2.1.

Process Analytical Technology and Nondestructive Testing

Process analytical technology (PAT) is a system for designing, analyzing, and managing the manufacturing process. The United States Food and Drug Administration (FDA) has published guidelines for introducing PAT into pharmaceutical production. Consequently, there is an increasing need for the analysis of medicines to reassure consumers and increase safety. Also the polymer processing industry is continuously investigating new process control and nondestructive testing techniques.^40–43 Many plastic materials are transparent to THz radiation and serve as a base material for passive THz system components. In return, THz systems can reveal valuable information of the composition of polymers. Offline measurements for the characterization of molecular properties, considering the following inline process monitoring with real-time feedback, and referring finally to quality inspection of the polymeric components are some of the applications of the THz technology in polymer industry.⁴⁴

2.2.

Passive Spectroscopy and Astronomy

CW THz systems have also been used in the field of astronomy for the past few decades for passive spectroscopy. THz waves can penetrate in a solid and can be used to discriminate intermolecular interactions between molecules or crystals inside the solid. For THz frequencies above 1 THz, there are many vibration modes of molecules or crystals that occur due to intermolecular interactions. Consequently, the spectral fingerprint, in which the vibration modes absorb THz waves, allows us to identify the materials. The molecular interaction is stronger as the frequency increases; however, the penetration of THz waves within solids tends to decrease because the shorter wavelengths at higher frequencies are easily scattered by particles. Therefore, there is a limited region inside the frequency range from 0.3 to 5 THz where the two advantages of deep penetration and spectral fingerprint are both obtained. Even within the THz spectrum in the low frequency region of 0.1 to 0.3 THz, it is difficult to identify molecules or crystals even though penetration is easy, whereas in the higher frequency region of 5 to 10 THz, extremely high loss limits the available sample thickness within thin films or surfaces.⁴⁵

2.3.

Reflection and Stand-Off Imaging

CW THz imaging is advantageous for specific applications due to its higher single-frequency dynamic range and the nature of possessing a narrow spectral bandwidth. One important advantage of imaging with a single-frequency source is the ability to select the source wavelength to optimize the imaging capability. This is very useful in the case of imaging at a stand-off distance since at greater than a few meters distance. Stand-off imaging is challenging because of the presence of atmospheric water vapor, which significantly attenuates the THz beam. However, at certain frequencies within the THz range, the atmospheric attenuation is minimized because there are no nearby strong water vapor absorption lines. The ability to tune the THz source to a water window is a considerable advantage. For example, for a 25-m stand-off, the power throughput from transmitter to receiver increases by more than a factor of 10 if the atmospheric loss decreases by $0.5\mathrm{dB}.{\mathrm{m}}^{-1}$.⁴⁶ Real-time imaging at a 25-m stand-off has been demonstrated using a THz QCL and a room-temperature microbolometer array.^{6,9,11,16,19,20,23,25,26,35,36,39,40,46–82} In addition, because time-delay scan is not a compulsion requirement in a CW system, the acquisition speed of a CW THz imaging system can be increased relative to that of a pulsed system, in which time-delay scanning is generally necessary.

CW imaging is first demonstrated by Siebert et al.⁸³ and Kleine-Ostmann et al.⁸⁴ Siebert et al. employed the room temperature optoelectronic detection scheme of photomixing two CW lasers in a photoconductor. They used a 200-ms lock-in time constant and measured a signal-to-noise ratios of 100:1. However, femtosecond lasers are typically complex and expensive. In Ref. 84, an imaging system using a two-color external-cavity laser diode is presented. They measured images of biological tissue, with an SNR of around 75:1. Detection was achieved using a bolometer which is typically not phase sensitive and severely limits the modulation bandwidth. From a commercial perspective, using a Ti:Sapphire laser and bolometric detection respectively which needs expensive laser sources and cannot perform room-temperature phase-sensitive detection. Gregory et al.⁷¹ demonstrated a compact CW THz imaging system that combined diode lasers with optoelectronic detection.

Currently, there are two methods that are commonly used for CW THz imaging: a raster scan of a focused incident beam, or the formation of an image on a detector array. In the former, a single detector, such as a Schottky diode, Golay cell, or pyroelectric detector, is used to detect the full power of the beam. This has the advantage of a high dynamic range, but the disadvantage is that the image must be formed point by point using a scanning system, which is time-consuming and not applicable to moving targets. The development of a sensitive THz detector array is still an active research area. Detector arrays also have the disadvantage of being severely affected by distortions and aberrations in the focusing system, whereas for a raster scanning system, the beam can be focused to a diffraction-limited spot. In general, a CW system can outperform systems based on time-domain photoconductive sampling in frequency resolution, spectral brightness, system size, and cost.

2.4.

Medical Imaging

It has been shown in recent years that THz transmission imaging can be used to generate three-dimensional (3-D) visualization of objects’ internal structure, which can be valuable for biological imaging applications. Other use case for 3-D THz imaging could be the noninvasive analysis of archeological findings, such as inspection of paintings, wrapped mummies,⁸⁵ or human bones.⁵¹ Many techniques have been investigated for the acquisition of 3-D images at THz frequencies, including diffraction tomography,⁶² use of binary lenses,⁸⁶ time-of-flight measurements in reflection mode and tomosynthesis,⁸⁷ and more recently computed tomography (CT) with ultrashort THz pulses,⁵² or CW sources.⁵⁴ THz tomography competes against the longtime used Xray CT, which usually provides high spatial resolution and high contrast images. However, there are three opportunities for THz frequencies in this field. First, THz waves may provide valuable supplemental information, enabling additional extraction of the spectroscopic object properties⁵² and providing different absorptive contrast as compared to x-rays. Second, ongoing advances in silicon-integrated THz components and photonic circuits should enable the realization of ultra-low-cost 3-D THz-CT imaging systems,⁷⁶ which promises an increased exploitation for future industrial applications as compared to expensive x-ray machines. Third, THz waves do not ionize the samples as they go through them which makes them less risky and more suitable for biological detections and medical imaging.^49,88 More importantly, a better image contrast for biological soft tissues can be obtained by the THz imaging technique^80,89 thereby getting more accurate and comprehensive structural views and biological information. In a recent paper, the authors demonstrated the use of a CW THz CT system to reconstruct two-dimensional (2-D) cross-sectional images of the chicken ulna to visualize the internal structure of it.⁹⁰ Compared with the pulsed THz CT systems,^62,91 the CW THz system is more compact and low cost. The proposed CW THz CT system is shown in Fig. 5 which is based on BWO that can produce a CW THz and a Golay cell detector. The testing chicken ulna is fixed on the precision electric rotation stage and the electric 2-D translation stage, and it is rotated and translated during the recording process of projection data and they have looked at the effect of different projection angle intervals on the quality of the images. In Fig. 6, the optical photographs of sections II and IV of the chicken ulna using the optical microscope and THz imaging are shown. Since the internal substance of the chicken ulna has different absorptions for the THz wave, the internal structure distribution and profile information of the chicken ulna can be obtained in the 2-D cross sectional images by the CW THz CT system.

