Extreme confinement

and propagation

regimes of tHz surface

waves on planar

metallic waveguides

J. J. MangeneyMangeney11, , D. D. GacemiGacemi33, , R. R. ColombelliColombelli22 and A. and A. DegironDegiron22

11Laboratoire Laboratoire Pierre Pierre AigrainAigrain, UMR 8551, Ecole Normale Supérieure, France, UMR 8551, Ecole Normale Supérieure, France

22Institut Institut d’Electronique Fondamentale, UMR 86622, CNRS, d’Electronique Fondamentale, UMR 86622, CNRS, UnivUniv--Paris Sud, Paris Sud, FranceFrance

33 Laboratoire Laboratoire MatMatéériaux riaux et et Phénomènes Phénomènes Quantiques, UMR Quantiques, UMR 7162, CNRS, Université Paris, France7162, CNRS, Université Paris, France

Confinement of THz wavesConfinement of THz waves

• Integrated THz technology (high-speed electronic circuits,…)

• Imaging and spectroscopy of small objects

• Biological sensing

• …

� Requirement of highly confined THz waves

22

� Diffraction limit of THz waves ~150 µm

Plasmonic Concepts -> Sub-λλλλ confinement at optical frequencies

� Plasmonic for confining THz waves (<λλλλ)

� Can sub-λλλλ confinement be achieved at THz frequencies ?

Surface waves propagating at the interface between a

dielectric and a conductor.

Microfluidic channel

Dispersion relationDispersion relation

k =ω

c

εm

ε1+εm

1 2

THzTHzTHzTHz

Surface waves at the interface

of metal and dielectric :

OpticsOpticsOpticsOptics

� Surface wave’s properties highly change from optics to THz

33

Dispersion relationDispersion relation

k =ω

c

εm

ε1+εm

1 2

Re(ωωωω/c)ωωωω=ck

� Surface Plasmon Polariton

375 THz (λ=450 nm)

k

� Zenneck waves

375 THz (λ=450 nm)

1 THz (λ=300 µm)

δdiel=0.18 µm < λ

δair=63 mm >> λλλλ

ω p 2

� Challenge : achieve sub-λλλλ confinement of the THz surface waves

Optical rangeOptical rangeOptical rangeOptical range

THzTHzTHzTHz rangerangerangerange

44

PlanarPlanar metallicmetallic waveguidewaveguide

Yansheng Xu et al., MOTL. 43, 290, (2004).Akalin at al, IEEE VOL 54, N°6,2762 (2006).

� Single conductor deposited on thin dielectric layer

Yansheng Xu et al., MOTL. 43, 290, (2004).

Christopher Russell, et al., Lab Chip, to be published 2013

Treizebre, A, Int. J. Nanotechnol. 5, 784-795 (2008).

55

1/ Coupling between EM fields and the free electrons at the metal surface

2/ Interaction of the EM fields with the metal surface modified by the thin

dielectric layer.

� Physical mechanisms that bind the surface wave to the surface :

Akalin at al, IEEE VOL 54, N°6,2762 (2006).

� Extremey simple geometry adapted for complex integrated

schemes with high functionalities

OutlineOutline

�� Study of planar metallic waveguides to achieve electric field Study of planar metallic waveguides to achieve electric field

confinementconfinement

•• Planar metallic waveguides based on the coupling between EM fields and Planar metallic waveguides based on the coupling between EM fields and

free electrons at the metal surface free electrons at the metal surface (Simulation)(Simulation)free electrons at the metal surface free electrons at the metal surface (Simulation)(Simulation)

•• Planar metallic waveguides based on the interaction of the EM fields Planar metallic waveguides based on the interaction of the EM fields

with a metal surface modified by the thin dielectric layer with a metal surface modified by the thin dielectric layer (Simulation)(Simulation)

•• Planar metallic waveguides based on hybrid mode Planar metallic waveguides based on hybrid mode (Experiments(Experiments))

�� Study of the propagation regimes of planar metallic Study of the propagation regimes of planar metallic

waveguideswaveguides

66

Single Single Au Au stripestripe

Au: metal with finite conductivity

-2.5

0.0

2.5

5.0

y p

os

itio

n (

µm

)

0

1

1/ Coupling between EM fields and the free electrons at the metal

surfaceSingle Au stripe embedded in a homogeneous medium

77

Comsol MultiPhysics :

- Cross Section of the power

- Effective index of propagating modes

-5.0 -2.5 0.0 2.5 5.0-5.0

y p

os

itio

n (

µm

)

x position (µm)

-11 THz

� Existence of only one mode at 1 THz : radial field distribution

h=120 µm, w=50 µm h=50 µm, w=50 µm h=25 µm, w=25 µm h=10 µm, w=10 µm

tranversetranverse size of metal stripesize of metal stripe

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed

Po

we

r (

a.u

.)

