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THz measurement systems
Giovanni Cavallo, Annalisa Liccardo and Leopoldo Angrisani
Dip.%di%Ing.%Elettrica%e%delle%Tecnologie%dell’Informazione,%Università%degli%Studi%di%Napoli%
Federico%II,%Naples,%Italy.%giovanni.cavallo@unina.it,%aliccard@unina.it,%angrisan@unina.it%
Gian Paolo Papari and Antonello Andreone
Dipartimento%di%Fisica,%Università%degli%Studi%di%Napoli%Federico%II,%Naples,%Italy.%
papari@fisica.unina.it,%andreone@unina.it%
!!!!!!!!
Abstract: The terahertz (THz) frequency region is often defined as the last unexplored area
of the electromagnetic spectrum. Over the past few years, the full access and exploitation of
this frequency window in order to close the so-called “THz gap” have been the objective of
intense research efforts both in academia and industry. Progress in this area has played an
important role in opening up the possibility of using THz electromagnetic radiation (T-
waves) in science and in many real-world applications. T-waves are not perceptible by the
human eye, are not ionizing and have the ability to cross many non-conducting materials
like paper, fabrics, wood, plastic and organic tissues. Moreover, the use of THz radiation
allows contactless and non-destructive analysis of the materials under investigation both by
study of their “fingerprint” via spectroscopic measurements and by high-resolution spatial
imaging operations, exploiting the see-through capability of T-waves. Such technology can
be applied in diverse areas, spanning from biology to chemical, pharmaceutical, and
environmental sciences, and everyday applications within a broad range of industries
including the medical, security, cultural heritage, manufacturing and aerospace sectors.
In this chapter we will present the typical architecture of measurement systems based on the
THz technology. We will show in some detail what are the parameters that define their
performance, the measurement methods and the related errors and uncertainty, focusing at
the end on the use of time domain spectroscopy for the evaluation of different material
properties in this specific frequency region.
Keywords: THz systems; measurement techniques; THz spectroscopy
!
1. Introduction to THz technology
Terahertz (THz) spectrum refers to the frequency domain ranging approximately from 100
GHz to 10 THz, corresponding to wavelengths from 3 mm to 30 µm (T-waves). The lower
limit is the microwave region, where mobile and satellite systems operate, and the upper
limit is the far infrared, widely used for optical communications. Figure 1 shows the
characteristics of the T-waves in the electromagnetic (EM) spectrum.
Figure 1. Position of the THz waves in the electromagnetic spectrum
Terahertz frequency region is often defined as the last unexplored area of the e.m. spectrum,
since it represents an area of convergence between electronics and photonics presently
lacking a mature technology. Since T-waves are located between microwaves and far
infrared waves, there are two enabling technologies that can be considered for their full
exploitation: electronics and photonics. Over the past twenty years, the full access and
exploitation of this frequency window have been the objective of intense research efforts
both in academia and industry, in order to close the so-called “THz gap”. T-waves present
many important properties potentially with a shattering impact both in science and in many
real-world applications. First, they are not perceptible by the human eye, are not ionizing
and have the ability to cross many non-conducting common materials like paper, fabrics,
wood, plastic and organic tissues. [1, 2]. Then, in terms of energy, they give access to the
rotational and vibrational modes of many molecules and macro-molecules. These modes can
be observed as absorption peaks in the THz spectra, providing the “fingerprint” of
unknown compounds via spectroscopic measurements. Finally, the use of THz radiation
allows contactless and non-destructive analysis of the materials under investigation, by
spatial imaging operations [3, 4, 5] with resolution higher than micro- and milli-metre
waves. THz science can be applied in so many and different areas of interest, from biology
to physical, chemical, pharmaceutical and environmental research, within a broad range of
industries including the medical, security, cultural heritage, manufacturing and aerospace
sectors.
The objective of this chapter is to provide readers who are not familiar with the basics of this
breakthrough technology, a brief review of the typical architectures of measurement
systems and the different sources and detectors that are commonly used, and looking at
possible applications. Successively, the will provide details on the parameters that define the
performance of a THz system, the measurement methods and the related errors and
uncertainty, focusing at the end on the use of time domain spectroscopy for the evaluation
of different material properties in this specific frequency region.
%
2. Overview of THz sources
Since its early beginning, one of the main hurdles for the development of THz technology
was a lack of solid-state signal sources, rather than detectors. Since T-waves are located
between microwaves and far infrared waves, there are two enabling technologies that can be
considered for their emission: electronics and photonics.
One can roughly group THz sources into two major operational families based on the
emission mode and the operating frequency: the continuous-wave (or CW) and the pulsed
(or time-domain, TD) mode. [1, 6]
Most of CW systems have been developed from the electronics side, in particular the
microwave field. The typical way to generate THz emission, in fact, is by scaling the
frequency by using frequency multipliers. These CW systems usually operate in the lower
frequency range of the THz band with maximum frequencies around 0.8 THz. Still, there are
some systems able to emit at frequencies as high as 5 THz, for example Backward-Wave
Oscillators and Quantum Cascade Lasers. Nevertheless, CW systems could be realized from
the photonics side too, since down-conversion is possible by mixing two lasers that work at
different frequencies. [6]
These systems are capable to operate at a single frequency and their emission is continuous
or modulated up to GHz frequencies. Therefore, CW systems are intrinsically narrowband
and have often a limited tunability with a high spectral resolution (~ 100 MHz) very useful
for gas phase spectroscopy. Moreover, CW systems typically provide output power higher
than pulsed sources. They can be passive or active; in the first case the system detects the
radiation emitted by the sample or body whereas, in the second case, the system illuminates
the sample and detects the reflected or transmitted radiation. CW systems can be used in
telecommunications applications and non-destructive evaluation (NDE) applications.