Fig. 5

The setup of CW THz CT with BWO and Golay cell detector.⁹⁰

Fig. 6

The optical photographs and 2-D cross-sectional images of the chicken ulna at sections (a) and (b) II and (c) and (d) IV in the schematic diagram of the chicken ulna.⁹⁰

Protein and DNA molecules typically have intramolecular vibrations in the THz range. High hydration level to ensure homogeneous samples results in a large water background that increases the protein THz absorbency. Lack of narrow resonances for unoriented samples prevents use of THz for protein or DNA identification. Using linear dichroism measurements on protein crystals, distinct narrow resonances unique to both the protein and protein binding state have been observed.⁸¹ The ability to measure the intramolecular vibrations is a necessary tool to resolve the ongoing argument of their role in biological function. Also, interpretation of the resonant bands will be a challenge, as these consist not of single vibrations, but sets of vibrations with the same polarization dependence.⁶⁰

Rapid and accurate detection is essential for early diagnosis and cell activity monitor. Current cell detection methods mainly depend on labeling technology, such as flow cytometry, fluorescence molecular tomography, and multiphoton microscopy, with high sensitivity, precision, and selectivity. However, biological labeling can directly affect the biological activity and function of living cells. This fundamentally limits the ability of existing cell detection to molecular level resolution. Although the label-free cell detection method including electrochemical and piezoelectric technologies has been applied widely, potential radiation hazard and limited sensitivity still make them controversial. Hence, an alternative method for a label-free and noninvasive cell viability evolution is urgently needed for life sciences.⁵⁰ THz spectroscopy is developing into an optical, noninvasive, label-free, and reagent-free technique, which can be utilized for detection and identification of living cells.

One of the growing applications of THz technology is bacterial detection. Based on small size and low absorption coefficient of the bacteria, THz radiation can propagate through an entire object, allowing bacterial components contribute to the THz signature of objects. Extensive researches were conducted to realize qualitative and quantitative analyses of bacteria. The sensitive detection of bacteria in both ambient and aqueous environments is feasible using THz metamaterials (Figs. 7 and 8). A THz metamaterial based on the SRR pattern of 550-mm high resistance silicon substrate was used for high-sensitivity detection of bacteria in solid and liquid phases.⁵⁰

Fig. 7

A schematic of specifically selective bacteria detection using metamaterial in solution environment.⁵⁰

Fig. 8

THz transmission with and without the deposition of E. coli using the functional metamaterials in aqueous environments.⁵⁰

Several THz imaging systems have been developed for the noninvasive detection of tissues to assess the depth and severity of burned tissues. Because the cancerous or other diseased tissues can contain higher water content as a result of increased vascularity or edema, THz imaging has shown potential in differentiating tissue types. A recent simulation study found that InN-enhanced THz imaging enables highly sensitive diagnosis of early-stage skin cancer based on tiny water content changes.^50,92 The water contents of blood vessel and corneal tissue were also resolved using a THz imaging system.⁹³ Furthermore, the difference among various tissues is still significant after formalin fixing, suggesting that the difference is due to changes in water content and structural changes. Moreover, based on higher THz reflection intensities, fresh human early gastric cancer tissues have been distinguished from normal mucosa, (Fig. 9).⁹⁴ Interestingly, it is successful that the imaging of human hepatocellular carcinoma tissue has been obtained using CW THz digital in-line holography in the absorption and phase-shift distributions (Fig. 10).⁸⁰ By rejecting Fresnel reflections, the cross-polarized THz image of nonmelanoma skin cancer displays the approximate location of the tumor clearly.⁷⁹

Fig. 9

THz image of tissues from early gastric cancer.⁵⁰

Fig. 10

THz in-line hologram of human hepatocellular carcinoma tissue by phase-shift distribution reconstructing.⁵⁰

2.5.

Pharmaceutical Applications

Some of the recent pharmaceutical applications of THz are (1) discrimination and quantification of hydrates, (2) analysis of solid form transformation dynamics, (3) quantitative characterization of tablet coatings: off-line and on-line, (4) tablet coating and dissolution, and (5) spectroscopic imaging and chemical mapping. TeraView has applied its proprietary THz imaging and spectroscopy technology to increase pharmaceutical product and process understanding as an effective part of the quality by design initiative. Their 3-D THz imaging system is able to nondestructively estimate critical quality attributes in pharmaceutical products, such as crystalline structure, thickness, and chemical composition. Their THz imaging system monitors the impact of changing the solids level of a coating suspension from 15% to 25%, which reduces the coating process time. Figure 11 shows some sample results in which a change in adhesion between the substrate and coating.

Fig. 11

The 2-D THz image of a tablet to investigate the effects of film-coating process on a finished drug product.⁹⁵

2.6.

Noncontact Imaging for Conservation of Paintings, Manuscripts, and Artifacts

Recently artwork started to be scanned by THz systems.⁵⁷ These imaging systems have been used for scanning ancient mummified samples paintings.^74,75 Frequency-domain THz systems allow for the depth inspection of the object under investigation due to the frequency sweep of the emitted radiation.⁷⁴ Figure 12(a) shows the THz image of the global maximum of the signals recorded from the contemporary painting after contrast enhancement.⁵⁷ By comparing it with the THz surface topography of the painting obtained by illuminating the object with raking light Fig. 12(a), it can be seen that the black lines of the THz image correspond to the sharp edges of the thickest brushstrokes used by the artist to model the subjects in relief. Figure 12(b) shows the signals recorded at $(x,y)$ coordinates corresponding to low [in correspondence of the sharp edges, green and red curves in Fig. 12(c)], medium [yellow and orange curves in Fig. 12(c)], and high [blue and violet curves in Fig. 12(c)] reflectivity values, which have been collected from neighboring pixels in two different areas of the painting.

