Dielectric properties of materials at

THz and sub-THz frequencies

Welcome to the National Physical Laboratory

Mira Naftaly

❑Dielectric properties, quantities and units

❑Technologies for broadband dielectric measurements at THz and sub-THz frequencies

❑Dielectric processes in materials at THz and sub-THz frequencies

❑Low-loss materials at THz and sub-THz frequencies

2

Dielectric properties, quantities

and units

3

“Dielectric” quantities

• Complex permittivity: 휀′ + 휀′′

• Loss factor or tan-delta: tan 𝛿 =𝜀′′

𝜀′

“Spectroscopic” quantities

• Absorption coefficient: 𝑎 𝐿−1

• Extinction: 𝑘• Refractive index: n

Conversion between quantities

𝑘 =𝑐

4𝜋𝑓𝛼

휀′ + 휀′′ = 𝑛 + 𝑖𝑘 2 = 𝑛2 − 𝑘2 + 𝑖 2𝑛𝑘

𝑛 = 휀′ + 𝑘2 = Τ1 2 휀′ + 휀′2 + 휀′′2 1/2

𝑘 =휀′′

2𝑛

tan 𝛿 =휀′′

휀′=

2𝑛𝑘

𝑛2 − 𝑘2

4

Frequency and wavelength unit

conversion

5

Frequency

(THz)

Wavelength

(m)

Wavenumber

(cm-1)

Energy

(meV)

= c/ = /c eV = hc/108

1 299.8 33.35 4.136

299.8 1 10000 1240

0.02998 10000 1 0.1240

0.2418 1240 8.065 1

6

❑Dielectric properties, quantities and units

❑Technologies for broadband dielectric measurements at THz and sub-THz frequencies

❑Dielectric processes in materials at THz and sub-THz frequencies

❑Low-loss materials at THz and sub-THz frequencies

Technologies for broadband

dielectric measurements

▪ Time-domain spectroscopy

▪ Frequency-domain spectroscopy

▪ VNA-based spectroscopy

▪ Fourier transform spectroscopy

7

8

THz spectrometer instruments

Closed-loop• TDS – Time-domain spectrometer (pulsed)

• FDS – Frequency-domain spectrometer (CW)

• VNA – Vector network analyser (CW)

➢ Coherent detection measures field amplitude and phase

Open-loop• FTS – Fourier transform spectrometer (CW)

• Scanning spectrometer – any combination of a tunable

source and a broadband detector

➢ Incoherent detection measures field intensity

Coherent systems strongly dominate broadband terahertz measurements

Open-loop and closed-loop

systems

9

emitter detectoroptics

An open loop system consists of:

• an emitter and a detector which operate independently;

• optics to guide radiation from emitter to detector.

emitter detectoropticspump

source

A closed loop system consists of:

• an emitter and a detector which are activated by the same source;

• optics to guide radiation from emitter to detector.

Time-domain spectrometer (TDS)

TDS is the dominant device for broadband THz measurements

– accounting for >90% of published results.

TDS components:

▪ Pump laser – femtosecond pulsed

▪ Differential variable delay

▪ THz emitter – photoconductive antenna (most common)

▪ THz detector – photoconductive antenna (most common)

▪ THz beam guiding optics

THz

emitter beam optics detector

pump laser probe beam

pump beam

delay

TDS performance

• Broadband operation

• One-shot spectral acquisition

• Large bandwidth:

• 4-5 THz as standard

• up to 20 THz is possible

• Frequency resolution 1-10 GHz

10

11

Photoconductive THz emitters

and detectors

VDC

THz polarization

pump

beam

THz

beam

probe

beam

THz

beam

A

AA

Emitter Detector

THz

beamTHz

beam

THz polarization

TDS operationF

ield

am

plit

ude

Time

0

THz

Probe

a

Uses a single-cycle THz pulse

Data is acquired in time domain

by scanning the probe pulse over the THz pulse using variable time-delay.

probe pulse length

pump pulse length signal proportional to THz field

coherent detection

𝑆𝑖𝑔𝑛𝑎𝑙 (𝑡0) ∝ න−∞

∞

𝐼𝑝𝑟𝑜𝑏𝑒 𝑡 − 𝑡0 𝐸𝑇𝐻𝑧 𝑡 𝑑𝑡

Spectral data from TDS

13

Amplitude and phase spectra obtained via Fourier Transform.