In pulsed or time-domain (TD) systems the distinctive element is an optical-to-THz signal
conversion technology, based on the generation and detection of an electromagnetic
transient having duration of few picoseconds by means of ultrafast pulsed lasers. [6]. The
short pulse is composed of many frequencies, which can be accessed with a Fourier
Transform of the pulse. Contrary to what happens in CW systems, pulsed systems can be
only active, are broadband in nature and don’t benefit of a continuous emission, so that they
are ideal to study ultrafast phenomena and for general purpose spectroscopic applications.
In Figure 2 the major differences between CW and pulsed systems are summarized.
Figure 2. Characteristics of the two major operational families for the THz sources: continuous-wave
and time-domain
In the following the most commonly used THz sources will be described, with some
emphasis on those based on electro-optical conversion, since they form the base for the
development of coherent systems operating in the time domain.
2.1. Backward-Wave Oscillator (BWO)
The Backward-Wave Oscillator is one of the most important and successful sources based on
up-conversion, allowing to extend the frequency of microwave sources to the THz range
using harmonic generation. The mechanism of a BWO is very similar to a travelling wave
amplifier, with the difference that it is a slow-wave structure, deliberately designed to
provide feedback. In particular, a BWO seems a sophisticated high vacuum diode, where the
cathode is heated by a low voltage heater and emits electrons accelerated by a high voltage
field travelling toward the anode. The electrons are collimated by a uniform external
magnetic field and pass over the slow-wave structure like a comb. This mechanism
produces the required quantity for the transfer of the kinetic energy of the electrons to an
electromagnetic wave that builds up from noise fluctuations. The most important advantage
of BWOs is their tunability, in fact the tuning rate is ~10 𝑀𝐻𝑧 𝑉 for low frequency devices,
rising to ~100 𝑀𝐻𝑧 𝑉 for devices operating at 1 THz or above. In addition, the output
power of each BWO varies quite rapidly with frequency and the useful tuning range is
approximately ±10% from the centre frequency. [7]
2.2. Quantum Cascade Laser (QCL)
The Quantum Cascade Laser belongs to the semiconductor-based THz sources. Over the
years, the enormous progress in the field of nanotechnology is making QCL the most
employed source in the CW family. In typical semiconductor lasers, light is generated by the
recombination of electrons in the conduction band with holes in the valence band, separated
by the gap of the active material. In QCLs, the presence of coupled quantum wells (QWs)
splits the conduction band by quantum confinement into a number of distinct sub bands. In
fact, the structure of a QLC is composed from hundreds to thousands layer semiconducting
layer (like InGaAs/AlGaAs) QWs [8]. Applied electric field, lifetimes and tunneling
probabilities of each level are fundamental to obtain population inversion between two sub-
bands in a series of identical repeat units. The output radiation frequency is defined by the
energy spacing (or QW thickness) of the lasing sub bands. The active regions are connected
with injector/collector structures allowing electrical transport through injection of carriers
into the upper laser level, and extraction of carriers from the lower laser level [9, 10].
2.3. Stimulated Terahertz Amplitude Radiation (STAR) emitters
STAR (Stimulated Terahertz Amplified Radiation) are compact and technologically simple
all solid-state emitters based on superconducting devices. Coherent electromagnetic waves
are generated at THz frequencies because of the Josephson effect between one or more
Superconductor-Insulator-Superconductor (SIS) junctions. Biased by a dc voltage V, a
Josephson junction is essentially a two-level system with energy difference of 2eV. As
Cooper pairs are tunnelling, EM waves are emitted from the junction . The radiation from a
single junction, however, is only about 1 pW and the frequency is below THz, limited in
conventional low Tc superconductors by the small superconducting energy gap. The
radiation power can be enhanced by fabricating an artificial array of Josephson junctions.
Nevertheless, the crucial aspect relies on the coherent emission of EM waves, which requires
synchronized oscillations of individual elements. The synchronization looks easier to
achieve for the so-called intrinsic Josephson junctions (IJJs) that are densely packed inside
high-quality single crystals of a high transition temperature Tc superconductor, usually
Bi2Sr2CaCu2O8+δ (BSCCO). IJJs are formed naturally in BSCCO where Bi-Sr-O layers between
the superconducting CuO2 layers act as a non-conducting barrier of nano-scale thickness
[11]. The main feature rendering the STAR emitters so attractive is the nature of the emitted
radiation, which is fairly robust, reasonably intense (~ µW) and characterized by high
spectral purity. Furthermore, the line width is so sharp that its observation is limited by the
resolution of the conventional spectrometers (0.25 cm-1). Then, the frequency of the THz
radiation can be tuned considerably, approximately up to 10-15% of the central frequency,
by varying the bias voltage applied to the N IJJs stack, even if its variable range of frequency
strongly differs from sample to sample, depending on the preparation conditions [12].
2.4. Photoconductive Antenna (PCA)
A photoconductive antenna is the most commonly used source in THz TDS systems. It
consists of a semiconductor substrate where two metallic electrodes are deposited and
separated by a gap of few microns. The substrate is typically a direct III-V semiconductor
such as GaAs or low-temperature grown GaAs, sometimes doped silicon is adopted. In
PCA, photo-carriers are produced by the laser pulse and then accelerated by a bias field
applied across the gap. In order to generate photo-induced free carriers it is necessary that
the photons of the laser pulse have an energy higher than the bandgap of the
semiconductor. If the laser is focused at the gap between the electrodes, the photo-induced
carriers are accelerated by the bias field across the gap, which generates a current. The
amplitude of the current is a function of time and, thus, the derivative of the current respect
time generates the THz pulse; In fact, for the pulsed nature of the laser beam [13, 14]:
𝐸!"# = !"
!!!!!!!
!" !
!" 𝜇𝐸! (1)
where A is the area under beam illumination, e the electron charge, 𝜀! the vacuum
permittivity, c the light velocity, z the pulse penetration inside the semiconductor, N the
photo-carrier density, µ the carrier mobility, and 𝐸! the bias field. The main contribution to
the photo-current comes from the electrons, since their mobility is often higher than that of
holes. In Figure 3 the photoconducting antenna is excited by a fs laser pulse. The dipole
structure is biased at a voltage Vbias to increase the THz signal emitted from the device.