Fig. 12

(a) The contemporary painting front, (b) THz image of the contemporary painting after contrast enhancement, parameter: signal global maximum, (c) signals recorded at the $(x,y)$ coordinates reported in the legend, corresponding to the colored dots of Fig. 12(b).⁵⁷

2.7.

Terahertz Communication

Wireless data traffic has been expanding in the past few years. In particular, mobile data traffic is expected to increase sevenfold between 2016 and 2021 due to increase in whereas video traffic. Such remarkable growth of wireless traffic has driven the urge to investigate suitable regions in the radio spectrum to fulfill the accelerating demands. To this end, the THz frequency band has received considerable attention in the research fraternity.⁶¹ As a result of the exponential growth of wireless traffic, the demand for higher bandwidth never seems to subside before the capacity of the generation beyond 5G technology has reached its upper limit. THz communications are expected to enable the seamless interconnection between ultrahigh-speed wired networks, achieving full transparency and rate convergence between wireless and wired links. This will facilitate the use of bandwidth-intensive applications across static and mobile users. Some specific applications are high-definition holographic video conferencing (virtual reality office) or high speed wireless data distribution in data centers. Figure 13 shows a schematic of the application of THz back haul links in future cellular networks.⁹⁶

Fig. 13

Application of THz backhaul links in future cellular networks.⁹⁶

2.8.

Commercial Terahertz Companies

The Global Terahertz Market is valued at USD 0.09 billion in 2016 and is expected to reach a value of USD 0.67 billion by the end of 2022 (based on Orbis Research Report⁹⁷). THz technology was initially used in very few areas such as planetary science and astronomy. Recent innovations in this technology enabled its spread across many areas such as food and agriculture, pharmaceutical manufacturing, plastics and ceramics, and communications. Recent developments in THz device technology such as generation of THz pulse for spectroscopy applications user NIR laser, low loss waveguide circuits, submicron-scale lithography, and silicon micromachining, which is used for compact and integrated packing, offer a plethora of opportunities. A recent increase in the number of manufacturing companies, and a rise in worldwide demand for precise security systems, defense, and medical sectors are driving the global THz technologies market. However, the high cost is the main obstacle for market growth. Based on the type of technology, the market is categorized as THz imaging (active and passive systems), THz spectroscopy (time- and frequency domains), and communication systems (modulators, emitters, and antennas). Based on end-user application, the market is segmented into medical and healthcare, nondestructive testing, defense, and agriculture. Currently, North America holds the major market share and Asia-Pacific is expected to grow at a considerably high rate. Major global market players in the THz market are Advantest Corporation, Traycer, Terasense, Microtech Instrument Inc., Menlo Systems GmbH, Gentec Electro-Optics, Teraview, and Toptica Photonics AG. In the following, a brief introduction to each of these companies (in alphabetic order of the company name) is provided.

Advantest⁹⁸ offers a series of low-cost, all-purpose THz spectroscopic systems that enable spectroscopic measurements. The tools are capable of performing nondestructive analysis on a wide variety of sample types, making it applicable to a broad range of fields from life sciences to electronics, where precise chemical and material characterization is critical. The systems are ideal for settings ranging from basic research to product development, as well as for manufacturing and quality control, and employ easy-to-use spectroscopic methods that do not require specialized knowledge of THz-wave generation or optics. One example is the TAS7400 product line (Fig. 14), which is capable of performing nondestructive analysis on a wide variety of sample types, making it applicable to a broad range of fields from life sciences to electronics, where precise chemical and material characterization is critical. The systems are ideal for settings ranging from basic research to product development, as well as for manufacturing and quality control, and employ easy-to-use spectroscopic methods that do not require specialized knowledge of THz wave generation or optics.

Fig. 14

A full product line-up of TAS7400 product line.⁹⁸

Gentec Electro-Optics produces different components for THz power measurement. The company offers pyroelectric-based THz measurement systems that are very easy to use at room temperature. As an example, the T-RAD (Fig. 15) is a microprocessor-based digital radiometer that includes a 12-bit ADC and powered by a USB connection, which also acts as a virtual COM port. The LabView software supplied with the device makes it very easy to set up the radiometer, measure a THz or broadband source and record data.⁶³

Fig. 15

T-RAD is a microprocessor-based digital radiometer from Gentec.⁶³

Menlo Systems GmbH⁹⁹ produces high-speed THz scanning systems without out any mechanically moving parts and a large scanning range of nanoseconds. As an example, the compact THz spectrometer TeraSmart (Fig. 16) integrates the latest achievements in broadband THz time-domain spectroscopy into an easy-to use turnkey solution. The modular design based on our OEM laser platform ensures a flexible configuration of the system to meet the needs for integration in any industrial or scientific environment. Custom fiber lengths to THz emitter and detector are available. Moreover, multibranch configurations are possible, enabling simultaneous measurements of several emitter/detector pairs using only one fs fiber laser oscillator.

Fig. 16

TeraSmart, a compact industry-proven THz spectrometer from MenloSystems.⁹⁹

Microtech Instrument Inc.¹⁰⁰ produces different THz spectrometers, generators, detectors, and passive components. One of their interesting products is T-Vision system which is video rate imaging system. It is the solution for imaging applications that require high frame rates. The T-Vision system is an all-in-one system based on a nonlinear process, where the THz image is mixed with a near-IR pulse, generating an upconverted near-IR image that is detected with a CMOS camera (Fig. 17).

Fig. 17

T-Vision imaging system from Microtech.¹⁰⁰

National Optics Institute (INO)⁷⁸ is another company that offers THz illumination source especially designed to build a complete THz imaging system when paired with INO’s THz camera. Their THz imaging system can be used for both see-through imaging (transmission imaging) and reflection mode. One example of their products is MICROXCAM-384i-THz THz camera that allows you to see through materials in real time. It is based on INO’s $384\times 288\text{pixel}$ uncooled microbolometric detector, optimized for the THz waveband (Fig. 18).

