Terahertz cross-correlation spectroscopy enables phase-sensitive measurements without the need for a laser source and, hence, presents a cost-efficient and versatile alternative to common terahertz time-domain spectroscopy approaches. This review article presents the development of this technique over the past two decades as well as applications of this approach. It is completed by a detailed mathematical description proving the irrelevance of the optical phases of the employed pump light modes. Numerical investigations of the resulting signal demonstrate the applicability and are compared to state-of-the-art measurements. Terahertz cross-correlation spectroscopy is a valuable alternative for moderate-demand applications already. Further possible improvements are discussed.
I. INTRODUCTION
With the development of ultrafast lasers1 in the last decades of the previous century and the rise of sampling techniques like pump-probe measurements, the measurement of ultrafast physical phenomena started. These pump-probe techniques also enabled the exploitation of the terahertz spectral range via coherent photonic measurement techniques most prominently represented by the well-established time-domain spectroscopy (TDS).2 Terahertz TDS was the enabler of a wide variety of applications, ranging from scientific topics such as spectroscopy,3,4 semiconductor characterization,2,5–7 and near-field spectroscopy8 to industrial measurement tasks such as layer-thickness measurements,9–11 volume inspection,12 and quality control.13–16 One of the outstanding features of TDS in this spectral range is the ability to measure the amplitude and phase of the electric field. In particular, the retrieval of the phase is comparatively easy to achieve and, therefore, has enabled a plethora of evaluation possibilities for diverse applications. Having gained from the tremendous development of lasers and related equipment in the telecommunication wavelength range (∼1.5 µm), terahertz TDS has overcome the purely academic stage and has entered real-world applications, with a variety of system suppliers sharing the growing market. However, the employed ultrafast lasers are the cost-driving components of these measurement systems and might hinder fast penetration into the market.
Already about two decades ago—at the threshold of the millennium—an alternative technique was invented that overcomes the need of ultrafast lasers and enables essentially the same phase-sensitive measurements: terahertz cross-correlation spectroscopy (CCS).17 Two important experiments paved the way for this discovery: An interferometer-based (Martin–Puplett type) measurement system was demonstrated by Tani et al.18 who employed a multimode laser–pumped photoconductive switch and incoherent detection by a bolometer. They showed that the output of the multimode, but non-mode-locked19 laser is suitable to drive the photoconductive switch and causes it to emit equally spaced spectral components at subterahertz frequencies, while the spacing originates from the free spectral range of the employed multimode, non-mode-locked laser diode. Already then, by using the interferometry principle, subterahertz frequency components up to 450 GHz were detected and resolved. The application of this principle to spectroscopic investigation of samples was demonstrated 2 years later in 1999 by Morikawa et al.,20 who characterized semiconductors with respect to the sample thickness and doping concentration. The corresponding setup is shown in Fig. 1.
Based on these two preliminary studies, Morikawa et al.17 advanced this technique and demonstrated that a coherent measurement principle can be realized by using a standard setup for TDS (shown in Fig. 2) consisting of two photoconductive switches [based on low-temperature–grown GaAs (LT-GaAs)] as emitter and detector and a linear stage as delay unit but using light of a multimode (non-mode-locked) diode laser instead of an ultrafast laser.
Already in this first report on terahertz CCS, simple semiconductor measurements were performed showing the delay of the terahertz cross-correlation maximum. What might have hindered the broader impact of this work in the terahertz community is the usage of an abscissa in units of micrometers (as shown in Fig. 3) instead of a delay axis in units of picoseconds as is common for TDS signals. Nevertheless, this work most probably has been the first demonstration of coherent detection of subterahertz radiation by using the CCS principle in combination with multimode, but non-mode-locked diode lasers. A spectral coverage from a few tens of gigahertz to ∼0.5 THz was obtained, and the refractive indices of semiconductor samples were investigated with this system.
From this first demonstration on, several improvements and application examples have been demonstrated in the past two decades, finally also showing that not even laser light is needed to drive a terahertz CCS system. These will be presented later after first giving a detailed description of the working principle of this method phenomenologically, mathematically, and numerically.
II. THEORY
A. Comparison of time-domain spectroscopy and cross-correlation spectroscopy
To better evaluate the differences between time-domain and cross-correlation spectroscopy, we will briefly revisit the principle of TDS, which can be described in a phenomenological manner by considering individual pulses as depicted in Fig. 4. Ultrashort optical pulses of a femtosecond laser are split into two branches. One branch leads to the emitter module, and the pulses traveling there each trigger the emitter to emit a terahertz pulse. The second branch includes an optical delay line enabling the sampling principle, which is shown in Fig. 5.