Performances of PCAs can be appreciated considering some important and fundamental
aspects as: semiconductor bandgap, carrier life and mobility, antenna gap and bias field.
Finally, PCAs structures can be resonant or non-resonant. The first ones generate THz
radiation around a central frequency, which depends on the gap distance, the second ones
have variable gap distances and provide broader frequency THz emission [13,15].
Figure 3. Sketch of the THz emission mechanism induced in a photoconductive antenna by a fs laser
pulse
2.5. Electro-Optical Conversion (EOC)
Another type of THz source is based on the Electro-Optical rectification. It is a nonlinear
optical effect and THz waves are generated as a result of a difference-frequency process
between the frequency components contained in the femtosecond laser pulse, occurring in
materials having a higher order susceptibility that is different from zero.
Mathematically, the polarization induced by the electric field associated with the optical
pulse can be expressed in power series [16]:
𝑃𝑟,𝑡= 𝜒!𝐸𝑟,𝑡+ 𝜒!:𝐸𝑟,𝑡𝐸𝑟,𝑡+ 𝜒!:𝐸𝑟,𝑡𝐸𝑟,𝑡𝐸𝑟,𝑡+ … (2)
EO rectification comes from the second term in the previous equation. If the incident light is
a plane wave, the polarization induced by the second order susceptibility can be expressed
as:
𝑃
!" 𝑡=2𝜒!: 𝐸𝜔+Ω𝐸!𝜔𝑒!!!!𝑑Ω𝑑𝜔
!
!
!
! (3)
Here Ω is the difference between two frequency components of the laser pulse whereas 𝜒!
is the second order susceptibility, depending on the material crystalline structure. The
radiated electric field due to the EO induced polarization can be expressed as [17,18]:
𝐸!"# ∝!" !
!" = !!!!
!!!= 𝜒!!!!!"#$% !
!!! (4)
It is worth to emphasize that in EO rectification no bias is necessary to realize THz
generation (Figure 4). For a given material, the radiation efficiency and bandwidth are
affected by factors such as thickness, laser pulse duration, absorption and dispersion, crystal
orientation and phase matching conditions [19].
Figure 4. Skectch of the Electro-Optical mechanism
2.6. Photomixing for the generation of THZ radiation
The term “photomixing” describes the generation of T-waves as a difference frequency in a
nonlinear element. In the case of the THz region, it is necessary to use two IR or two visible
laser photons, so that the laser frequency difference lies in this frequency range. Basically, a
THz photomixer consists of two independently tunable sources (usually, solid state diode
lasers) lighting a photoconductive antenna PCA and yielding the desired difference
frequency by heterodyning [20], as shown in Figure 5.
Figure 5. Operation of a THz photomixer.
The device serves as a terahertz coherent wave emitter. Changing the temperature or the
operation current of the laser diodes, the value of the beat frequency can be
straightforwardly regulated.
The band of the photomixer depends on the spectral width of the employed diodes; in
particular, in order to enlarge the band or to move the band of the photomixer into higher
frequencies, diodes with different central frequencies are necessary [21].
Table 1 summarises the major strengths and weaknesses for the operation of the sources
reported above in the THz region.
Table 1. List of pros and cons for different THz sources
%
Source
Advantages
Drawbacks
BW Oscillator
ü High tunability
ü High output power
û Bulky
û Low frequency
QC Laser
ü High integration
ü Moderate output power
û Small tunability
û Low operation temperature
STAR Emitter
ü High integration
ü High spectral purity
ü Moderate tunability
û Small output power
û Low operation temperature
Photo-conductive
antenna
ü Broadband
û Small output power
û Bulky
Electro-Optical
Conversion
ü Broadband
û Small output power
û Bulky
Photomixing
ü Moderate output power
ü High frequency
û Bulky
!
3. Overview of THz detectors
In general, detectors are transducers converting an input signal into some convenient
formthat can be observed, recorded and analyzed. In case of THz technology, the signal is
an electromagnetic wave whose amplitude and phase both hold important information.
According to the nature of EM wave, detectors can be grouped into two classes: incoherent
or direct detectors that detect the amplitude only, and coherent detectors that detect both
amplitude and phase.
The performance of a THz detector depends on a number of parameters, some of them
correlated among them. The most important are: bandwidth (the spectral range over which
the detector responds), responsivity (input–output gain of the detector system), noise
characteristics (characterized by the Noise Equivalent Power NEP, that is the signal power
required to yield a Signal-to-Noise Ratio of unity at the output of the detector in a 1 Hz
bandwidth), dynamic range, response time and sensitive area.
3.1. Thermoelectric detectors
The photon energy of a THz wave is relatively weak and comparable to the phonon energy
of a crystal; for this reason it could be detected as thermal energy. In principle, the response
of such thermoelectric detectors is very slow – in the order of ms - because of the
thermoelectric reaction of the crystal, but it is usually ultra-broadband.
The most commonly used thermoelectric detectors are: Golay cell, pyroeletric and
bolometer.
The Golay cell is a gas cell detector in which an IR-absorptive gas is encapsulated and its
thermal expansion produced by THz waves is optically detected. The pyroelectric detector is
a photovoltaic detector made with a dielectric material, exhibiting temperature-sensitive
surface polarization and high sensitivity to THz Imaging. Typical value of NEP is
100pW/√Hz. Finally, the bolometer is a temperature-sensitive semiconductor, like Si or Ge,
and detects the THz radiation as the change in resistivity by the heating due to absorption of
THz radiation. The bolometer could operate at cryogenic temperatures, ultimately
minimizing the background noise level. The typical value of NEP is 10!!" 𝑊𝐻𝑧 at 0.3K
and 1p𝑊𝐻𝑧 at 300K.
3.1.1. Golay detectors
The mechanism of a modern version of this detector, with its main features, is shown in
Figure 6.