Fig. 18

T-Vision imaging system from Ino.⁷⁸

Terasense Group Inc. is one of the leading manufacturers of portable THz imaging systems with products. Terasense makes new type of semiconductor detectors for imaging sensor arrays, which effectively cover sub-THz and THz ranges of electromagnetic spectrum (50 to 700 GHz). The company has developed and patented a ground-breaking technology for making new-generation semiconductor imaging systems for THz and sub-THz frequency ranges. As an example, one of imaging cameras produced by this company is TeraFAST-256 system (Fig. 19), which has image acquisition rate of 5000 fps (5 KHz) and scanning speed up to $15\mathrm{m}/\mathrm{s}$ ($900\mathrm{m}/\min$) with 256 pixels ($256\times 1$ array of detectors).¹⁰¹

Fig. 19

TeraFAST-256: a THz imaging camera from Terasense.¹⁰¹

TeraView⁹⁵ is solely focused upon the application of THz light to provide solutions to customer issues. TeraView has developed its proprietary technology across a number of markets such as fault analysis and quality assurance for semiconductor chips used in mobile computing and communications, nondestructive inspection of high value coatings used in the automotive, pharmaceutical, food and solar industries. As an example, the EOTPR 3000 is one of their products. The system is configured with a manual probe station to meet today’s tough FA environment, which requires to isolate fault location in minutes rather than hours or days, while maintaining the EOTPR’s world leading sub-$5\mu \mathrm{m}$ fault isolation accuracy.

Toptica¹⁰² has been working with leading researchers in the THz arena from day one and is now able to serve scientists and engineers working with the two most important optoelectronic approaches—pulsed and CW THz generation. The company manufactures different frequency-domain, time-domain, and THz screening platforms. For frequency-domain THz spectroscopy, Toptica offers two systems—TeraScan 1550 and TeraScan 780 (Fig. 20). Based on precisely tunable distributed feedback (DFB) lasers, digital control electronics, and latest GaAs and InGaAs photomixer technology, the TeraScan systems combine ease of use with best-in-class specifications.

Fig. 20

TeraScan: frequency-domain THz platform from Toptica.¹⁰²

Tracer¹⁰³ has been one of the leaders in THz knowledge since 2008, developing unique IP for the detection, imaging, and creation of THz light. One of the company products is (Fig. 21) a real-time (25-100 Hz) imager with a commercial name “THEIA” for THz application development with a large formal focal plane array with integrated readout electronics can be deployed with electronic or photonic sources and application-specific optics. THEIA is designed to integrate into most optical setups for the THz or submillimeter wave researcher or application developer.

Fig. 21

THEIA: a real-time (25 to 100 Hz) imager Tracer.¹⁰³

3.1.

Delay Line Systems

A simple way to extract the amplitude information of a THz signal is a variation of phase using a delay stage in the THz or optical beam path.^{59,65,71,72,83,107–112} Main problem of this simple implementation is that it is slow. Because velocity of a mechanical translation stage is limited to a few millimeters per second. In the delay line setup, the scanning delay in the detector or THz beam path generates an interferogram in the time domain by varying the phase relationship between the incoming THz beam and the beat in the optical field at the receiver. The detected signal varies with the time delay, $t^{\prime }$, between the THz and optical beams according to the autocorrelation function:

The detected THz signal power is very low (usually in $\mu \mathrm{W}$ range). Signal averaging and lock-in detection are the two techniques that are used to achieve a acceptable SNR. In the signal averaging method, each measurement is done several times and then averaged. This almost eliminates the random noise of the detected signal and increases the SNR. But the measurement time is increased drastically. In the lock-in detection method, either a mechanical chopper included into the optical or the THz path or the DC bias of THz emitter has to be modulated. Assuming the chopper or the bias voltage is modulated at frequency $\omega$ [$V_{\mathrm{sig}}=\cos (\omega t)$], based on the THz path parameters, the detected signal will have an additional phase $\varphi$ [$V_{\det }=V_s\cos (\omega t+\varphi )$]. Multiplying the reference signal with the detected signal

The disadvantage of the first two options is that a bulky mechanical chopper has to be used.⁶⁵ The drawback of modulating the DC bias is that either the DC current, DC voltage, or temperature of the emitting photomixer is modulated at the lock-in frequency. This creates a parasitic distortion that can be picked up by the detector. This parasitic signal can appear as an additional DC background in the detected signal or as an additional noise which is independent of the THz signal phase.

As one of the first attempts to implement a THz transmitter/receiver system in Ref. 107, two antenna-coupled photomixers were used to test a photomixer transceiver (Fig. 23). The amplitude and phase of the THz electric-field transmission coefficient $T(\nu )=|T(\nu )|\exp [j\varphi (\nu )]$ are measured as a function of time. The phase $\varphi =2\pi \nu \mathrm{\Delta }L/c$ was determined by measuring the change in path between zeroes in the fringe pattern. Here, $\mathrm{\Delta }L$ is the deviation from zero path difference between the two lengths of optical fiber between the beam splitter and the photomixers. The amplitude is determined by changing the zero phase distance offset $d$ and obtaining the ratio of the fringe amplitudes with the sample in and out of the beam.

Later, Siebert et al.^83,111 performed CW THz imaging using an all-optoelectronic system using a two color Ti:sapphire laser (Fig. 24). Hyperboloidal polyethylene (PE) lenses are employed to enhance the spatial resolution of the system. Each photomixer is illuminated at 100 mW of optical power. The maximum SNR obtained at 1 THz without a sample in the beam path is 100:1. At each frequency, the spatial resolution of a THz system is defined by the spot size of the Gaussian beam on the sample which is directly proportional to the $f$-number of the focusing element. The $f$-number is given by $f/d$, where $f$ is the focal length and $d$ is the diameter of the focusing element (in case paraboloidal mirrors are used, $d$ is the off-axis distance). For paraboloidal mirrors, $f/d$ is always larger than $1/2$ if an object has to be brought into the focus. In contrast, hyperboloidal lenses allow for $f/d<1/2$.