0 10 20 30 40 50 60-80

-60

-40

-20

0

20

40

Sig

nal (m

V)

Delay (ps)

main peak

system artifacts

a

0 1 2 3 4 51E-7

1E-6

1E-5

1E-4

1E-3

-60

-40

-20

0

Am

plit

ude (

arb

.)

Frequency (THz)

bsinusoidal

oscillations

due to system

artifacts

noise floor

amplitude Phase (

rad)

phaseFFT

Time domain Frequency domain

Parameter extraction in TDS

Most TDS measurements are performed to obtain n & !

Calculating refractive index and absorption coefficient of material from TDS data:

Field amplitude: Eref & Esample

Phase: 𝜙ref & 𝜙sample

Refractive index: n

Absorption coefficient: [L-1](units: 1/L)

Sample thickness: d [L]

𝑛 𝜔 = 1 +𝜙𝑟𝑒𝑓 −𝜙𝑠𝑎𝑚𝑝𝑙𝑒 𝑐

2𝜋𝑓𝑑(1)

𝑇(𝜔) = 1 −𝑛 − 1 2 + 𝑘2

𝑛 + 1 2 + 𝑘2(2)

𝑘 𝜔 =𝛼𝑐

2𝑓(3)

𝛼 𝜔 = −2

𝑑ln 𝑇

𝐸𝑠𝑎𝑚𝑝𝑙𝑒

𝐸𝑟𝑒𝑓(4)

Note: when k is non-negligible, Eqs. 2-4 must be calculated iteratively.

Example: lactose monohydrate

Time-domain data

Calculated

optical

properties0 10 20 30 40 50

-2

-1

0

1

a

Reference

Lactose

Sig

nal (a

.u.)

Time (ps)

0.0 0.5 1.0 1.5 2.0 2.51E-3

0.01

0.1

1

reference amplitude

lactose amplitude

Am

plit

ud

e (

a.u

.)

Frequency (THz)

-10000

-5000

0 reference phase

lactose phase

Ph

ase

b

0.0 0.5 1.0 1.5 2.0 2.50

20

40

60

80

100c

Absorp

tion c

oeffic

ient (c

m-1

)

Frequency (THz)

1.5

1.6

1.7

1.8

1.9

Re

fra

ctive

in

de

x

Lactose

absorption

coefficient

refractive

index

Frequency-

domain data

(via FFT)

16

Frequency-domain spectrometer

(FDS)

FDS has a narrower measurement bandwidth than TDS, but

has the advantage of much higher frequency resolution.

FDS components:

▪ Two stabilised CW lasers with offset wavelengths

- THz is generated as the difference frequency

▪ THz emitter – photoconductive mixer

▪ THz detector – photoconductive mixer

▪ THz beam guiding optics

FDS performance

• Broadband operation

• Frequency scanning

• Bandwidth: up to 2.5 THz

• Frequency resolution <50 MHz

THz

emitter

beam

optics

detectorlaser 2optical fibres

laser 1

Example: whispering-gallery-

mode resonance

Phase-sensitive (coherent) detection gives rise to phase “fringes”

(these are not standing waves!)

Therefore an envelope function must be applied to the data.

617.6 617.8 618.0 618.2 618.4

-3

-2

-1

0

1

2

3

4

Reference

Sample

Ref. envelope

Sample envelope

Photo

curr

ent (n

A)

Frequency (GHz)

a

617.6 617.8 618.0 618.2 618.41E-4

0.001

0.01

0.1

1b

Tra

nsm

issio

n

Frequency (GHz)

FWHM = 42 MHz

Frequency-domain data Calculated transmission

(Figure courtesy of Dominik Vogt, University of Auckland, New Zealand)

VNA-based FDS

1818

VNA-based spectrometers have a narrower measurement

bandwidth than TDS or FDS, but higher frequency resolution.