Figure 6. Structure of a Golay cell.
The main component is a sealed cell where a gas having a low thermal conductivity, usually
xenon, is inserted. One side of the cell ends with a window that allows the transmission of
the THz radiation in the adopted frequency interval. The other side instead is closed with a
flexible mirror. The cell is completed with a thin absorbing metallic film whose impedance
nearly matches that exhibited by free space. The metallic film absorbs the THz radiation
thus heating the surrounding gas and causing a slight movement of the mirror. This
displacement is subsequently converted into an electrical signal. In particular, a lens system
is exploited to concentrate the light emitted by the source through a grid towards the mirror;
then, the mirror reflects the light back to the detector through the grid. If a displacement of
the mirror occurs, the reflected image of the grid is distorted and, thus, the amount of light
reaching the light detector changes. For THz frequencies, the most useful window materials
are high-density polyethylene (HDPE), high-resistivity Si, crystalline quartz, and diamond
[22].
3.1.2. Pyroelectric detectors
A pyroelectric detector (or pyrometer) is an ac thermal sensor characterized by a frequency
response spanning a large frequency range, which includes the THz region. It is based on
the pyroelectric effect exhibited by a thin, permanently poled, ferroelectric crystal (i.e.
LiTaO3), in which the instantaneous polarization is dependent on the rate of change of the
crystal temperature. Pyrometers are commercially available either as single devices or as
arrays for the entire IR and THz spectral regions. Besides being very sensitive, they have
many advantages, including being relatively cheap and rugged, with room temperature
operation. Their most useful property is that, with appropriate design of an associated
amplifier, they can exhibit response times ranging from ms to less than a ns [23]. In Figure 7
the scheme of a pyroelectric detector and its equivalent circuital model are presented.
Figure 7. Pyroelectric detector and equivalent representation of electric circuit diagram.
3.1.3. Bolometer detectors
Semiconducting bolometers are among the most important of THz detectors. A design for a
bolometer is shown in Figure 8. It consists of a small chip of doped semiconductor, Si or Ge.
Typical doping concentrations are 1016 cm-3 for Ge and 1018 cm-3 for Si. The detector element
is suspended in vacuum by two thin lead wires between the electrical contacts, which
provide the electrical connections as well as the thermal link to the heat sink. Two aspects
determine the optimum level of doping: (i) the temperature coefficient of the resistance
should be large; (ii) the bolometer should have a resistance that allows for an efficient
coupling to a low noise amplifier [24].
Figure 8. Simple design of a semiconducting bolometer.
A specific bolometer is the Superconducting Hot-Spot Air Bolometer (SHAB) where the
detector element consists of a microscopic narrow Nb or NbN strip creating a free-standing
bridge structure on top of a substrate. When a voltage bias is applied to the structure, this
produces the formation of a hot spot in the middle of the strip where the incoming radiation
energy is dissipated, and therefore the switch from the superconducting to the normal state.
The overall effect is a modulation of the suspended strip resistance, with a consequent
modulation of the current flowing because of the voltage bias. From the recorded current,
one can extract a measure of the THz radiation [25].
3.2. Photoconductive antenna
A photoconductive antenna could be considered also to detect THz waves. The structure is
very similar to the structure of PCA for emission. In this case PCA as detector measures the
photocurrent, which is collected by the electrons generated by the probe beam across the
antenna gap and biased by the THz electric field. When no electric field is present, the
photocarriers produced by the laser pulse move randomly and no current is observed. On
the contrary, when the THz wave irradiates the gap, it generates an electric field separating
electrons from holes, and therefore a current, proportional to the amplitude of the electric
field, is observed. It is important to emphasize that PCA for detection and PCA for emission
are differently designed. The narrower is the gap, the lower is the electric field required for
obtaining an appreciable current, therefore PCA for detection exhibits narrower gaps (~10
um) if compared with typical gaps of PCA for emission (> 50 um) [14, 26, 27]. Factors
affecting the performance of a PCA are similar to those for the emitter: semiconductor
bandgap, carrier lifetime and mobility, and antenna gap [14].
3.3. Electro-Optical Sampling (EO)
Electro-Optical (EO) sampling is based on the Pockels effect, in which the application of an
electric field, on a material, induces or modifies the birefringence properties of it. In other
words the Pockels effect is a change in the refractive index or birefringence that depends
linearly on the electric field. It is important to say that the Pockels effect can be observed
only in crystals characterized by no inversion symmetry, like those belonging to the
zincblende group such as the ZnTe [19, 27].
Using this detection method, the THz electric field is sensed by measuring the change of the
birefringence properties of the crystal, caused by the field itself. These changes can be
measured by analysing the polarization properties of an optical probe beam going through
the crystal. The most common setup to measure the THz waveform with EO sampling is a
balanced measurement approach, as shown in Figure 9.
Figure 9. Sketch of the Electro-Optical sampling
The operating principle is as follow. An optical probe beam characterized by linear
polarization is first passed through a polarizer and then propagates within the EO crystal. A
quarter wave plate (QWP) is positioned just after the EO crystal in order to modify the
probe beam ellipticity; moreover, a suitable Wollaston prism is exploited to split the
elliptical polarization into its two perpendicular components. A proper photodiodes
assembly mounted in differential configuration detects the diverse polarization intensity. In
the absence of THz radiation impinging on the EO crystal, the probe beam ellipticity can be
regulated in such a way that both polarization intensities are equal; as a consequence, the
net current flowing from the differential photodiodes is equal to zero. On the contrary,
when the THz wave is present, the birefringence of the EO crystal is modified by the electric
field, thus changing accordingly the ellipticity of the probe beam. As a result, the balance
between the two polarizations is broken and the photodiodes assembly can generated a net
current whose intensity is proportional to the amplitude of the electric field associated with
the impinging THz wave.
Table 2 summarises the major strengths and weaknesses for the operation of the detectors
reported above in the THz region.