Fig. 24

Set-up of the all-optoelectronic CW THz imaging system.⁸³ (Copyright 2002, Institute of Physics Publishing.)

Gregory et al.^71,72 introduced a CW THz imaging system that incorporates for the first time all the elements for a commercially viable system (Fig. 25). It is driven by two independent diode lasers. Two external-cavity, tunable diode lasers (TOPTICA Photonics DL100) operating at around 830 nm are combined using a 50:50 beam-splitter. The resulting two combined beams are focused onto the emitter and detector photomixers, with a delay stage in the detector beam. The optical power at the emitter (detector) was 50 mW (20 mW).

Fig. 25

CW THz schematic diagram showing combining beam splitter, optical delay line, and imaging optics. Insets: Micrographs showing: (a) resonant dipole emitter, (b) spiral detector on same scale, and (c) close-up of interdigitated finger pattern at feed point of both emitter and detector.⁷² (Copyright 2004, IEE.)

In Ref. 109, for the first time, a CW THz system with log periodic transmitter and receiver antennas on LT-GaAs substrate is reported. The system is optically driven by two laser diodes operating at a wavelength around 830 nm. As it can be seen in system schematic (Fig. 26), to overcome excess transmitter noise, the pump beam is mechanically chopped and the current is measured using a lock-in amplifier. A scanning Fabry–Perot interferometer is used to monitor the spectral mode purity. The autocorrelator monitors the optical modulation depth. An optical spectrum analyzer is used to measure the difference frequency. The SNR around 1000:1 with time constant of 300 ms and chopper speed of 1.25 KHz is achieved.

Fig. 26

CW-THz schematic diagram.¹⁰⁹ (Copyright 2005, Springer.)

In general, efficiency of photomixing is lower than that of pulsed spectrometers. Photomixers typically contain interdigitated electrode structures^53,71,107 that are very fragile and easily experience a voltage- or temperature-induced breakdown. On the other hand, photomixers with a simple gap without interdigitated structures are considerably less efficient as a THz source. However, they are more durable and can last for years if driven at moderate voltages and optical powers. Wilk et al.¹¹² presented a low-cost THz spectrometer with coherent detection based on two simple and robust dipole antennas driven by two laser diodes. The spectrometer covers frequencies up to 1 THz, with a peak SNR of 40 dB for a lock-in integration time of 30 ms. The setup in Ref. 112 is used to measure the thickness of a PE wedge as a test sample. On the right (thinner) side, the thickness varies between 0.3 and 0.8 mm (Fig. 27). Figure 27 shows the measured thickness of the sample at 0.3 THz. The optical delay line was fixed during the experiment. Since the sample thickness exceeds the THz wavelength, the measured signal exhibits a sine shape. In the transmission setup, after inserting the sample, the phase of the THz signal shifts as

Fig. 27

(a) THz amplitude image of wedge-shaped PE and (b) its 3-D representation.¹¹² (Copyright 2008, Optical Society of America.)

Fig. 28

Experimental setup of THz wave generator and homodyne receiver using single PCA. The emitted THz waves are reflected by concave mirror M and focused onto the same PCA.¹¹⁰ (Copyright 2010, The Japan Society of Applied Physics.)

A conventional CW THz system employs two antennas in which optical parts cause system complexity and large system size. In Ref. 110, a homodyne detection system in which a single PCA is used for both emitting and receiving the THz waves (Fig. 28). The transceiver setup reduces the system size and simplifying the alignment of optics. Since the homodyne output is considerably weak (because of the low generation efficiency in the PCA), the homodyne output is strongly affected by noise in the photocurrent. Hence, the incident laser power and bias voltage applied to the PCA must be set carefully.

3.2.

Electro-Optic Modulator Systems

In the measurement setup based on the electro optic modulator (EOM), a path length change of the laser wavelength in order to achieve a $2\pi$ phase variation is done electronically using an optical phase shifter.^{64–67,113–119} Applying voltage in the EOM changes the refractive index and thus, the optical length of the crystal which is part of the optical path. The advantages of using optical phase modulator for phase shifting are lower measurement time rates, possible compact all-fiber set-up, and efficient use of the available laser power. This is due to the fact that there is no free space part which generates radiation loss. Figure 29 shows a setup based on EOM. Output of each of the lasers goes through a 50–50 splitter, and one of the outputs from each splitter is combined with an output from the other splitter in a 50–50 combiner. The outputs of the combiners go to the transmitter (Tx) and receiver (Rx). The phase modulator can be placed between the splitter and combiner in the transmitter or receiver path. As it can be seen in the figure only half of the power from each laser reaches to transmitter or receiver. The main drawback of this approach is that half of the laser power is lost in the second set of beam splitters. Additional laser amplifiers may be required to provide the required optical power on the photomixer. The main problem with this setup is the sensitivity of the THz phase on the optical path length. Path length jitters on the order of $\sim 1\mu \mathrm{m}$ results in a complete loss of phase information, even though the THz amplitude is still measured accurately.⁶⁵ The other shortcomings are the significant costs for the fiber assembly and the high-voltage driver for the EOM.

Fig. 29

General schematic of a CW THz system using optical phase modulator.⁶⁵ (Copyright 2008, IEE.)

The detected current in the setup in Fig. 29 is

In an interesting system topology in Ref. 65, optical phase modulator is used instead of the chopper. This is done by introducing an additional phase modulation (${\varphi }_{\mathrm{chop}}$) to ${\varphi }_{\mathrm{mod}}$. ${\varphi }_{\mathrm{chop}}$ is change stepwise between 0 and $\pi$ at the lock-in frequency, which changes stepwise the sign of the detected current $I_{\det }^{\mathrm{DC}}$ at lock-in frequency. This approach keeps the average optical power on emitter and receiver constant, and neither DC current, DC voltage nor temperature of the THz emitter are modulated. Therefore, no parasitic signal influences the detected current that reduces the noise level in the detected current. Further, the detected signal is twice as large as in the case of a mechanical chopper. Figure 30 shows the measured SNR for the mentioned three methods. The configuration with the mechanical chopper has the worst performance. The signal is 3 dB less compared to both other chopping techniques and the noise level is the highest. The signal obtained by optical phase chopping and bias modulation is identical, but the noise level achieved with the optical chopper is the lowest. The best SNR performance is obtained with chopping operation of the optical phase modulator.