Components:

▪ VNA with frequency extenders

▪ Horn antennas or other optics

▪ All-electronic

VNA performance

• Frequency scanning

• Bandwidth: up to 1.5 THz

• Frequency resolution <0.1 MHz

Much more

information in

other talks!

VNA

extenders with horns

Fourier Transform Spectrometer

(FTS)

FTS measures incoherently. It is an interferometric device.

Its major advantage is an extremely broad bandwidth.

FTS components:

▪ Broadband source (e.g. Hg lamp)

▪ Broadband power detector

▪ Optics

▪ Precision scanning mechanism

Michelson Mach-Zender

mirror 1

mirror 1

mirror 2

mirror 2

beam splitter

beam splitter 1

beam splitter 2

source

source

detector

detector

FTS performance

• Broadband operation

• Single-scan full-spectrum

• Bandwidth:

• 1-180 THz standard

• 0.05-840 THz available

• Frequency resolution

• 1 GHz standard

• <0.1 GHz available

FTS operation

2 4 6 8 10 12 14 16-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Sig

nal (a

.u.)

Displacement (mm)

standing

waves

5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issio

n

Frequency (THz)

SiC

Data is acquired as an interferogram

FFTTransmission is calculated by

1. Taking FFT

2. dividing by reference

• Oscillations are etalon fringes due

to standing waves in the sample.

• Fringes disappear when the

sample has strong absorption

Parameter extraction in FTS

Step 1: n is extracted from the fringe spacing:

f = c/2nd (ideal case)

Step 2: is extracted from the etalon

transmission function:

𝑇 𝑓 = 𝐼𝑇(𝑓)/𝐼0(𝑓) =1

ℳ+ℱ sin2 𝛽𝑑

ℱ 𝑓 =4𝑅

1 − 𝑅 2

ℳ 𝑓 =1 − 𝑅𝑒−2𝛼𝑑

2

1 − 𝑅 2𝑒−2𝛼𝑑> 1

𝑅 𝑓 =𝑛−1 2

𝑛+1 2

𝛽 = 2𝜋𝑓𝑛/𝑐

Note: extracting n

from fringe spacing

is non-trivial!

Example: high-resistivity Si

2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

Ab

so

rptio

n c

oe

ffic

ien

t (c

m-1

)

Frequency (THz)

3.413

3.414

3.415

3.416

3.417

3.418

Re

fra

ctive

in

dex

Parameter extraction in FTS is not straightforward,

with many potential sources of error.

Comparative advantages –

a personal view

22

FTS

VNA

FDSTDS

Criteria

Science

• Bandwidth

• Frequency resolution

• SNR & dynamic range

• Unambiguous parameter extraction

• Accuracy & precision

Industrial

• Speed of measurement

• Ease of measurement

• Repeatability

• Size of instrument

• Suitability for in-line applications

• Cost

23

❑Dielectric properties, quantities and units

❑Technologies for broadband dielectric measurements at THz and sub-THz frequencies

❑Dielectric processes in materials at THz and sub-THz frequencies

❑Low-loss materials at THz and sub-THz frequencies

24

Very few materials are THz-transparent!

Absorption loss mechanisms

• Absorption by free charge carriers

• Absorption by lattice modes (phonons)

• Absorption via dielectric relaxations in polar materials

• Disorder-induced absorption in amorphous materials

Absorption by free charge

carriers

25

▪ Free charge carriers in the material give rise to complex conductivity which

is frequency-dependent.

▪ Complex conductivity in turn determines the value of the complex dielectric

constant.

►THz-transparent materials must have high resistivity.