The pulses being guided in this branch activate the detector with a variable delay with respect to the incident terahertz pulse. As the active time span is much shorter than the duration of the terahertz pulse, quasiconstant parts of the electric field are sampled. By varying the delay line length, the full time-dependent electric field (amplitude and phase) of the terahertz pulse is sampled.
In contrast to the TDS principle, which is based on said ultrashort optical pulses, the CCS principle relies on a varying optical field intensity, consisting of several optical modes, which are not locked to each other but can have an arbitrary relative phase. The setup and the corresponding optical intensities and corresponding terahertz fields are schematically shown in Fig. 6. Except for the source of the optical pump wave and the design of the modules, the setup is analogous to that of the TDS setup. Most commonly, photomixers are used as emitter and detector modules, whereas the emitter is built of positive-intrinsic-negative (PIN) diodes,21 and the detector is a photoconductive switch specially optimized for cw excitation.22–24 In the case of illumination with multiple spectral modes, the intensity of the resulting light field possesses frequencies in the subterahertz or even terahertz range, depending on the spectral bandwidth of the used illumination. In the case of the emitter, the accelerated charge carriers excited by this light lead to the emission of the corresponding terahertz waves. If the same optical multimode light is used for illumination of the detector, the resulting photocurrent is the cross correlation of the incident terahertz wave and this optical field.
A phenomenological description of the cross-correlation–based signal formation is given in Fig. 7. As the detector illumination consists of several optical spectral modes without any phase relation, it does not provide isolated ultrashort pulses but, rather, an intensity envelope containing high-frequency components in the (sub)terahertz region. The detector responsivity is modulated with this time-dependent intensity. As the incident terahertz radiation is the derivative of the optical field intensity in a first approximation, the cross correlation results in a signature, reminding on the sampling result of a typical TDS setup. What is neglected here, is the change of the phase relation with time, alternating not only the pattern but also the terahertz field for each delay line position. Nevertheless, this does not change the sampling result, but finally enables the creation of signals similar to that of TDS systems, despite the periodicity and accessible bandwidth. It is important to understand that the waveforms acquired with a CCS system do not represent the time-dependent electric field, but a cross correlation results in dependence on the delay between two optical branches. (Therefore, we emphasize the designation of the x axis of the waveform plots as delay and not as time in our own results obtained with CCS.) To clarify this difference and to work out that we still can perform the same measurements, we will analyze the process in detail in Sec. II B.
B. Mathematical description
While the sampling result for a TDS measurement is widely understood and can be intuitively explained, the origin of a CCS signal is not as easy to explain. Hence, we will show with a mathematical model that the two measurement methods rely on the same principle. In 2009, Scheller and Koch25 reported on the first signal theory of terahertz CCS but did not present the role of the individual phases of the involved modes. Recently, a detailed analysis of the terahertz TDS signal theory in the frequency domain was given by Kolpatzeck et al.26 We present here a theoretical investigation of signal formation for CCS, with a focus on the insignificance of the optical phases, while keeping the consideration in the time domain.
The optical power of an electromagnetic wave is proportional to the square of its amplitude. Assuming an electromagnetic field consisting of N individual light modes in Eq. (1),
whereas the light modes can be represented by fundamental oscillations in Eq. (2),
The absolute of a complex function can be expressed as in Eq. (3):
For the sake of simplicity, we assume , as only the time dependence of the contributions is of interest here. Then, Eq. (1) becomes Eqs. (4) and (5),
with
and as well as .
The sum can be rearranged to Eq. (6):
As the argument of the exponential function is 0, the product becomes 1.
With the definition of the trigonometric functions following Euler's formula, Eqs. (7)–(9) show that P(t) becomes
while the summand N represents the sum of the amplitudes, which were simplified to be 1 each.