Table 2. List of pros and cons for different THz detectors
%
Detector
Advantages
Drawbacks
Golay cell
ü Broad spectral response
ü High sensitivity
ü Large sensing area
û Limited Dynamic Range
û Slow response
û Bulky
û Fragile
û Expensive
Pyrometer
ü Broad spectral response
ü High Dynamic Range
ü Fast response
ü Compact
ü Inexpensive
û Large NEP
û Microphonic response
Bolometer
ü Broad spectral response
ü Highest sensitivity
ü Lowest NEP
ü Compact
û Slow response
û Low operation temperature
û Small sensing area
Photo-conductive
antenna
ü Fast response
ü Moderate sensitivity
û Low detection current
û Relatively expensive
Electro-optical crystal
ü Broad spectral response
ü Fast response
ü Moderate sensitivity
û Complex readout
û Relatively expensive
!
4. THz Systems
As already described in Section 2, the operation of THz systems can be schematically
divided in continuous-wave and pulsed mode.
Frequency domain (THz-CW) systems work at a fixed frequency, which depends on the
type of THz emitter. As an example, in Figure 10 the case of a QCL source coupled to a
thermal detector (a pyrometer or a bolometer) is shown. Between THz emitter and detector
there is an ellipsoidal mirror that allows to collimate the laser beam. In this configuration
scheme, the reference signal produced by the source and the output signal recorded by the
detector are sent to a lock-in amplifier in order to provide a coherent detection. [28]
Figure 10. Sketch of a THz-CW system. A QCL is used as THz source and a bolometer or a pyrometer
as THz detector.
In the following the attention will be focused primarily on the characteristics and
performance of THz measurement system working in the time domain (THz-TD). A typical
architecture is shown in Figure 11.
Figure 11. Typical scheme of a THz-TD system in transmission mode.
A beam splitter is adopted to divide the ultrafast optical pulse generated by an ultrafast
laser into two beams, referred to as probe and pump, respectively. T-ray pulsed radiation is
stimulated at the emitter by the optical pump beam via either charge transport or optical
rectification effect, according to the specific type of exploited emitter. A suitable set of lenses
and a pair of parabolic mirrors is adopted in this configuration to collimate and focus the
diverging T-ray beam on the sample of interest. A similar combination of lenses and mirrors
are then needed to re-collimate and focus onto the receiver the T-ray beam passed through
the sample. At receiver side, the originally split probe beam acts as an optical gate for the T-
ray receiver; the optical gate signal is characterized by a shorter time duration compared
with that of the arriving T-ray pulse. It is worth noting that a proper synchronization
between the gating and T-ray pulse is mandatory to assure T-ray coherent detection at a
time instance. By carefully controlling the optical delay line by means of the proper micro-
motion of a mechanical stage, it is possible to achieve a complete temporal scan of the T-ray
signal [29].
Reflection measurements can be also used for practical applications, when bulky samples
are considered, that are impossible to measure in a transmission mode (see Figure 12) [30].
Figure 12. Typical scheme of a THz-TD system in reflection mode.
4.1. Performance of THz systems
In this paragraph the various characteristics and limitations associated with a THz system,
in particular when defining its performance are discussed. The parameters commonly used
are the dynamic range (DR) and the signal-to-noise ratio (SNR), which mainly affect the
accuracy in THz measurements. They should always be evaluated during the
measurements, to avoid false interpretation of the results; therefore some recommendations
for the best practice are presented [31].
4.1.1. Dynamic Range and Signal to Noise Ratio
The dynamic range (DR) is defined as the ratio between the highest and lowest measurable
signal, and therefore describes the maximum signal change that can be quantified. As a
matter of practice it is calculated as the ratio between the maximum signal amplitude and
the root mean square of noise floor. The signal-to-noise ratio (SNR) is defined as the ratio
between the mean peak amplitude and the standard deviation (SD) of the signal amplitude.
It indicates the minimum detectable signal change, and is a complementary system
parameter with respect to the dynamic range. Therefore the DR determines the
measurement bandwidth, whereas the SNR reflects the amplitude resolution or sensitivity.
DR and SNR may be evaluated either with respect to the time domain waveform or to the
spectrum obtained through Fourier transform. Two specific aspects are involved when these
parameters are considered. First, data are acquired as time-domain waveforms, whereas
measured optical parameters are derived from the Fourier Transform (FT) spectra. In
particular, the DR and SNR of time-domain signals may result different from that of the
corresponding spectra, and there is not a straightforward analytical relationship between
the parameters estimated according to the two methods. Moreover, both DR and SNR of
spectral data are strongly frequency-dependent, and typically decreases steeply with
frequency.
The recommended procedure for estimating the DR and SNR of THz through time-domain
data is based on the following steps:
1. Acquiring the time-domain waveform and measuring the maximum peak value.
2. Acquiring the noise signal in absence of THz, e.g., before the arrival of the main
pulse.
3. The mean signal in the absence of THz should be constant (zero for electro-optic
detection, non-zero for a photoconductive antenna). However, its standard
deviation (SD) has to be measured.
4. DR is given by the ratio between the mean value of the measured peaks and the SD
of the noisy signal.
5. SNR is given by the ratio between the mean value of the measured peaks and their
SD.
The recommended procedure for estimating the DR and SNR of THz through the amplitude
spectrum is based on the following steps:
1. Calculating the FTs of a defined number of time-domain records, their mean and
SD, and estimating the noise floor of the mean FT. If only the DR is required, one
FT spectrum is sufficient.
2. DR is given by the ratio between the mean FT amplitude and the noise floor.
3. SNR is given by the ratio between the mean FT amplitude and the SD.
4. The sampling frequency and observation interval of the time-domain acquisition
have to be constant throughout the procedure, because both affect the SNR and the
DR.
5. It is desirable to test the performance of the system by varying the scan parameters
in order to identify the ranges characterized by the best SNR and DR values.