The frequency dependence of complex conductivity is described by the

Drude model:

𝜎 𝜔 =𝜎0

1 − 𝑖𝜔𝜏𝑐=

𝜎0

1 + 𝜔2𝜏𝑐2 + 𝑖

𝜎0𝜔𝜏𝑐

1 + 𝜔2𝜏𝑐2

which gives the complex dielectric constant as:

휀 = 휀′ + 𝑖휀" = 휀∞ + 𝑖𝜎(𝜔)

𝜔= 휀∞ +

𝑖𝜎0𝜔(1 − 𝑖𝜔𝜏𝑐)

= 휀∞ −𝜎0𝜏𝑐

1 + 𝜔2𝜏𝑐2 + 𝑖

𝜎0

𝜔 1 + 𝜔2𝜏𝑐2

휀∞ - intrinsic dielectric constant (real)

𝜎0 - DC conductivity (real)

𝜏𝑐 - carrier relaxation time

26

Absorption and refractive index

according to the Drude model

Abs - low conductivity

Abs - high conductivity

Absorp

tion c

oeffic

ient

Frequency

RI - low conductivity

RI - high conductivity

Refr

active index

Note: free-carrier absorption is the only type

of loss mechanism which falls with frequency.

Absorption and dispersion

increase with conductivity.

27

Drude absorption and refractive index:

example

dots:

𝜎0 = 8.1 cm

circles:

𝜎0 = 9.0 cm

solid lines:

Drude model

M van Exeter & D Grischkowsky, Phys Rev B 41 (1990-I) 12140-12149

28

Absorption by lattice modes

(phonons)

▪ Resonant phonon absorption occurs when the incident frequency matches that of vibrational modes of the lattice.

▪ Narrow phonon absorption lines occur only in crystals.

▪ Phonon resonances clustered in broad frequency bands are termed Reststrahlen bands. These can occur in both crystalline and amorphous materials.

▪ At Reststrahlen frequencies the material is opaque, and its reflectivity is close to unity.

►THz-transparent materials must have phonon

frequencies above the THz band of interest.

29

Reststrahlen bands and refractive

index

▪ In materials that have a Reststrahlen band, the refractive index is nearly

always higher at frequencies below the band than it is above it.

▪ This is because the Reststrahen band signals the onset of ionic polarisability.

▪ At frequencies above the band, only electronic polarisability contributes to the

real permittivity.

▪ At frequencies below the band, both electronic and ionic polarisabilities

contribute to real permittivity.

▪ Real permittivity is related to polarisability via the Clausius-Mossotti equation:

휀′ − 1

휀′ + 2=𝑁𝑝

3휀0𝑝 – material polarisability

𝑁 – number of atoms or molecules per unit volume

휀0 – permittivity of free space

►In materials with a Reststrahlen band:

THz refractive index is higher than that in the visible.

Phonon absorption in crystalline

materials: examples

0.4 0.5 0.6 0.7 0.80

10

20

30

40

50

60

70

80

90

2.9

3.0

3.1

3.2

3.3

3.4

3.5

Ab

sorp

tio

n c

oe

ffic

ien

t (c

m-1

)

Frequency (THz)

GaSe

Re

fra

ctive

in

de

x

0.0 0.5 1.0 1.5 2.0 2.50

20

40

60

80

100

120

1.6

1.7

1.8

1.9

Lactose

Ab

sorp

tio

n c

oe

ffic

ien

t (c

m-1

)

Frequency (THz)

Re

fra

ctive

in

de

x

31

Absorption via dielectric relaxations in

polar materials

▪ Absorption via dielectric relaxations occurs in polar materials, i.e. materials that have

polarisable bonds.

▪ When an oscillating electromagnetic field interacts with polarizable bonds in a

material, it causes charge separation and creates dipoles which oscillate in response

to the field.

▪ At low frequencies these dipole oscillations are unhindered, and the material is

transparent.

▪ At higher frequencies the dipole motions are impeded by friction in the material.