Distance from the metal stripe (µm)

h:120 µm, w: 50 µm

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed

Po

we

r (

a.u

.)

Distance from the metal stripe (µm)

h:120 µm, w: 50 µm

h:50 µm, w: 50 µm

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

No

rmaliz

ed

Po

we

r (

a.u

.)

Distance from the metal stripe (µm)

h:120 µm, w: 50 µm

h:50 µm, w: 50 µm

h:25 µm, w: 25 µm

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed

Po

we

r (

a.u

.)

Distance from the metal stripe (µm)

h:120 µm, w: 50 µm

h:50 µm, w: 50 µm

h:25 µm, w: 25 µm

h:10 µm, w: 10 µm

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed

Po

we

r (

a.u

.)

Distance from the metal stripe (µm)

h:120 µm, w: 50 µm

h:50 µm, w: 50 µm

h:25 µm, w: 25 µm

h:10 µm, w: 10 µm

h:5 µm, w: 5 µm

h=5 µm, w=5 µm

h

w88

Influence of the Influence of the stripestripe sizesize

1.460

0.02

0.04

0.06 w=30µm

yx

h

m (

ne

ff)

w1.465

1.470

1.475

w=10µm

w=5µm

w=2µm

Re

(ne

ff)

Frequency : 1 THz

�The mode evolves into a highly confined solution as the

transverse dimensions of the metal waveguide tend to zero

Re(neff) ���� Field confinement ����

0.2 0.4 0.6 0.8 1.00.00

Im

Heigth h (µm)

0.2 0.4 0.6 0.8 1.00.00

Heigth h (µm)

1.4600.06w=20µmw=30µm

w=10µm

Im(neff) ���� Field confinement ����

99

A A perfectlyperfectly conductingconducting stripestripesupportedsupported by a by a dielectricdielectric layer layer

-2.5

0.0

2.5

5.0

y p

os

itio

n (

µm

)

0

1

2/ Interaction of the EM fields with the metal surface modified by

the thin dielectric layer

1010

Perfect electric

conductor

-5.0 -2.5 0.0 2.5 5.0-5.0

-2.5

y p

os

itio

n (

µm

)

x position (µm)

-11 THz

� Existence of only one mode at 1 THz : : radial field distribution

Influence of the Influence of the stripestripe sizesize

1.11

1.14

1.17

w=2 µm

w=5 µm

w=10 µm

ne

ff

Frequency : 1 THz

1111

0 2 4 6 8 10

1.08

Heigth h (µm)

�Shrinking the transverse size of perfect conducting stripe

increases the electric field confinement at THz frequencies

neff ���� -> Field confinement ����

Transverse Size Transverse Size rolerolew=30µm, h=10µm

0.5

1.0

Norm

aliz

ed p

ow

er

(a.u

,)

38µm 38µm 38µm 38µm ~~~~ λλλλ ////5555

AAAA

BBBB

w=2µm, h=20nm

0.6

0.8

1.0

No

rma

lize

d p

ow

er

(a.u

.)

407µm>407µm>407µm>407µm>λλλλ

BBBB

AAAA

A : A : A : A :

B : B : B : B :

Frequency : 1 THz

0 10 20 30 40 50

0.0

Norm

aliz

ed p

ow

er

(a.u

,)

y (µm)

2.2µm ~2.2µm ~2.2µm ~2.2µm ~ λλλλ /93/93/93/93

1212

BBBB

0 5 10 15 20 25 300.0

0.2

0.4

y (µm)

No

rma

lize

d p

ow

er

(a.u

.)

2.2µm ~2.2µm ~2.2µm ~2.2µm ~ λλλλ /136/136/136/136

BBBB

Frequency : 1 THz

D. Gacemi et al., Scientific Reports 3, 1369 (2013)

�Extreme confinement (sub-λλλλ ) of the electric field at THz

frequencies whatever the binding mechanisms

ExperimentalExperimental studystudyGuided –wave time domain THz spectroscopy

1313

3/ Hybrid Mode : a combination of both mechanisms

dielectric layer

metal stripe 1/ Coupling between EM fields and the

free electrons at the metal surface

2/ Interaction of the EM fields with the

metal surface modified by dielectric layer.

