Daniel Mittleman Electrical & Computer Engineering

Rice University

Tapered plasmonic waveguides for

terahertz radiation

Terahertz + plasmonics

• Plasmons: an effective strategy for confining light

• Terahertz examples:

• Sommerfeld waveguide

• slot waveguide

• Field enhancement?

Plasmons

metallization pattern on a surface

guided surface plasmon wave

Electrons in a metal: an incompressible fluid

a tapered metal nanowire:

calculated plasmon intensity:

Nanostructures can be used for transforming a propagating surface plasmon into a nanolocalized plasmon.

Plasmons for subwavelength confinement of electromagnetic waves

How about for terahertz waves?

THz receiver (detects only vertical polarization)

to lock-in amp.

Chopper

Vertical needle (excitation by scattering)

Movable stage

THz transmitter (emits horizontal polarization)

“Sommerfeld wave” – a radially polarized mode (ca. 1899)

A guided wave on a metal wire

0 5 10 15 20 25 30

y = −3 mm

Ampli

tude

(arb

. unit

s)Delay (ps)

y = +3 mm

Wang and Mittleman, Nature, 432, 376 (2004).

scan the receiver position…

0 5 10 15 20 25 30

y = −3 mm

Am

plitu

de (a

rb. u

nits

)

Delay (ps)

y = +3 mm

…at a fixed delay

Imaging the radially polarized guided mode

Wang and Mittleman, Nature, 432, 376 (2004).

x position (mm)

y po

sitio

n (m

m)

-10 -5 0 5 10 -10

-5

0

5

10

experiment

Finite Element Method (FEM)

simulation

A finite element simulation of a Sommerfeld wave.

Plasmon mode dispersion diagram

0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0 25µm dia. Al wire Flat Al surface

x1016

ω (s

-1)

k (m-1)x108

ωsp

in air

0 10 20 300

3

6

9

ω (s

-1)

k - k0 (m-1)

x1013

Dispersion diagrams for flat and cylindrical plasmons

K. Wang and D. Mittleman, Phys. Rev. Lett., 96, 157401 (2006).

Phase velocity of the surface plasmon

× 18 µm diameter

∆ 51 µm diameter

• 813 µm diameter

0.0 0.1 0.2 0.3 0.4 0.50.995

0.996

0.997

0.998

0.999

1.000

1.001

v p / c

Frequency (THz)

Wire waveguides: bending loss

0 5 10 150

5

10

15

20

Tran

smiss

ion

(%)

Radius of curvature (cm)

90º bend transmitter

receiver

Curved wire waveguide: a model for bending loss

Astley et al., Opt. Lett. 35, 553 (2010)

M. Awad, M. Nagel, and H. Kurz, Appl. Phys. Lett. 94, 051107 (2009).

Y. B. Ji, E. S. Lee, J. S. Jang, and T.-I. Jeon, Opt. Express 16, 271 (2008).

N. C. J. van der Valk and P. C. M. Planken, Appl. Phys. Lett. 81, 1558 (2002).

Tapered wires: much recent interest

S. Maier, S. Andrews, L. Martin-Moreno, & F. Garcia-Vidal, Phys. Rev. Lett. 97, 176805 (2006).

J. Deibel, M. Escarra, N. Berndsen, K. Wang, D. M. Mittleman, Proc. IEEE 95, 1624 (2007).

x

z scattering probe

4.7° 500 μm

THz • Probe tip radius ~10 µm • Radiation scatters off tip

• Detects Ez field component

• Subwavelength resolution

• Modulated for high SNR and increased resolution

• Spatially-resolved pattern

Laser

radial THz emitter

wire waveguide

translation stage

optical delay and fiber coupler

THz receiver

Our approach: scattering probe imaging

Astley et al., J. Appl. Phys. (2009)

First step: an untapered wire waveguide

FWHM ~ 630 µm

-4 -2 0 2 4

0

1

2

3

4

5

-4 -2 0 2 4

0

2

4

THz

Am

p. (a

rb. u

nits

)

Position (mm) 0.00 0.25 0.50

0

1

2

3

4

5

THz

Am

p. (a

rb. u

nits

)

z Position (mm)

1/e ~ 130 µm

LATERAL scan LONGITUDINAL scan

-4 -2 0 2 4

0

1

2

3

4

5

THz

Ampl

itude

(arb

. uni

ts)

Position (mm)

FWHM ~ 30 µm

Next step: a tapered wire waveguide

0.00 0.25 0.50

0

1

2

3

4

5

THz

Amp.

