dielectric properties of materials at thz and sub-thz .... naftaly... · to the field. at low...
TRANSCRIPT
![Page 1: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/1.jpg)
Dielectric properties of materials at
THz and sub-THz frequencies
Welcome to the National Physical Laboratory
Mira Naftaly
![Page 2: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/2.jpg)
❑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
![Page 3: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/3.jpg)
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
![Page 4: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/4.jpg)
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
![Page 5: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/5.jpg)
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
![Page 6: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/6.jpg)
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
![Page 7: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/7.jpg)
Technologies for broadband
dielectric measurements
▪ Time-domain spectroscopy
▪ Frequency-domain spectroscopy
▪ VNA-based spectroscopy
▪ Fourier transform spectroscopy
7
![Page 8: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/8.jpg)
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
![Page 9: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/9.jpg)
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.
![Page 10: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/10.jpg)
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
![Page 11: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/11.jpg)
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
![Page 12: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/12.jpg)
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
![Page 13: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/13.jpg)
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
![Page 14: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/14.jpg)
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.
![Page 15: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/15.jpg)
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)
![Page 16: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/16.jpg)
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
![Page 17: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/17.jpg)
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)
![Page 18: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/18.jpg)
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
![Page 19: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/19.jpg)
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
![Page 20: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/20.jpg)
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
![Page 21: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/21.jpg)
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.
![Page 22: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/22.jpg)
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
![Page 23: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/23.jpg)
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
![Page 24: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/24.jpg)
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
![Page 25: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/25.jpg)
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
![Page 26: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/26.jpg)
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.
![Page 27: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/27.jpg)
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
![Page 28: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/28.jpg)
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.
![Page 29: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/29.jpg)
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.
![Page 30: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/30.jpg)
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
![Page 31: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/31.jpg)
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 ∞ .
![Page 32: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/32.jpg)
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
![Page 33: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/33.jpg)
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
![Page 34: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/34.jpg)
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.
![Page 35: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/35.jpg)
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
![Page 36: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/36.jpg)
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
![Page 37: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/37.jpg)
37
THz-transparent materials
Few materials are THz-transparent!
▪ Inorganic crystals
▪ Non-polar polymers
![Page 38: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/38.jpg)
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
![Page 39: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/39.jpg)
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)
![Page 40: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/40.jpg)
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)
![Page 41: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/41.jpg)
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)
![Page 42: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/42.jpg)
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.
![Page 43: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/43.jpg)
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)
![Page 44: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/44.jpg)
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)
![Page 45: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/45.jpg)
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)
![Page 46: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/46.jpg)
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
![Page 47: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/47.jpg)
47
Non-polar polymers
Polymers containing only C and H (or F) atoms
How to recognise non-polar polymers?
![Page 48: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/48.jpg)
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)
![Page 49: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/49.jpg)
PolypropyleneAppearance: colourless & transparent
![Page 50: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/50.jpg)
Poly-methyl-pentene PMP (TPX)Appearance: colourless & transparent
![Page 51: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/51.jpg)
Cyclo-olefin copolymer COCAppearance: colourless & transparent
![Page 52: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/52.jpg)
52
Polystyrene Appearance: colourless & transparent
![Page 53: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/53.jpg)
53
Polytetrafluoroethylene PTFE (Teflon) Appearance: bright white
![Page 54: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/54.jpg)
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.
![Page 55: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/55.jpg)
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
![Page 56: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/56.jpg)
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.
![Page 57: Dielectric properties of materials at THz and sub-THz .... Naftaly... · to the field. At low frequencies these dipole oscillations are unhindered, and the material is transparent](https://reader034.vdocuments.net/reader034/viewer/2022052002/60155f8008380f7d6a2d7300/html5/thumbnails/57.jpg)
57
Thank you