Assuming a photoconductive material with sufficient short carrier lifetimes, the conductivity of the emitter follows the optical power sent to the emitter (Tx). With the applied constant bias, a photocurrent is induced, which then is also proportional to the optical power in this approximation. The emitted terahertz radiation results from the alternating current and is therefore proportional to the derivative, as shown in Eqs. (10)–(13):27
In the detector, this electromagnetic wave drives the photoexcited carriers, which follow the same density function, as they are driven by the same optical field except for an optical delay τ. The measurable current in dependence on τ is shown in Eqs. (14)–(16):
where T is the period time of the periodic functions. Using Euler's formulas, this can be further simplified to Eq. (17):
For and/or , the periodicity T, which is needed to be able to calculate the convolution, becomes Eq. (18):
Then, becomes 0, as the integral of a sine across its periodicity vanishes. The physical meaning of this is that a terahertz frequency generated at cannot be detected with an optical beat at , if and/or .
For n = k and m = l, the current becomes Eq. (19):
with the periodicity as shown in Eq. (20):
The integral from 0 to T of the t-dependent sine (second term) vanishes so that the result is as shown in Eqs. (21) and (22):
The second term does not vanish, as it is time independent and only depends on τ being the delay introduced by the imbalanced optical paths, which is controlled by an optical delay line in a classical CCS setup. Remarkably, this term is independent from and , which is the most important result here: The measurement result in this kind of setup is independent of the individual phases of the modes. Therefore, the signal is qualitatively the same for locked modes from an ultrashort pulsed laser and for random modes from a multimode, non-mode-locked laser diode.
C. Numerical investigation
Apart from the analytical mathematical considerations, the signal can be comprehended by numerical approaches. For this, the scheme in Fig. 8 is numerically realized. The model starts with the construction of the optical pump field consisting of the N optical modes with frequencies ωn, amplitudes En, and phases for . Depending on the assumed pump source, the phases are random or locked (). The frequency spacing of the modes is set to a specific free spectral range of the assumed laser diode source. The intensity of this electric field is then convoluted with the lifetime of the photoexcited charge carriers in the photoconductive mixers used as emitter and detector. In the case of the emitter, the result is then derived with respect to time. This gives a function proportional to the emitted electromagnetic terahertz field . This field is then numerically propagated in humid air by using the data from the high-resolution transmission molecular absorption database (HITRAN).28,29 The outcome then is cross-correlated with the free charge carrier density in the detector. The result is averaged for a high number of sets of phases (≫100), as in the experiment, in realistic measurement times, the light source has emitted a large number of sets of modes. [By a set of modes, a defined number of modes with a corresponding (random) phase relation is understood. The phases of the modes, and therefore the random phase relation, changes over time so that the set of modes changes, whereas the frequencies of the modes might stay the same.] In other words, the measurement time is much longer than the coherence time of the individual modes. Considering a single sampling point in delay time, the measurement time is in the range of tens to hundreds of microseconds, whereas the coherence time is in the range of a few nanoseconds or less.
The result is shown in Fig. 9. Qualitatively, the results for random and locked phases are the same: Cross-correlation signatures occur with a spacing equivalent to the free spectral range of the assumed laser source (defined directly by the difference of the individual modes ). The width of the cross-correlation signatures depends on the spectral width of the pump field (number of modes × the mode spacing) and on the lifetime of the photoexcited charge carriers and . The ringing after the cross-correlation maxima is caused by the resonances of water vapor, which were included in this numerical model and are well known from experimental findings.
Analogous to the analytical discussion, these simple numerical investigations demonstrate the insignificance of the individual optical phases on the qualitative cross-correlation spectroscopy signal in the delay domain.
III. SYSTEM DEVELOPMENT
In the early years of CCS, not too many groups were joining this field of research. This changed over the years, as several improvements, alternative concepts, and application demonstrations have been achieved by an increasing number of groups, of which some are listed in Table I. The most important milestones in the field of terahertz CCS are ordered with respect to the year of publication along with some important demonstrations of applications in the timeline shown in Fig. 10. We refer to these milestones and demonstrations of applications in Sec. III A–D and IV.