Fig. 30

SNR performance of three different chopping techniques.⁶⁵ (Copyright 2008, IEE.)

To measure phase in the system in Ref. 65, multiple measurement points at each frequency have to be done. On the other hand, the system introduced in Refs. 66, 67, and 117 allows determination of both THz amplitude and phase with a single sampling point (SSP) per frequency (known as SSP method). This direct detection increases the measurement speed compared to the standard procedure. In the SSP method, THz phase is controlled by shifting the optical phase (${\varphi }_{\mathrm{mod}}$) of one optical beam before a beam combiner. Therefore, the phase of the optical beat signal and the emitted THz signal is shifted by the same phase ${\varphi }_{\mathrm{mod}}$. The optical phase shift for a specified shift of the THz phase is independent of the THz frequency of the system. This allows to operate the phase modulator with the same driving voltage pattern at every THz frequency, which is the basis for method introduced in Ref. 66 in which a voltage ramp is applied to the phase modulator, which alters the THz phase by $2\pi$ [Fig. 31(a)]. This is done periodically with the desired chopping frequency. As a result, the phase of the signal detected by the receiving photomixer is periodically modulated between 0 and $2\pi$ [Fig. 31(b)]. The lock-in amplifier is locked to the control voltage of the phase modulator. Thus, the phase monitor of the lock-in amplifier does directly display the phase of the detected THz signal, enabling to detect both the THz amplitude and phase with a single measurement point. The measured phase shift (${\varphi }_{\text{lock-in}}$) contains contributions due to the difference of the optical-path length in the system (${\varphi }_{\mathrm{opt}}$), as well as the phase accumulated in the THz part of system (${\varphi }_{\mathrm{THz}}$). The contribution of ${\varphi }_{\mathrm{opt}}$ is also present in any other common CW THz system, and it is eliminated with the help of calibration measurements. Figure 32 shows the measured SNR for both methods. The SNR values for the direct detection are slightly larger. The received photocurrent for both approaches is comparable, but the modulation of the transmitter bias performed for the phase-scan detection scheme induces parasitic distortions at the lock-in frequency, which leads to a higher noise level.

Fig. 31

Operation mode for direct phase detection. The required modulation of the THz phase is illustrated in (a), the corresponding detected signal is shown in (b).⁶⁶ (Copyright 2008, IEEE.)

Fig. 32

SNR performance of both detection schemes.⁶⁶ (Copyright 2008, IEEE.)

In Ref. 117, phase modulation ramp is used as driving signal for the lock-in detection, eliminating the need for further mechanical or electronic chopping of the THz wave. Modulation rates of 100 kHz have been employed which is approximately six orders of magnitude faster than a motor-driven translation stage. The need for a complete $2\pi$ phase shift in the modulator is shown in Fig. 33. For voltages below the equivalent of a $2\pi$ phase shift, the output waveforms [Fig. 33(a)] are not complete sinusoids. For voltages that are too large [Fig. 33(b)], a waveform swing larger than one cycle is observed. The maximum scanning speed of the system in Ref. 117 is limited by the electronic bandwidth (around 400 kHz) of the THz receiver. In a classic THz imaging configuration in which the object’s position is scanned in transmission mode, fast scanning system operating at 100 kHz will enable an averaging of 100 oscillations of the THz waveform with roughly 1000 pixels imaged per second. If synthetic aperture imaging methods⁴⁸ were utilized, video rate imaging would be attainable.

Fig. 33

THz detector voltage output versus time as a function of applied voltage to the modulator. (a) The applied voltage is 20 and 160 V (middle and bottom waveforms, respectively). The sawtooth waveform (top) illustrates the timing of the modulator voltage. Waveforms are vertically offset for clarity. (b) THz detector output for a thin card inserted (solid curve) between the THz TX and RX of Fig. 1 and removed (dashed curve).¹¹⁷ (Copyright 2008, Optical Society of America.)

Fig. 34

Scheme of the CW THz setup¹¹⁶ (Copyright 2009, OSA).

In Ref. 116, high speed photodiodes that are based on waveguide integrated devices are used (Fig. 34). They behave like side illuminated devices, and high absorption even for thin active layers can be achieved. High speed and high efficiency can therefore be combined. The system is completely assembled using fiber technology. The key devices emitter, receiver, lasers are telecom-related products for $1.5\mu \mathrm{m}$ operation. The optical power in the fiber was 30 mW at the emitter and 40 mW at the receiver. The photocurrent in the PCA (preamplified ${10}^8\mathrm{V}/\mathrm{A}$) was measured with the lock-in technique at 460-Hz modulation frequency.

Implementations of electro-optical control setups in Refs. 66, 67, and 117 are arranged in an optical interferometer geometry and are extremely sensitive to environmental changes. In the system configurations used in these papers, the laser signals are spatially separated for wavelength selective optical phase modulation. External influences such as thermal expansion or vibrations affect the optical phase differently in the interferometer arms. This phase jitter is directly transferred into the THz phase, thus preventing high-quality measurements. The technique presented in Ref. 119 [known as wavelength selective phase modulation (WSPM)], is an in-fiber technique and realizes the speed advantage of electro optic modulation while avoiding the phase jitter normally introduced. The same phase and therefore amplitude stability as conventional systems is maintained. In WSPM, the two wavelengths remain in a single fiber. The modulation of only one wavelength is achieved by using crossed polarization for both wavelengths, together with a polarization-sensitive phase modulator (Fig. 35). Hence, if the optical phase is shifted due to environmental influences such as temperature change or mechanical stress, both wavelengths are affected identically. Thus, optical phase jitter always occurs identically on both wavelengths, and the THz phase is not affected. By applying SSP detection, high-speed measurements were demonstrated by recording a 1.5-THz spectrum with a resolution of 100 MHz in less than 24 s. This is more than 20 times faster than any previous broadband scans.¹²⁰

Fig. 35

Setup for in-fiber WSPM for THz phase control.¹¹⁹ (Copyright 2011, IET.)

