Optics Express 17, 21320-21325 (2009).


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


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.


Strong field enhancement in the nanohole due to the slot effect

Geometry

Field distribution


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


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


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).


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


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)


h rrctm

1

0

Round corner effect for the plasmon laser

*Y. S. Bian, Z. Zheng, 2010 Frontiers in Optics


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)


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


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


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


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


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


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.


Thank you!

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