Year . | Authors . | . | fMax(THz) . | DR (dB) . | Application . | Achievement . |
---|---|---|---|---|---|---|
1997 | Tani et al.18 | 802 nm | 0.4 | Semiconductor characterization | Photomixing with MMLD, incoherent detection | |
1999 | Morikawa et al.20 | 810 nm | 0.45 | Semiconductor characterization | Application of Ref. 18 | |
2000 | Morikawa et al.17 | 810 nm | 0.5 | Semiconductor characterization | First demonstration of terahertz cross correlation | |
2004 | Morikawa et al.30 | 810 nm | 0.6 | Semiconductor characterization | Spatial pump filtering | |
2007 | Shibuya et al.31 | 830 nm | 0.2 | Imaging | First application to imaging | |
2009 | Scheller and Koch25 | 660 nm | 0.6 | 50 | Semiconductor characterization | First mathematical model |
2010 | Brenner et al.32 | 830 nm | 0.6 | Spectral characterization of a dielectric mirror | ||
2011 | Scheller et al.33 | 660 nm | Imaging | Birefringence imaging | ||
2011 | Molter et al.34 | 785 nm | 1.4 | Spectroscopy | Spectral tunability | |
2011 | Morikawa et al.35 | 810 nm | 0.5 | Spectroscopy | ||
2012 | Scheller et al.36 | 660 nm | 0.6 | Spectral tunability | ||
2013 | Morikawa et al.37 | 810 nm | 0.5 | Semiconductor imaging | ||
2015 | Probst et al.38 | < 850 nm | Determination of the refractive index of liquid crystal polymers | Low-cost delay | ||
2017 | Kohlhaas et al.39 | 1.55 µm | 2.0 | 60 | Detection of n of ceramics and POM | First CCS at telecom wavelength |
2018 | Gente et al.40 | < 850 nm | Detection of water content of a plant leaf | First mobile application | ||
2018 | Rehn et al.41 | 660 nm | 1 | Spectral broadening by pulsed operation | ||
2019 | Molter et al.42 | 1.55 µm | 1.7 | 60 | Spectroscopy | First use of nonlaser light source |
2019 | Rehn et al.43 | 1.55 µm | 2.5 | 70 | Spectral broadening by feedback |
Year . | Authors . | . | fMax(THz) . | DR (dB) . | Application . | Achievement . |
---|---|---|---|---|---|---|
1997 | Tani et al.18 | 802 nm | 0.4 | Semiconductor characterization | Photomixing with MMLD, incoherent detection | |
1999 | Morikawa et al.20 | 810 nm | 0.45 | Semiconductor characterization | Application of Ref. 18 | |
2000 | Morikawa et al.17 | 810 nm | 0.5 | Semiconductor characterization | First demonstration of terahertz cross correlation | |
2004 | Morikawa et al.30 | 810 nm | 0.6 | Semiconductor characterization | Spatial pump filtering | |
2007 | Shibuya et al.31 | 830 nm | 0.2 | Imaging | First application to imaging | |
2009 | Scheller and Koch25 | 660 nm | 0.6 | 50 | Semiconductor characterization | First mathematical model |
2010 | Brenner et al.32 | 830 nm | 0.6 | Spectral characterization of a dielectric mirror | ||
2011 | Scheller et al.33 | 660 nm | Imaging | Birefringence imaging | ||
2011 | Molter et al.34 | 785 nm | 1.4 | Spectroscopy | Spectral tunability | |
2011 | Morikawa et al.35 | 810 nm | 0.5 | Spectroscopy | ||
2012 | Scheller et al.36 | 660 nm | 0.6 | Spectral tunability | ||
2013 | Morikawa et al.37 | 810 nm | 0.5 | Semiconductor imaging | ||
2015 | Probst et al.38 | < 850 nm | Determination of the refractive index of liquid crystal polymers | Low-cost delay | ||
2017 | Kohlhaas et al.39 | 1.55 µm | 2.0 | 60 | Detection of n of ceramics and POM | First CCS at telecom wavelength |
2018 | Gente et al.40 | < 850 nm | Detection of water content of a plant leaf | First mobile application | ||
2018 | Rehn et al.41 | 660 nm | 1 | Spectral broadening by pulsed operation | ||
2019 | Molter et al.42 | 1.55 µm | 1.7 | 60 | Spectroscopy | First use of nonlaser light source |
2019 | Rehn et al.43 | 1.55 µm | 2.5 | 70 | Spectral broadening by feedback |
A. Improvements in signal quality
As for all spectroscopy techniques, the signal quality is a major criterion for the applicability to measurement tasks for scientific as well as for industrial applications. While the first demonstrations of terahertz CCS showed rather subterahertz bandwidths and moderate signal-to-noise ratios, the signal quality impressively improved in the past few years. In their first publication, Morikawa et al.17 demonstrated the phase-sensitive detection of frequencies up to 450 GHz. The first improvement introduced was obtained by spatial filtering.30,35 In their work, Morikawa et al. aimed for and demonstrated the enhancement of continuous spectral components, but the signal strength per pump power is enhanced as well. The introduction of a small aperture or, finally, a single-mode fiber coupling led to the enhancement of the system efficiency, which can be understood as the improvement of the overlap of the used laser modes as they have to efficiently interfere in the gap of the photoconductive antennas. If the excited photocarriers within the pump spot experience unequal modulation or excitation, the resulting emission is lowered. Only if the modulation is homogeneous across the excitation area can an efficient terahertz generation be ensured. This also requires equal polarizations of all optical modes involved. As demonstrated by several groups, a broad external feedback into the employed multimode (non-mode-locked) diode lasers results in the broadening of the spectral coverage of the CCS system as well as the enhancement of the stability of the signal.44