If DR and SNR are evaluated through the FT, the signal averaging is recommended, in order
to reduce the noise effects. It is worth to notice that if a jitter affects the peak position, which
often is due to errors in the initial position of the delay stage, the time domain average will
be distorted; the FT amplitude spectra and their average value, on the contrary, will remain
correct. As expected, the approach for the evaluation of DR and SNR of a THz TDS system
strictly depends on the specific domain adopted for the measurements. In other words, if the
measurements are carried out in time-domain, then the DR and SNR must be directly
calculated from the available time-domain data. On the contrary, DR and SNR must be
evaluated from FT amplitude spectra when measurement based spectroscopic data are
taken into account.
Another fundamental parameter to describe characteristics of a THz system is the spectral
resolution. It is determined from the span of the time delay sweep, and it is given by the
ratio between the light velocity c and the effective delay line length (multiplied by 2).
In principle, the pump laser pulse repetition rate is the only limitation of resolution if the
ideal conditions of noise-free system and unlimited delay line are met. On the contrary, the
actual frequency resolution is hardly reduced in presence of noise, and mainly influenced by
the time-domain SNR of the system. For increasing length of the delay line, the signal
amplitude is reduced because of the increasing delay from the main pulse, and the SNR
approaches unity. As expected, THz pulses in the train must be identical with one another to
make optical sampling works successfully. If this condition is not satisfied (i.e. the evolution
of THz pulse shape occurs on time scales comparable to (or shorter than) the measurement
time), no reliable samples of the waveform can be acquired. Besides this main drawback,
another minor disadvantage affects the performance of optical sampling. As for the other
sampling techniques, optical sampling also takes long time to acquire the desired data. The
lower bound for the acquisition time is given by 𝑁∗𝜕𝑡, (N and 𝜕𝑡 being, respectively, the
number of measured electric fields and the train pulse-to-pulse distance). Since it is possible
to take advantage of signal averaging, the acquisition time is usually much longer than this
minimum value. Another problem inherent to sampling measurements is that they require a
method for varying the delay of the sampling gate relative to the THz pulse. This
requirement is often accomplished by means of a mechanical delay line consisting of a
mirror that is moved to vary the optical path length [1].
4.1.2. TDS Calibration
A typical device used for calibrating the linearity of amplitude/power measurements of THz
system has to exhibit constant loss within the THz bandwidth. The most convenient and
preferred solution is the employment of optically flat silicon plates as loss elements. Fresnel
reflections are solely responsible for transmission losses in such a plate. Using a stack of
plates parallel to each other, orthogonal to the incident THz beam and separated by air gaps,
one can manage the loss level since it is dependent on the number of plates in the stack.
When the device is placed in the beam path, particular attention has to be paid to avoid
distorting the THz beam or altering its focusing; in fact, it is desirable to position the device
in a collimated beam. The device can be used in both THz CW and THz TDS systems, where
the plates must be angled to the incident beam so as to destroy the etalon interference. There
are two methods to verify the linearity and either time domain or frequency domain data
can be processed:
a. In the time domain method, the signal is processed in order to identify the peak value
of the amplitude signal. Then the obtained peaks are plotted in a semilog graph versus
the number of Si plates in the beam path. The system is supposed to be linear if the
plotted curve exhibits a linear behaviour characterized by a slope equal to 0.7.
b. The second method of testing a TDS involves the calculation of THz spectra. The
amplitude at chosen frequencies is plotted against the number of Si plates in the beam
path. As in the time domain method, the semilog plots are expected to be linear with a
slope of 0.7.
It is worth noticing that the linearity of a TDS should not be assumed, but it should be
experimentally verified.
4.2. Errors and Uncertainty in THz-TDS
Many sources of error can affect a THz-TDS measurement and data extraction. As for
example, laser intensity fluctuations, optical and electronic noise, delay line stage jitter,
registration noise are common error sources. Moreover, contributions to the error in the
estimated optical constants are not only from the randomness in the signal, but also from
imperfections in the physical setup and parameter extraction process. Examples are the
sample thickness measurement, the sample alignment, and so on. Significant sources of
error are shown in the scheme of Figure 13. The uncertainty sources (green lines) can
influence both the THz-TDS measurements and the parameter extraction process. Each of
them determines a variance, that can be propagate along the process and determine a
variance on optical constants [32, 33].
Figure 13. Scheme showing the propagation of uncertainties in THz-TDS measurements (taken from
[33]).
Two major sources of thermal noise can be singled out in a THz-TD system:
1. Johnson-Nyquist noise is generated when charge carriers fluctuate in a substrate. It
results in an artefact voltage measured with no T-ray incident electrical field,
whatever is the presence of optical gating pulses;
2. background noise gives rise to a random voltage across the receiving antenna.
Other relevant noise sources are quantum fluctuations and laser & shot noise. One of the
most efficient methods to remove noise in a T-ray signal is by means of digital signal
processing technique such as wavelet de-noising, that can actually improve the signal SNR,
particularly when intensities are strongly reduced in biological samples. Ultimately, the
noise in a THz-TDS system limits the spectral resolution; the best achievable resolution in a
defined frequency interval depends, in fact, on the maximum time duration, which is, in
turn, directly related to the actual SNR within that frequency range. In this way,
improvement of the system dynamic range (obtained by either increasing the power of the
transmitted THz waveform or decreasing the system noise floor) turns out to be mandatory
to assure suitably high frequency resolution.
Another uncertainty source is the positioning of the stage for optical delay line (ODL); thank
to the exploitation of a couple of moving mirrors, ODL mechanically induces a delay either
on the probe or, equivalently, pumping pulse. As a consequence, the sampling time of the
optically-gated detector is characterized by uncertainty; due to its combination with the
other sources (electronic and optical noise), a final uncertainty on the amplitude
measurements of the sampled T-ray pulse arises. The uncertainty associated with the
amplitude of the acquired T-ray pulse affects also the spectral components obtained through
the Fourier Transform and the deconvolution process. Another uncertainty source that
cannot be neglected involves the procedure for unwrapping the phase. Moreover, the
thickness and the alignment of the samples have to be known in order to extract the model
parameters; as a consequence, the uncertainty associated to these inputs affects the whole
parameter detection process. Finally, the overall uncertainty is affected by the uncertainty
associated to the estimation of the air refractive index. Each uncertainty source, however,
can be taken into account by means of a proper model describing the uncertainty
propagation in the measurement process.