▪ This results in a delayed response relative to the field, giving rise to absorption.

►THz-transparent materials must be non-polar.

The frequency dependence of the dielectric constant arising from the response time of dipoles is described by the Debye model:

휀 = 휀 ∞ +휀 0 − 휀 ∞

1 + 𝜔2𝜏𝑑2 + 𝑖

휀 0 − 휀 ∞ 𝜔𝜏𝑑

1 + 𝜔2𝜏𝑑2

휀 0 - DC dielectric constant

휀 ∞ - high-frequency dielectric constant

𝜏𝑑 - response time of the dipoles

Polar materials have large values of 휀 0 − 휀 ∞ .

32

Absorption and refractive index

according to the Debye model

Abs - strongly polar

Abs - weakly polar

Absorp

tion c

oeff

icie

nt

Frequency

RI - strongly polar

RI - weakly polar

Refr

active index

Absorption rises with frequency;

refractive index falls.

Absorption increases with

both 휀 0 − 휀 ∞ and 𝜏𝑑.

0 1 2 30

200

400

600

2

4

6

8

Absorp

tion c

oeffic

ient (c

m-1

)

Frequency (GHz)

Refr

active index

liquid water

Example: pure liquid water

Disorder-induced absorption in

amorphous materials

▪ Disorder-induced absorption

occurs in all types of amorphous

materials.

▪ Amorphous materials have

featureless THz absorption

spectra that rise with frequency

due to a broad continuum of

lattice modes.

▪ Disorder-induced absorption rises

with frequency: 𝛼(𝜔)𝑛(𝜔)=𝐾𝜔𝛽 ;

K is material-dependent; ~2.

▪ Spectral features are an indication

of crystallinity.

►THz-transparent materials

should be crystalline.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

5

10

15

20

25

1.90

1.95

2.00

2.05

2.10

2.15

Abs quartz

Abs silica

Absorp

tion c

oeffic

ient (c

m-1

)

Frequency (THz)

RI quartz

RI silica

Refr

active index

Example:

effect of disorder-induced

absorption –

quartz vs silica glass

34

Scattering loss

▪ In inhomogeneous materials scattering gives rise to (additional) transmission loss.

▪ Scattering is of particular concern in:

1. Porous materials (e.g. foams, ceramics);

2. Powders;

3. Pellets made of compressed powders;

4. Materials with rough surfaces;

5. Textured materials.

▪ Scattering increases with the size of the scattering centers.

In cases of a featureless loss edge, it is not possible to differentiate spectroscopically between scattering and absorption losses.

35

Scattering loss: examples

Y C Shen et al, Appl Phys Lett 92 (2008) 051103

M Franz et al, Appl Phys Lett 92 (2008) 021107

36

❑Dielectric properties, quantities and units

❑Technologies for broadband dielectric measurements at THz and sub-THz frequencies

❑Dielectric processes in materials at THz and sub-THz frequencies

❑Low-loss materials at THz and sub-THz frequencies

37

THz-transparent materials

Few materials are THz-transparent!

▪ Inorganic crystals

▪ Non-polar polymers

38

Inorganic crystals

▪ Carbon group crystals

• Diamond

• High resistivity silicon

• High resistivity germanium

• Hexagonal silicon carbide

▪ Oxides

• Quartz

• Sapphire

▪ Nitrides

• Aluminium nitride

• Gallium nitride

• Silicon nitride

39

Diamond C

Crystal

properties

Chemical formula

Crystal type

Crystal system

C

Isotropic

Cubic

Fdത3mOptical

properties

Transparency (visible)

Colour

Birefringence

Refractive index @ 590 nm

Band gap eV

YES

Colourless

NO

2.4175

5.47

Physical

properties

Density g/cm3

Moh’s hardness

3.515

10

0 5 10 15 200.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ab

so

rptio

n c

oe

ffic

ien

t (c

m-1

)Frequency (THz)