B. From near-infrared to telecom wavelengths
Analogous to the development in the field of terahertz TDS or continuous-wave photomixing, the first CCS systems were based on laser wavelengths in the near-infrared. Morikawa et al.20 used a center wavelength of 810 nm in their first setup. Scheller and Koch25 used components from the consumer market (DVD player components), which provided center wavelengths of ∼660 nm. As in the past decade semiconductor materials became broadly available for telecom wavelengths, the transition to this spectral range as pump source has been performed. The telecom mass market enables the cost-efficient availability of optical components suitable for wavelengths ∼1.55 µm. This has been demonstrated for both photomixing terahertz systems22,23,45 and TDS systems in the late 2000s.46 It took almost 10 years, before this has been transferred to the CCS systems: The first demonstration of CCS at telecom wavelength was reported in 2017 by Kohlhaas et al.39 who achieved a bandwidth of up to ∼2 THz. Material characterization on ceramics and polyoxymethylene (POM) was successfully demonstrated and compared to TDS measurements.
C. Employment of incoherent light sources
Driven by the restriction of a terahertz spectrum with discrete lines instead of a continuous spectrum, we introduced in 2019 the use of a superluminescent diode (SLD) to drive a CCS system.42 This resulted in an isolated cross-correlation maximum in the delay domain, which corresponds to a truly continuous spectrum, and this spectrum can be used for spectroscopic investigation of samples. The use of this time-incoherent light source can be understood as a multimode source without frequency spacing between the individual modes and non-mode locking. An important conclusion of this demonstration is that no laser light is needed for this measurement principle as long as a suitable spectral width is provided at the wavelength needed for driving the terahertz modules (photoconductive mixers or similar). In Fig. 11, the comparison of the signals of a CCS system is given when driven by a multimode (non-mode-locked) laser diode or an SLD. Both signals were acquired using the same pump wavelength of 1.5 µm and the same power of ∼20 mW at each module.
In the case of a multimode (non-mode-locked) laser diode, the periodicity of the delay-dependent cross-correlation amplitude is directly related to the free spectral range of the employed laser diode. This directly translates to a discrete spectrum with only a few lines in the spectral domain and limits the application of a multimode laser-driven CCS system. Whereas when driven by an SLD, an isolated cross-correlation maximum is generated, corresponding to a truly continuous spectrum. This can be understood by the lack of a cavity, which in the case of laser sources, defines the supported spectral modes with the spacing of the free spectral range. In the case of a cavity-less source, there is no cavity-dependent restriction to the emitted frequency, which in the case of an SLD only depends on the used medium. As the spectral width of an SLD is typically several THz, it is beneficial to use optical bandpass filtering to efficiently drive the terahertz modules, which has already been experimentally demonstrated.42
Based on the numerical framework presented in Sec. II, the signal of a CCS system driven by incoherent light can be simulated as well. The result is presented in Fig. 12. When decreasing the mode spacing in the numerical modeling or assuming a high number of randomly spaced modes, the periodicity of the cross-correlation result vanishes. This approaches the case of using a spectrally continuous pump source like an SLD.
D. Cost-efficiency
The main advantage of the multimode laser diode–driven CCS systems is the cost-efficiency due to the comparatively cheap pump source. Hence, the focus of development of these systems has mostly been the realization of very cost-efficient setups. The employment of laser sources from the consumer market was investigated by Scheller and Koch.25 Even the use of the linear drive of a DVD drive was reported to realize an optical delay unit,38 further improving the cost-efficiency. On the data acquisition side, open-source hardware like a Raspberry Pi was used, which is powerful enough to control and analyze the data of these systems, offering comparatively low cost to standard computer solutions. This also enabled the operation of such a system with the power of a car battery to investigate the water content of a leaf outdoors.40 The remaining cost drivers of these systems are the emitter and detector modules, which were not yet tackled by efforts concerning the cost-efficiency. On the side of the optical components, the systems profit from the telecom market when driven at a center wavelength of ∼1.55 µm.