The system in Ref. 115 consists of the $\lambda /4$ phase-shifted detuned dual-mode laser (DML) and an all-fiber path for the laser beams in order to increase the flexibility and compactness (Fig. 36). The optical beat signal is amplified by an erbium-doped fiber amplifier (EDFA). The amplified spontaneous emission generated by the EDFA was filtered out by an optical band pass filter (BPF). The output signal from the BPF was coupled to a fiber-optic 50:50 splitter and divided into two integrated photomixer/antennas. The proposed system can be used to measure the thickness of a sample without considering the modulo $2\pi$ ambiguity.

Fig. 36

Schematic diagram of a coherent homodyne CW THz system setup.¹¹⁵ (Copyright 2012, OSA.)

Fig. 37

CW-coherent homodyne detection system with EO phase modulation and direct lock-in detection; UTC-PD, unitraveling-carrier photodiode; PCA, photoconductive antenna.¹¹⁴ (Copyright 2013, IEEE.)

Fig. 38

Schematic of the applied CW THz system, consisting of an optical beating source (Agilent 8163B), DAO unit, and THz reflection head. The notebook is used for presentation purpose only.¹¹⁸ (Copyright 2014, IEEE.)

In the setups in Refs. 67 and 113 which mentioned before phase control of THz waves in high speed, direct lock-in detection of the resulting waveform using the phase control signal as reference clock is performed. Thus, the magnitude chopping of THz wave is no longer required, and a fast THz spectroscopy system can realize millisecond-order acquisition time. However, in this scheme, the delay unbalance of the optical path or nonlinear amplitude modulation of optical signal as a parasitic effect of the electro-optic phase modulation can limit the dynamic range because the detection signal. In Ref. 114, a CW THz coherent homodyne detection system that uses push-pull electro-optic phase modulation for wide dynamic range (Fig. 37). The factors limiting detection signal quality, such as laser-induced phase noise and parasitic amplitude modulation of THz waves, are evaluated and suppressed with overall delay balance control and the push-pull phase modulation scheme. Moreover, by direct lock-in detection, fast spectroscopy and imaging measurement was demonstrated from 0.2- to 2-THz frequency range.

In Ref. 118, a CW THz photomixing system (Fig. 38) which is capable of multilayer thickness measurements in reflection geometry with micrometer precision is presented which is based on Ref. 119. It also minimizes the uncertainty of the phase due to its high frequency resolution. The proposed system can replace THz time-domain systems in the field of multilayer thickness measurement due to its easier handling and much lower costs.

3.3.

Fiber Stretcher Systems

The conventional mechanical delay stage in the THz path is rather slow because the travel of the delay line has to be comparable to or larger than the THz wavelength (i.e., 3 mm at 100 GHz). Also it requires a collimated beam in the THz path.^70,121–123 Furthermore, modulating the THz path strongly affects the standing waves, i.e., parasitic interference effects, which arise from multiple reflections of the THz beam.^68,124 Because of these standing waves, significant deviations from a cosine-like behavior of photoelectric current appears if the of the THz path is varied. On the other hand, a conventional delay stage in the path of the optical beat requires a free optical beam and thus prevents a compact all-fiber-based setup.

Fiber stretchers can be used for rapid phase modulation in the optical beam path.⁷⁰ In a typical fiber stretcher phase shifter, several tens of meters of fiber [usually polarization-maintaining (PM) fiber] are wound around a piezoelectric actuator. The piezoelectric actuator is driven by an AC voltage with an amplitude of typically 100 to 500 V. In Ref. 121, CW THz spectrometer is realized with two fiber stretchers at the two optical arms of the THz setup. Both the THz amplitude and phase are determined from 0.06 to 1.8 THz with a 1-GHz step size in less than 10 min. In their setup (Fig. 39), two DFB diode lasers are used (850 nm). Lasers are frequency stabilized by electronic feedback from a low-finesse quadrature interferometer.⁵⁹ Absolute frequency accuracy of $\sim 100\mathrm{MHz}$ is achieved. The relative frequency resolution is in the MHz range. The laser beams are amplified at both wavelengths in a semiconductor amplifier, the output of which is once again fiber coupled. The main advantage of the dual stretcher configuration is that it reduces the sensitivity to thermal drifts and doubles the modulation amplitude compared to a single stretcher setup. Each fiber stretchers consists of 60 m of PM fiber wound around a cylindrical piezo actuator which are driven with bipolar voltages of up to $\pm 400\mathrm{V}$. By operating the stretchers in opposite directions, the optical path length can be changed with a twofold speed. The fiber stretchers are modulated by a continuous sinusoidal voltage to avoid switching artifacts of, e.g., a saw tooth waveform (modulation frequency is about 1 kHz).

Fig. 39

Setup of the THz spectrometer for a face-to-face configuration of the two photomixers.¹²¹ (Copyright 2011, IEEE.)

Frequency resolution of the THz signal is not influenced by the fiber stretchers. The use of fiber stretchers yields the THz amplitude and phase for each frequency separately (Fig. 40). The main advantage of the fiber stretcher concept, compared to a delay stage in the THz beam path, is that the THz path and therefore also the unavoidable standing waves are not changed, yielding a reduced sensitivity of the amplitude and phase data to standing waves (i.e., to parasitic interferences of the THz wave). The THz photocurrent as a function of the delay length shows a “perfect” sinusoidal dependence (Fig. 41).

Fig. 40

THz photocurrent around $\nu =300\mathrm{GHz}$ measured either using the fiber stretchers (red) or a frequency-scanning method with constant path difference (black).¹⁰⁶ The fiber stretcher data correspond to the envelope of the oscillating pattern recorded by the frequency scan.¹²¹ (Copyright 2011, IEEE.)

Fig. 41

Photocurrent as a function of the optical path length difference for a THz frequency of about 100 GHz.¹²¹ (Copyright 2011, IEEE.)