4.3. THz spectroscopy
The term spectroscopy refers to a series of experiments aiming to investigate the excited
states of a specimen, exploiting the interaction of a proper electromagnetic perturbation
with a sample. Reflected and/or transmitted waves release specific information on the
electromagnetic properties of the sample as function of the frequency. Therefore, according
to the spectral content of the electromagnetic signal-probe, different excitations can be
investigated ranging from the quantum properties (energy levels of atomic bonds, roto-
vibrational states etc.) of molecules to the impedance of a macroscopic samples or
transmission lines. The THz band is ideal to study electrodynamic properties of materials
from metals to insulators, since the frequency is lower than the typical plasma frequency of
metals (about 1015 Hz) that defines the frequency above which the metal becomes
transparent to radiation. Coherent THz radiation can provide valuable information on the
complete set of the complex electrodynamic parameters [34] (refractive index ( 𝑛)
permittivity (𝜀) and /or conductivity (𝜎) characterizing a material whatever it is an insulator
or metallic-like. The complex refractive index (𝑛=𝑛+𝑖 𝑘) furnishes information on both the
delay (𝑛) and the absorption (𝑘). Once 𝑛 and 𝑘 are obtained (see below) the permittivity
𝜀=𝜀!+𝑖 𝜀! can be reached exploiting the following relationship 𝑛=𝜀𝜇/𝜀!𝜇! where 𝜇 is
the complex magnetic permeability, 𝜀! is the vacuum permittivity and 𝜇! is the vacuum
permeability. Since most of materials have 𝜇=1 a direct relation between the refractive
index and permittivity can be extracted 𝑛≅𝜀 which deals 𝑛=𝜀!
!+𝜀!
!+𝜀!2 and
𝑘=𝜀!
!+𝜀!
!−𝜀!2. Conductivity (𝜎=𝜎
!+𝑖 𝜎!) and permittivity are also reciprocally
related through the formulas 𝜎
!=𝜀!𝜔 𝜀! and 𝜎!=𝜀!𝜔(𝜀!−𝜀!), where 𝜔=2𝜋𝜈 and
𝜀!=𝜀 (𝜔→∞) can be obtained through a fitting procedure. From the practical point of
view, the most important parameter to obtain for a sample characterization is 𝑛, since the
other parameters are just a combination of 𝑛 and 𝑘.
The peculiar characteristic of using a TDS consists into directly manipulating the time
dependent electric field E(x, t) transmitted through the sample. The ratio between the
Fourier transforms of the transmitted signal and the reference signal is directly function of
the refractive index. The sketch of the measurement on a generic sample L thick is reported
in Figure 14. E(x,t) propagating from the Transmitter (Tx) to the Receiver (Rx) is linearly
polarized along y. Since the signal is generated and detected in air, the proposed scheme
allows to generalize the measurements in multilayer samples.
The transmitted signal through the sample 𝑆(𝜔), can be expressed as function of the Fresnel
coefficients 𝑇
!,!(𝜔)=2𝑛!/(𝑛!+𝑛!) and 𝑅!,!𝜔=𝑛!−𝑛!/(𝑛!+𝑛!) and the
propagation factor 𝑃
!𝜔,𝑑=𝑒𝑥𝑝 −𝑖 𝑛! 𝜔 𝑑, where the labels refer to the material [35]. The
complete signal can be expressed as:
𝑆𝜔=𝜂𝜔𝑇
!,!𝜔𝑃
!𝜔,𝑑𝑇
!,!𝜔𝑅!,!𝜔𝑃
!
!𝜔,𝐿𝑅!,!𝜔
!
!
!!!∙𝐸𝜔 (5)
where 𝐸(𝜔) is the generated THz pulse and 𝜂(𝜔) accounts for all the reflected and
transmitted signals which do not reach Rx. In eq. (1) the factors 𝑇
!,!(𝜔)𝑃
!(𝜔,𝑑)𝑇
!,!(𝜔) take
into account of the fraction of signal reaching Rx in one path, whereas the term
𝑅!,!𝜔𝑃
!
!𝜔,𝐿𝑅!,!𝜔
!
!
!!! accounts for the delayed K-pulses originated by the
reflections of the primary pulse between the sample boundaries (usually 𝐾≤3). This
phenomenon known as Fabry-Perot (FP) effect is depicted in Figure 14 through the dashed
arrows displaying the reflected signals. In the time domain, the FP effects shows up in the
appearance of copies of the primary transmitted signal. In Figure 15 a comparison is
proposed between the reference signal (air) and the signal (Si) through a silicon slab 500 µm
thick. Black arrows point out the copies of the primary signal. The delay between copies is
due to the roundtrip walk in the sample and is about ∆𝑡≅2𝐿𝑛/𝑐~11.4𝑝𝑠 for 𝑛𝑆𝑖 =3.46.
Figure 14. Scheme of the measurements trough the THz-TDs system. Tx and Rx stand for transmitter
and receiver respectively. L represents the mean size of the sample while ni with i =1,2,3 are the
refractive index of different through THz pulse.
Figure 15. Time dependent signal measured through THz-TDS system. The black curve is the
reference signal acquired in free space whereas the red curve is the signal through a Si sample 500
µm thick. The arrows indicate the primary signal copies generated by the Fabry-Perot effect.
Equation (1) also defines the transmittance
𝑇𝜔=
𝐸!"#$%&
𝐸!"# (6)
that, according to eq. (5), in the case of a simple slab can be expressed as
𝐻𝜔=!!!!!!!!