IV. APPLICATIONS
As terahertz CCS in general provides access to the same part of the electromagnetic spectrum as TDS, the conceivable applications are the same as well. Since its first proof of principle, there have been several demonstrations of applications. The first one was characterization of semiconductor wafers with respect to their thickness and resistivity (or carrier density). Its application to spectroscopic measurement tasks was proven as well as its suitability for raster scan imaging purposes. We discuss the different applications in more detail in Sec. IV A–C.
A. Materials characterization
Already in their first demonstration of terahertz CCS in 2000, Morikawa et al.17 demonstrated the applicability of this measurement principle to semiconductor characterization. Two Si wafers with thicknesses and resistivities of 630 µm and 440 µm and 2.5 Ω cm and 100 Ω cm, respectively, have been characterized by measuring their transmittance and phase retardance. The corresponding spectra and the evaluation results are shown in Fig. 13.
From the results, the carrier densities were calculated and showed a good agreement with results from direct current resistivity measurements. This was intensified in further publications,30,37 where also a spatial mapping of the carrier density distribution of a 6″ Si wafer was carried out with a CCS setup. In 2009, Scheller and Koch25 measured the spectral birefringence of a liquid crystal polymer by using a terahertz CCS system. They measured the refractive indices of the slow and fast axis in the range between 200 GHz and 600 GHz to be ∼2.05 and 1.85, respectively. The spectral transmittance and phase shift of a metal hole array measured with a terahertz CCS system was demonstrated in 2011 by Morikawa et al.,35 where a prominent resonance feature ∼0.3 THz was measured as shown in Fig. 14. It is shown that the results are in good agreement with measurements with a conventional terahertz TDS system. The focus of this publication is on the effect of spatial filtering of the used laser light.
In the first report on terahertz CCS at telecom wavelength, spectroscopic measurements on a ceramic sample and a POM sample were demonstrated in the range between 0.4 THz and 1.8 THz.39 The results were compared to that from a standard TDS system and showed a good agreement. In 2019, we demonstrated spectroscopic absorption measurements on para-amonibenzoic acid, α-lactose monohydrate in the range between 0.1 THz and 1.5 THz as well as water vapor in the range between 0.5 THz and 1.5 THz.42 These measurements were taken with an SLD-driven CCS system, so no limitations from discrete spectral lines occurred. The corresponding spectra are shown in Figs. 15 and 16 and are compared to measurements with a conventional TDS system and to HITRAN simulations, respectively.
These spectroscopic applications all demonstrated that terahertz CCS is useful for the same type of measurements that phase-sensitive terahertz measurement systems (as TDS) address. Both amplitude and phase can be retrieved for the accessible spectral range. This spectral coverage is the only difference where TDS systems are most commonly superior to CCS systems. Nevertheless, as discussed in Sec. III D, if spectral coverage is not of utmost importance, the potential benefit of cost saving is high.
B. Imaging
The first reported demonstration of terahertz imaging with a CCS system was published in 2007 by Shibuya et al.31 By using a raster scanning scheme, a railway IC card pass was imaged using terahertz frequencies at ∼0.2 THz, revealing the inner antenna structure of the sample. Employing a fiber-coupled multimode, non-mode-locked laser diode, a dynamic range of ∼30:1 was achieved. Amplitude and phase images were obtained by measuring the subterahertz signal at different positions of the used optical delay line. The recorded images are reprinted in Fig. 17.
Later on, the group of Martin Koch also presented imaging applications: An airbag cover and a fiber-reinforced polymer plate were investigated with a terahertz CCS system by raster scanning imaging.33 Perforations were reliably imaged on the airbag cover. For the fiber-reinforced polymer plate, polarization sensitivity was demonstrated showing pronounced image contrast due to the fibers orientated parallel or perpendicular to the incoming polarization, leading to birefringence of the sample. As discussed in Sec. IV A, Morikawa et al.37 presented in 2013 a spatial mapping of the carrier density of a Si wafer, demonstrating the usefulness of this approach to image semiconductors with respect to their physical properties.