Surface mode Surface mode propertiespropertiesHorizontal component of E

D. Gacemi et al. Optics Express 20, 8466 (2012)

w=10 µm , t=200 nm, quartz substrate 250 µm

0 20 40 60 80 100 120 140 160 180 200

Am

plit

ude (

a.u

.)

z position (µm)

(b)

L1/e=64.5 µm

Vertical component of ED. Gacemi et al. Optics Express 20, 8466 (2012)

�Experimental determination of the mode confinement ~ λλλλ/101414

Propagation Propagation characteristicscharacteristics

2 mm

1.6 mm

1.2 mm

800µm

400µm

Am

plit

ude

(a

rbitra

ry u

nits)

Ref

1.0

4 6 8 10 12 14 16 18 20 22 24

Time (ps)

0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

Fre

que

ncy (

TH

z)

ky(mm

-1)

δL =1

ky

2 − k0

2

Decay Length

at 0.5 THz, δδδδL= 54 µm

1515

�Experimental determination of the mode confinement ~ λλλλ/10

Influence of the stripe widthInfluence of the stripe width

1.4

1.5

1.6

3.0

3.5 Y=1000µmY=500µm

ud

e (

a.u

.)

L=30µm

Yref

200 µm 30 µm

D. Gacemi et al. , Scientific Reports 3,

1369 (2013)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.1

1.2

1.3

1.4

Re

(neff)

Frequency (THz)0 2 4 6 8 10 12

1.0

1.5

2.0

2.5

L=200µm

No

rma

lize

d a

mp

litu

Delay (ps)

L=30µm

1616

� Reducing transverse size of a metallic structure provides a

powerful tool for confinement of THz surface waves

State of the artState of the art

metal tip apexes metallic nanoslits

Astley, V., App. Phys. Lett. 95, 031104-031106 (2009).

Liu, J. Appl. Phys. Lett. 100, 031101-031103 (2012).

Zhan, Opt. Express 18 ,9643-9650 (2010).

Zhan, H., JOSA B, 28, 558-566 (2011).

λλλλ/250

parallel-plate waveguides

J. B. Pendry et al., Science 305, 847 (2004)

C. R. Williams et al., Nature Photonics 2 (2008)

~λλλλ

corrugated metal

A.J. Huber, Nano Lett. 8, 3766-3770 (2008)

J.A. Deibel, Proc. of IEEE 95 1624-1640 (2007)

λλλλ/3000

metal tip apexes

SeoM. A. et al., Nature Photon. 3, 152-156 (2009).

SholabyM. et al, Appl. Phys. Lett. 99, 041110-041112

(2011).

λλλλ/25

metallic nanoslits

1717

� All design strategies involved reduced dimensions of metal

structures

Dielectric layer propertiesDielectric layer properties

2 mm

Ref

Am

plit

ude (

a. u.) 3.2 mm

200 µm

58 µm

0.12

0.16

0.20

1818

0 2 4 6 8 10 12 14 16 18 20

Am

plit

ude (

a. u.)

Time (ps)

Low losses (< 0.4 mm-1) up to 0.8 THz

� Performances of these single conductor waveguides are fully

compatible with key THz applications

Dispersion coefficient of 0.28 ps/mm

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.04

0.08

0.12

Im(n

eff)

Frequency (THz)

Distinct propagation regimesDistinct propagation regimes

)15.0(0 +≈ dieleff ελλD. Gacemi et al. APL 191117

(2013)

1919

� e=0, the mode is bound to the metal stripe because of its finite conductivitya variant of a Sommerfeld wave

� e ->λλλλeff/4, the dielectric film provides additional confinement to the mode. a Goubau mode

� e>λλλλ eff /4, the mode looses its confinement to the point that it ceases to be bound beyond a certain cut-off condition.

cut-off frequency

ConclusionsConclusions

�� Size Size effects can be used as a simple effects can be used as a simple formidable formidable tool for high tool for high

electric field confinement at THz electric field confinement at THz frequencies (frequencies (smaller than smaller than

λλ/100/100). ).

�� Au Au planar planar single conductor supported single conductor supported by thin layers of by thin layers of �� Au Au planar planar single conductor supported single conductor supported by thin layers of by thin layers of

dielectric show remarkable performances dielectric show remarkable performances

��Further works : Further works :

•• to to generalize this result into a unified theory (universalitygeneralize this result into a unified theory (universality).).

•• Develop BendsDevelop Bends, Mach, Mach--ZenderZender, , YY--splittingsplitting

2020

`collaborations`collaborations

� Institut d’Electronique Fondamentale

P. Crozat

� Institut d'Electronique de Microelectronique et de

Nanotechnologie

T. Akalin, J-F. Lampin, C. BlaryT. Akalin, J-F. Lampin, C. Blary

� Laboratoire Ondes et Matière d’Aquitaine

R. Yahiaoui

Funding support from:EMRP Researcher Grant NEW07

Research Project ‘THz Security’

Dispersion relationDispersion relation

0.6

0.7

0.8

0.9

1.0

Group velocity

Velo

city (

c) Phase velocity

0.08

0.12

0.16

0.20

Im(n

eff)

2222

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.4

0.5

0.6 Group velocity

Frequency (THz)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.04

Frequency (THz)

Maximum GVD of 5.6x10-22 s2/m Low Losses