0 5 10 15 202.3770

2.3775

2.3780

2.3785

2.3790

2.3795

Re

fractive ind

ex

Frequency (THz)

40

Silicon SiHigh resistivity (undoped)

Crystal properties Chemical formula

Crystal type

Crystal system

Si

Isotropic

Cubic

Fdത3mOptical properties Transparency (visible)

Colour

Birefringence

Refractive index @ 1.55 m

Band gap eV

NO

Metallic grey

NO

3.4777

1.12

Physical properties Density g/cm3

Moh’s hardness

2.329

6.5

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

Absorp

tion

coe

ffic

ien

t (c

m-1

)

Frequency (THz)

0 2 4 6 8 10 12 14 16 18 203.415

3.416

3.417

3.418

3.419

3.420

Re

fra

ctive

in

de

x

Frequency (THz)

41

Germanium GeHigh resistivity (undoped)

Crystal

properties

Chemical formula

Crystal type

Crystal system

Ge

Isotropic

Cubic

Fdത3mOptical

properties

Transparency (visible)

Colour

Birefringence

Refractive index @ 2.8 m

Band gap eV

NO

Metallic grey

NO

4.052

0.66

Physical

properties

Density g/cm3

Moh’s hardness

5.323

6.0

0 2 4 6 8 100

5

10

15

20

Ab

so

rptio

n c

oe

ffic

ien

t (

cm

-1)

Frequency (THz)

0 2 4 6 8 104.002

4.003

4.004

4.005

4.006

4.007

4.008

4.009

4.010

Re

fractive ind

ex

Frequency (THz)

Hexagonal silicon carbide SiCCrystal properties Chemical formula

Crystal type

Crystal system

Polytypes

SiC

Uniaxial

Hexagonal

C46v-P63mc

4H-SIC; 6H-SIC

Optical properties Transparency (visible)

Colour

Birefringence

Refractive index @ 590 nm

Band gap eV

YES

Colourless

YES

o – 2.56

e – 2.60

3.23 (4H); 3.05 (6H)

Physical properties Density g/cm3

Moh’s hardness

3.21

9.5

0 2 4 6 8 10 12 14 163.1

3.2

3.3

3.4

3.5

3.6

o-ray

e-ray

Re

fra

ctive

in

de

x

Frequency (THz)

Tarekegne et al. Optics express 27 (2019): 3618-3628.

43

Quartz SiO2

Crystal

properties

Chemical formula

Crystal type

Crystal system

Polytypes

SiO2

Uniaxial

Trigonal

P312 ; P322

Optical

properties

Transparency (visible)

Colour

Birefringence

Refractive index @ 590 nm

Band gap eV

YES

Colourless

YES

o – 1.544

e – 1.553

8.4

Physical

properties

Density g/cm3

Moh’s hardness

2.649

7

0 1 2 3 4 5 60

2

4

6

8

10

12

o-ray

e-ray

Ab

so

rptio

n c

oe

ffic

ien

t (c

m-1

)

Frequency (THz)

0 1 2 3 4 5 62.05

2.10

2.15

2.20

2.25

2.30

o-ray

e-ray

Re

fra

ctive

in

de

x

Frequency (THz)

44

Sapphire Al2O3

Crystal properties Chemical formula

Crystal type

Crystal system

Al2O3

Uniaxial

Trigonal

R3c

Optical properties Transparency (visible)

Colour

Birefringence

Refractive index @ 590 nm

Band gap eV

YES

Colourless

YES

o – 1.7680

e – 1.7600

9.9

Physical properties Density g/cm3

Moh’s hardness

3.97

9

0 1 2 3 4 50

10

20

30

40

o-ray

e-ray

Ab

so

rptio

n c

oe

ffic

ien

t (c

m-1

)

Frequency (THz)

0 1 2 3 4 53.0

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

o-ray

e-ray

Re

fra

ctive

in

de

x

Frequency (THz)