C. Layer thickness measurements
Being one of the most promising applications for terahertz technology in general, layer thickness measurements are of great interest for the cross-correlation systems as well. The benefits of measuring layer thicknesses with terahertz radiation are obvious when comparing with concurrent techniques: Individual layer thicknesses of multilayer structures can be measured contact free and nondestructively without harm to the user. When using pulsed TDS systems, the measurement principle is often understood as a time-of-flight measurement and corresponding evaluation. For the case of CCS, this simple conceptual picture might cause some problems of understanding, as there are no pulses as described above. Nevertheless, the results in the recorded data are essentially identical, despite some system-dependent performance differences (limited bandwidths and dynamic ranges) as described above. Perhaps the measurement principle can be better understood in comparison to time-domain optical coherence tomography (OCT) or Fourier-transform infrared (FTIR) spectroscopy with incoherent light, except for the fact that in OCT and FTIR spectroscopy, the original copy interferes with the light field after interaction with the sample before being detected, whereas in CCS, the light field after interaction is detected in a cross-correlator. Nevertheless, the results in the recorded data are essentially identical, despite some system-dependent performance differences (limited bandwidths and dynamic ranges) as described in Secs. II and III. The important difference is that in CCS, the terahertz radiation is not interfered with and detected directly with an intensity-sensitive detector but is cross-correlated in a corresponding detector with the copy of the light that was also used for generation. The retrieval of spectral amplitudes and phases are very similar if not the same, whereas the measurement concept differs.
The experimental setup of the system for layer thickness measurements is schematically shown in Fig. 18.
The output of a commercial SLD (Thorlabs SLD1550P-A40), followed by an optical insulator (40 dB), is fed into a motorized bandpass filter. The filter can be tuned in bandwidth from 1 to 25 nm and in center wavelength from 1540 to 1560 nm. To enhance the optical power, a self-built erbium-doped fiber amplifier (EDFA) with variable gain is used. A 70:30 fiberoptic beam splitter feeds the optical branches, whereas the detector branch with the optical delay unit receives 70% to balance its losses. As delay unit, an interferometrically controlled optical delay line is used,29 which is capable of scanning 100 ps at rates up to 30 Hz (waveform acquisition rate 60 Hz) within a stationary (stepper motor–driven) time window of 2 ns. We use a waveform acquisition time of 25 ms in most of the data presented in the following. The interferometric control of the delay is provided by quadrature detection of a 1.3-µm laser-driven interferometer and ensures a timing accuracy of 1.08 fs. The terahertz reflection setup is built by four off-axis parabolic mirrors with focal lengths of 50.8 mm (next to the modules) and 101.6 mm (for focusing onto the sample). The detected signal is amplified by a transimpedance amplifier with 50-kHz bandwidth and 107 V/A and acquired by a 16-bit data acquisition card with 200 000 samples per second. For layer thickness evaluation, a central processing unit–based high-performance algorithm is used based on waveform retrieval using a physical model.47 This algorithm retrieves the thicknesses and, optionally, the optical parameters of the layers.
Varying the bandpass filter width enables the tuning of the terahertz spectrum to find a trade-off between maximizing the peak dynamic range at a moderate terahertz bandwidth and maximizing the highest terahertz frequency at moderate dynamic ranges. By using the motorized bandpass filter centered around 1560 nm and tuning its width from 1 to 25 nm, the acquired waveforms and the corresponding spectra can be tuned as shown in Figs. 19(a) and 19(b), respectively.
To investigate the performance of our approach, we measured different samples and compared the results with those from TDS as well as magnetic-inductive measurements. The TDS system used in this study is a state-of-the-art system driven by an ultrafast femtosecond laser at 1.55 µm. The delay line as well as the data acquisition and evaluation are the same for the SLD-driven CCS and the TDS measurements. The results for four different single-layer samples are shown in Fig. 20(a).
The results for the terahertz systems are derived from 1000 subsequent measurements each, whereas the magnetic-inductive measurements are repeated 100 times for each sample. The acquisition time for a single waveform is set to 25 ms. The optical constants for the terahertz evaluation are retrieved by using an optimization algorithm that uses not only the thickness as the fit parameter but also the refractive index as well as the extinction coefficient from the TDS data. Hence, in this case, no adjustment or calibration is done using the magnetic-inductive measurements. Nevertheless, the results of the three sensors are in good agreement for all four samples. In particular, the good agreement of the results from the SLD-CCS and TDS systems underlines the applicability of the presented approach to measurement of moderate single-layer thicknesses of down to some tens of micrometers. The slightly lower thickness of the fourth sample (tape) when measured by the magnetic-inductive sensor might be due to deformation, as this measurement method uses a contact-based method with a constant pressure. As the tape is softer compared to the coatings, this could be an explanation. Figures 21(b) and 21(c) show the histograms of the SLD-CCS and TDS measurements on the first sample in detail, revealing the difference between these measurement principles.