(arb

. uni

ts)

Z Position (mm)

1/e ~ 9 μm

3D confinement

Confinement in all three dimensions

-100 -50 0 50 1000.0

0.5

1.0

THz

Ampl

itude

(arb

. uni

ts)

x position (µm)

Simulation vs. experimental result

Astley et al., Appl. Phys. Lett. (2009)

Better than λ/100

waveguide alone

-100 -50 0 50 1000.0

0.5

1.0

THz

Ampl

itude

(arb

. uni

ts)

x position (µm)

waveguide + measurement

probe

0 5 10 15 20

-200

0

200

-200

0

200

400-200

0

200

400

(c)

Aver

age

Curre

nt (p

A)

Time (ps)

(b)

(a)

THz Beam E

E

E Parallel Plate Waveguide

Parallel plate metal waveguides

R. Mendis and D. Grischkowsky, Opt. Lett. 26, 846 (2001).

0.0 0.2 0.4 0.6 0.8 1.00.01

0.1

1

Fiel

d am

plitu

de

Frequency (THz)

cavity mode

H2O vapor

wav

egui

de c

utof

f

1 mm

THz beam

Parallel-plate metal waveguide

Resonator

R. Mendis et. al, Apl. Phys. Lett. 95, 171113 (2009).

RF and Microwave THz infrared & visible

Plasmon mode

Plasmons vs. TEM modes

y

x ˆ||

B yˆ||

E x

Relevant length scales: wavelength plasmon decay length into air geometrical parameters:

• plate width • plate spacing

TEM mode

ETHz THz receiver

w

b

L THz emitter

1 mm aperture Experiment: image the spatial mode at the output of the waveguide:

• Highly polished Al plates • Adjustable separation • 1 mm aperture at detector • Vertically polarized input

x

y

x

y

w = 10 cm w = 1 cm

input THz beam

(plate width >> beam size)

Near-field characterization of the output

-60 -40 -20 0 20 40 600.0

0.2

0.4

0.6

0.8

1.010 cm-wide PPWG

b = 10 mm b = 5 mm b = 2 mm

THz

signa

l am

plitu

de (a

rb. u

nits

)

x (mm)

(a)

2-D map Horizontal profile

Wide plates: equivalent to free-space diffraction in one dimension

(a)

(b)

-8 -6 -4 -2 0 2 4 6 80

2

4

6

8 separation = 10 cm separation = 5 cm

THz

ampl

itude

(arb

. uni

ts)

y (mm)

(c)

2-D map Vertical profile

Wide plates: hybrid mode

smaller plate separation = stronger coupling of plasmons across the gap

Narrow plates: plasmons at the corners

• enhanced mode confinement • mutual coupling of edge plasmons

-60 -40 -20 0 20 40 60

x (mm)

1 cm wide PPWG

b = 10 mm

b = 5 mm

b = 2 mm

0 2 4 6 8 10 12 14 16

40

60

80

100

Ener

gy co

nfine

men

t (%

)

plate separation (mm)

Metal

Air

Metal

% = +

Small plate separation: – Enhanced plasmonic

modes at the edges. – Strong coupling between

edge modes confine the guided modes.

– Significant lateral confinement.

Confinement improves as plate separation decreases

Tapered slot waveguide: scattering probe imaging

Sensitive to the z component of ETHz

V. Astley, et al., Journal of Applied Physics, 105, 113117 (2009).

ETHz

scattering probe

THz receiver x y

z

Sub-wavelength output aperture: use scattering probe imaging technique

2D field confinement

0 50 100 150-400

-200

0

200

400

z (µm)

x (µ

m)

xz plane

xy plane -10

0

10-40 -20 0 20 40

x (µm)y (

µm)

Mode area ≈ λ2 / 38,000

Ez is antisymmetric:

H. Zhan, et al., Optics Express, 18, 9643-9650 (2010).

-200 -100 0 100 2000.00

0.25

0.50

0.75

1.00 wout = 100 µm, bout = 110 µm wout = 40 µm,

bout = 50 µm wout = 10 µm,

bout = 18 µm

E z (a

rb. un

its)

x (µm)

2D sub-wavelength field confinement

Best result so far: λ / 250

H. Zhan, et al., Optics Express, 18, 9643-9650 (2010).

Confinement without spectral distortion

0 5 10 15 20-2

-1

0

1

2

E z (ar

b. u

nits

)

Delay (ps)

untapered tapered

0.0 0.1 0.2 0.3 0.4 0.5 0.60.0

0.2

0.4

0.6

0.8

1.0

Spec

trum

am

plitu

de (a

rb. u

nits

)

Frequency (THz)

untapered

tapered

No significant bandwidth limitations or phase distortion!

Scattering probe imaging: guided plasmons

end-on view

open area: 100 µm x 100 µm

x position (mm)

y po

sitio

n (m

m)

Quantifying the field enhancement

K. Iwaszczuk, et al., Opt. Express 20, 8344 (2012)

More than 20 times enhanced!

Acknowledgements

Dr. Rajind Mendis Marx Mbonye Daniel Nickel Jingbo Liu Kimberly Reichel Nick Karl Victoria Astley