Nitrides

Aluminium nitride AlN

0 2 4 6 8 100

5

10

15

20

25

o-ray

e-ray

Absorp

tion

coe

ffic

ien

t (c

m-1

)

Frequency (THz)

0 2 4 6 8 10

2.8

3.0

3.2

3.4 o-ray

e-ray

Re

fractive ind

ex

Frequency (THz)

Gallium nitride GaN Silicon nitride Si3N4

0 2 4 60

5

10

15

20

25

o-ray

e-ray

Absorp

tion

coe

ffic

ien

t (c

m-1

)

Frequency (THz)

0 2 4 63.0

3.1

3.2

3.3

3.4

o-ray

e-ray

Re

fractive ind

ex

Frequency (THz)

0 1 2 30

5

10

15

20

25

Absorp

tion

coe

ffic

ien

t (c

m-1

)

Frequency (THz)

0 1 2 32.74

2.75

2.76

2.77

2.78

Re

fractive ind

ex

Frequency (THz)

46

THz-transparent crystals

Crystal THz

refractive

index

Absorption

@ 1 THz

(cm-1)

Absorption

@ 3 THz

(cm-1)

Absorption

@ 10 THz

(cm-1)

Transparency

in the visible

Diamond

Silicon

Germanium

Silicon carbide (4H-SiC)

Z- cut Quartz

Z- cut Sapphire

2.38

3.42

4.01

3.13

2.11

3.1

0.1

0.1

0.2

0.1

0.2

1.0

0.12

0.1

1.3

0.4

1.2

9

0.27

0.3

20

6

45

68

Yes

No

No

Yes

Yes

Yes

47

Non-polar polymers

Polymers containing only C and H (or F) atoms

How to recognise non-polar polymers?

PolyethyleneAppearance: milky-white

High density polyethylene (HDPE)

Low density polyethylene (LDPE)

Linear low density polyethylene (LLDPE)

High molecular weight polyethylene (HMWPE)

Ultra high molecular weight polyethylene (UHMWPE)

PolypropyleneAppearance: colourless & transparent

Poly-methyl-pentene PMP (TPX)Appearance: colourless & transparent

Cyclo-olefin copolymer COCAppearance: colourless & transparent

52

Polystyrene Appearance: colourless & transparent

53

Polytetrafluoroethylene PTFE (Teflon) Appearance: bright white

54

Paraffin wax, jelly and liquid

▪ Alkanes whose formula is C2H2n+2 .

▪ Wax has chains of 20-40 atoms;

liquid has chains of 6-16 atoms;

jelly is a mixture of longer and shorter chains.

▪ Wax and jelly are both partially crystalline, and appear translucent.

▪ Liquid paraffin is colourless and transparent.

► Paraffins can be used as mounting or suspension media for a

wide variety of materials and powders, and as optical contact media.

55

Paraffin

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

2

4

6

1.47

1.48

1.49

1.50

wax

liquid

A

bsorp

tion c

oeffic

ient (c

m-1

)

Frequency (THz)

wax

liquid

Refr

active index

56

THz-transparent polymers

Polymer THz refractive

index (mean)

Absorption @

1 THz (cm-1)

Absorption @

3 THz (cm-1)

Absorption @

10 THz (cm-1)

Transparency

in the visible

LDPE

HDPE

PTFE

COC

PMP (TPX)

PP

PS

1.51

1.53

1.43

1.52-1.53

1.46

1.52

1.58

0.2

0.2

0.5

0.2

0.3

0.3

1.5

1.6

1.6

2.8

0.8

0.8

~1.5

2.5

~2

~3

>50

~2

~2.5

~3.5

~5

No

No

No

Yes

Yes

Yes

Yes

Paraffin liq.

Paraffin wax

1.47

1.49

0.5

0.8

1.7

4.2

NA

NA

Yes

No

Note: Polymers that are transparent in the visible and at THz have

similar refractive indices in both regions ( nvisible nTHz ).

This aids THz beam path alignment using visible light.

57

Thank you