While the results of the TDS system provide a standard deviation of 40 nm, the SLD-CCS system provides a standard deviation of 800 nm (which is still <1%). A waveform acquisition time of 25 ms was used for both approaches with this sample. By averaging (longer acquisition time), this standard deviation can be reduced further, while the absolute accuracy can be improved by using a calibration and adjustment employing the magnetic-inductive sensor or a cross-sectional microscopy method. As a further consistency test, we investigated a spatial feature by translating the sample by hand and measuring 16 sample positions on a straight line of a length of ∼75 mm. In this case, the optical constants for the terahertz evaluation were calibrated and adjusted by using the data of the magnetic-inductive sensor once. The result of this measurement is shown in Fig. 22 and shows a good agreement and the same spatial features regarding the uncertainties from manual translation and the standard deviation of the sensors.
Most commonly, coatings of products are often multilayer structures. The possibility to extract individual layer thicknesses using a nondestructive and contactless method is one of the key advantages of terahertz technology. Therefore, we also investigated the performance of the SLD-CCS approach to measure the individual layer thicknesses of a dual-layer sample. To enable a good comparison of the single-layer data with the dual-layer data, we added a layer of tape (thickness d 41 µm, refractive index n 1.5) on top of a single-layer coating (d 90 µm, n 1.7) also used in the previous experiment, which provided a contrast in refractive indices of ∼0.2. The optical constants were adjusted by using the individual thicknesses measured by the magnetic-inductive sensor. Again, the most important criterion in this investigation is the stability and, therefore, the standard deviation of subsequent measurements. Fig. 23 (a) shows the histograms of the extracted thicknesses of layer 1 and 2 and the total layer thickness in dependence on the measurement time per waveform. Fig. 23 (b) provides the corresponding standard deviations.
While the mean value for the different integration times is quite constant, the standard deviation for both layer thicknesses drops from several micrometers to <1 µm at a waveform acquisition time of 800 ms. As expected, the total layer thickness is more stable than the individual layer thicknesses at a given waveform acquisition time. These data show that multilayer thickness measurements are, in principle, also enabled by using the proposed SLD-CCS principle.
V. CONCLUSIONS AND OUTLOOK
Twenty years after the invention of terahertz cross-correlation spectroscopy, the main applications already extensively demonstrated using time-domain spectroscopy have been proven to be accessible for this specific approach as well. A rather small community is pushing this field forward, and significant improvements have been achieved in the meantime concerning measurement speed, obtained bandwidth, and degree of integration. It was proven that not even laser light is needed to drive these types of measurement systems, which widens the understanding of the principle as well as the conceivable applications. The utilization of terahertz cross-correlation spectroscopy on tasks like spectroscopy, semiconductor characterization, imaging, plant monitoring, and layer thickness measurements has been demonstrated. Nevertheless, a broad and commercial use of this principle is overdue so far.
Terahertz cross-correlation spectroscopy systems will continuously benefit from developments in the field of terahertz time-domain spectroscopy as well as in the field of continuous-wave photomixing systems. In particular, the emerging improvements of continuous-wave emitter and detector modules for photomixing systems will simultaneously enhance the performance of these systems. If the robustness of them will be enhanced in terms of withstanding high optical pump powers, the measurement performance will directly benefit. As the spectral width of the available light sources (especially of the incoherent light sources) surpasses the accessible bandwidth of these modules, the improvement of their bandwidth will be highly beneficial. It is feasible that the employed light sources for driving these modules will advance to more integrated packages, specifically satisfying the need of cross-correlation spectroscopy systems with respect to provided bandwidth, power, and stability. For example, if the supply of a spectrally shaped light source is simplified, the cost of this component will drastically shrink further as well. As the evaluation strategies from common time-domain spectroscopy systems can be directly applied to cross-correlation spectroscopy signals, the applications benefit here as well. Therefore, it is worth continuously investigating and improving these systems, as the potential for cost-effective realization of terahertz measurement systems is highly promising.
AUTHORS' CONTRIBUTIONS
D.M. and M.K. designed and carried out the experiments related to SLD-CCS. J.K. and S.W. contributed to the interpretation of the results on layer thickness measurements. All authors discussed the results and contributed to the writing of the manuscript.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.