!!!!!!!!!!
𝑒𝑥𝑝 −!!!!!!"# !"
!
𝐹𝑃 𝜔 (7) (3) (1)
where
𝐹𝑃 𝜔=!
!!!!!!!
!!!!!
!!!!!
!!!!!!"# {!!!!!!!/!} (8)
is the explicit form of the Fabry-Perot term when the echos in media 1 and 3 are negligible
[35].
The transfer function 𝐻(𝑤) in eq. (7) is used as theoretical reference for 𝑇(𝜔) to calculate
optical parameters of samples. Equations (6) and (7) describe the transmission through a
homogeneous slab with refractive index 𝑛! when the equivalence 𝑛!=𝑛!=𝑛!"# is verified.
Instead by putting 𝑛!=𝑛!"#, equations (6) and (7) are able to describe a system composed
by two layers as a thin metallic film on a dielectric substrate [36, 37].
Several techniques [36 - 40] have been developed in order to extract 𝑛 by computing the
minimum difference between the moduli and the phases of 𝐻(𝜔) and 𝑇(𝜔):
𝛿𝜌 𝜔=𝐻𝜔−𝑇𝜔
𝛿𝜑 𝜔=arg 𝐻𝜔−arg 𝑇𝜔 (9)
Equations (9) allow to define an error function, the Total Variation (TV) [38], defined by the
sum of differences 𝛿𝜌 and 𝛿𝜑 for each frequencial point
𝐸𝑅 =|𝛿𝜌 𝜔|+
! |𝛿𝜑 𝜔| (10)
This is a tridimensional paraboloid as function of the frequency and the sample thickness.
The computational search of the minimum of 𝐸𝑅(𝐿,𝜔) implies the contemporary knowledge
of the main quantities describing the system: the sample thickness, 𝐿 the refractive index 𝑛
and the extinction coefficent 𝑘 [39]. A fast resolution of the TV approach is affected by the
noise in the measured spectrum of 𝑇(𝜔). The most relevant noise source in thin samples are
the Fabry-Perot oscillations which shows a frequency inversely proportional to 𝐿. This
problem can be overcame imposing the quasi space (QS) optimization [46], where the
periodicity of the FP effect is employed to achieve the effective optical thickness of the
sample. The quasi space is defined by the Fourier transform of an electro dynamical
parameter 𝑦𝜔! which could be the refractive index or the extinction coefficient. Therefore
a new set of variables can be defined as follows
𝑄!!=𝑦𝜔!exp −𝑖 !!
!
𝑘 𝑛
!!!
!!!,𝑘=0,1,2…,𝑁−1 (11)
This function can be displayed in terms of the variable 𝐿!!=𝑥!!𝑐!/2, where 𝑐! is the speed
of light in vacuum and 𝑥!!=2𝜋/𝜔, showing a pronounced peak at the effective optical
length. Alternatively, the sample thickness 𝐿 can be accounted by locating the minimum of
𝑄!! (at a fixed frequency) for different 𝐿 values [40]. The QS approach is limited just by the
performances of the TDS system. In particular the maximum and minimum detectable
thickness can be expressed as 𝐿!"# =𝑐!4𝑛 𝑑𝑓 and 𝐿!"# =𝑐!2𝑛 ∆𝑓 where 𝑑𝑓 is the
minimum detectable frequency of the system while ∆𝑓 is its bandwidth. The former
thickness is based on the application of Nyquist theorem, whereas the latter is based on the
resolution of neighbor 𝑄𝑆’s peaks [40]. For instance, assuming as parameters 𝑑𝑓 ≅3𝐺𝐻𝑧,
∆𝑓≅3 𝑇𝐻𝑧 and, as effective refractive index, 𝑛≅2, the maximum and minimum length are
𝐿!"# ≅12.5 𝑚𝑚 and 𝐿!"# ≅12.5 𝜇𝑚 respectively. Whenever the best optical length is
found, the quality of the retrieved electrodynamic parameter depends also by the choice of a
good thickness of the sample. Thinner samples become transparent to THz radiation
whereas thick samples do not release much information because the transmitted signal is
low. In ref. [41] authors aim to find the best thickness in order to minimize the standard
deviations ( 𝑠!
!, 𝑠!
!) of electrodynamical parameter as 𝑛(𝜔) and 𝑘(𝜔) inherited by the
standard deviations of signals 𝐸!"#$%& (𝑡) and 𝐸!"#(𝑡) acquired in the time domain. The
functions 𝑠!
!, 𝑠!
! can be minimized with respect 𝐿 leading to get the optimal thickness as
function of the absorption coefficient:
𝐿!"# =𝑐!𝜔 𝑘𝜔=
2
𝛼𝜔
12
Equation (12) shows that 𝑛(𝜔) and 𝑘(𝜔) are affected by some indetermination as
consequence of the fixed extension of the sample. On the other hand, eq. (12) enables the
possibility to get reliable results also on very thin samples provided that the absorption
coefficient 𝛼(𝜔) is enough high. Indeed, full two dimensional systems like single graphene
layers have been extensively investigated through THz-TDS systems thanks of the robust
absorption coefficient 𝛼!"#$!!"!~5 𝜇𝑚!! [42 - 44].
%
5. Conclusions
Without claiming to be exhaustive, we presented a short overview of THz measurement
systems presently under development for scientific and industrial applications. We first
described the most common sources and detectors that are routinely in use for the
manipulation of T-waves. We then focused on the typical architectures that are presently
employed in time-domain spectroscopy and imaging. The importance of metrological
aspects in THz systems performance and measurements, and most of their related issues
and solutions, were discussed. Since each material has its own 'identity card' in this band of
the spectrum, a THz-TDS waveform transmitted through a sample is typically rich in
information. We therefore presented what are the main parameters that can be measured
from the material frequency response, namely optical or electrical complex quantities like
the refractive index, the conductivity and the dielectric constant, and what are the data
extraction methods and the related errors and uncertainty.
%
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