In Ref. 122, two identical fiber stretchers are placed in the transmitter and receiver arms. They are operated with inverted voltage with respect to each other. The receiver photocurrent is analyzed by signal averaging with a gate width of one stretcher cycle. About 240 cycles at each THz frequency step are measured, resulting in a net data acquisition rate of about 3 Hz for $f_s=800\mathrm{Hz}$ ($f_s$ denotes frequency of the path difference modulation). The main advantage of signal averaging compared to a standard lock-in technique is that signal averaging does not require the receiver photocurrent to be periodic with a known reference frequency. Thus, the modulation of the optical path difference does not have to be linear in time and the maximum change does not have to be an integer multiple of the THz wavelength.

In Fig. 42, fiber stretcher voltage and the THz photocurrent are plotted as a function of time. Around the extrema of voltage, the optical path difference and thus THz photocurrent change more slowly. A sinusoidal behavior is observed in Fig. 43 in which THz photocurrent is plotted in terms of fiber stretcher voltage.

Fig. 42

Voltage at the fiber stretcher and THz photocurrent at the receiver photomixer as a function of time for a THz frequency of 600 GHz. Here, the frequency of the voltage modulation is $fs=800\mathrm{Hz}$ and the photocurrent is averaged over $\approx 240$ periods (corresponding to $\approx 300\mathrm{ms}$).¹²² (Copyright 2012, Optical Society of America.)

Fig. 43

The THz photocurrent (same data as in figure 443) now plotted as a function of the voltage U at the fiber stretcher, which is proportional to the change s of the optical path difference. A cosine fit with $\lambda =c/\nu \approx 500\mu \mathrm{m}$ describes the data excellently (red line).¹²² (Copyright 2012, Optical Society of America.)

The setup in Ref. 122 is used to measure the complex refractive index of Si in transmission mode. To derive the physical properties of a sample, such as the complex index of refraction $N=n+jk$ ($n$ and $k$ are real and imaginary parts of refractive index), one has to compare amplitude of the THz signal ($A$) and phase of the THz signal (${\varphi }_0$) measured for the sample ($A_s$ and ${\varphi }_{0,s}$) with those of a reference measurement ($A_{\mathrm{ref}}$ and ${\varphi }_{0,\mathrm{ref}}$), which in a transmission geometry simply corresponds to a measurement on an empty aperture with the sample removed. The transmittance through the sample is $T(\nu )={[A_s(\nu )/A_{\mathrm{ref}}(\nu )]}^2$, and the phase shift introduced by the sample is $\varphi (\nu )={\varphi }_{0,s}-{\varphi }_{0,\mathrm{ref}}(\nu )+m(\nu ).2\pi$ with integer $m(\nu )$. The ambiguity in $m$ can be resolved in a broadband measurement. If we, for instance, neglect multiple reflections within the sample of thickness $d$, one finds $\varphi (\nu )\approx 2\pi (n-1)d\frac{\nu }{c}$, i.e., $\varphi$ extrapolates to zero for $\nu \to 0$ and is expected to increase linearly with $\nu$ in a frequency range with constant refractive index $n$. Finally, knowing $T$ and $\varphi$ as well as the sample thickness $d$, one can calculate the complex index of refraction.¹²⁴

Enhanced measurement speed and an all-fiber setup are the main advantages of the THz setup with fiber stretcher. A modulation of the optical path difference of 3 mm is obtained for a modulation frequency of $\approx 1\mathrm{kHz}$. A mechanical delay stage with the same amplitude typically operates at a few hertz. A data acquisition rate of a few Hertz is achieved in Ref. 122 with averaging over about 240 cycles per frequency point. If the phase is modulated by scanning the frequency, a very similar data acquisition rate can be employed but 10 or more frequency points need to be measured to observe a phase shift of at least $2\pi$, which yields one actual data point.¹⁰⁶ The fiber stretcher thus improves the measurement speed by at least an order of magnitude compared to the frequency scanning technique if the same integration times are used. It is possible to reduce the measurement time by increasing the frequency step size or to operate fiber stretchers at rates up to a few kilohertz.

Another important parameter of a THz system is the dynamic range. It is the ratio of the maximum signal to the minimum detectable signal. The amplitude of the signal depends on the optics, absorbing windows, or apertures within the THz beam, the optical power illuminating the photomixers, the bias voltage, and some other parameters. However, for equal conditions, the maximum THz amplitude is the same for the system with and without the fiber stretchers and its stability is not significantly influenced by the fiber stretchers. Other important parameters of the system are the spectral resolution and bandwidth of the system which are generally determined by the characteristics of the employed lasers.¹⁰⁶

Reliable measurements of the phase require a high stability of the experimental electrical lengths. Ambient fluctuations (mostly thermal) or alignment drifts may not exceed a small fraction of the wavelength. Large wavelengths such as about 1 mm at 300 GHz thus facilitate the determination of the phase. However, fluctuations of the optical path length cannot be fully suppressed even in an air-conditioned laboratory, and phase measurements in real-world applications in a less than ideal environment are challenging, in particular, if they rely on a robust fiber-based system. These difficulties can be surpassed in ellipsometry, which measures the phase difference between different polarization states. Similar idea can be used in CW spectroscopy in the frequency domain and consider the phase difference of waves with different frequencies.

In Ref. 123, waves at three THz frequencies are generated by photomixing three different lasers (Fig. 44). The waves travel along the same path at the same time and their phases are measured simultaneously. The phase at the fixed frequency is used to monitor length changes during the measurement. The normalized phases of the two other scanning frequencies are nearly insensitive to thermal drifts. The data obtained at the reference frequency monitor the length drift of the optical path-length difference with an accuracy of about 1 to $2\mu \mathrm{m}$. This can be used to self normalize the frequency dependence of the phase data measured at the scanning frequencies. The self-normalization is close to ideal because the drift correction is achieved by comparison of waves which traveled the same path at the same time, without reduction in measurement speed. This method allows for a reliable determination of the phase even in situations with large drifts such as in nonideal environmental conditions.

Fig. 44

Sketch of the setup with three lasers. The fiber array feeds 1/3 of the power of each laser into the amplifier. A face-to-face setup of the photomixers yields a short THz path length $L_{\mathrm{THz}}$. The optical path-length difference is modulated by two fiber stretchers.¹²³ (Copyright 2015, AIP Publishing.)

Fig. 45

Normalized homodyne signal recorded around 300 GHz with a 109.1-mm thick Teflon sample (dash line) and without (black line).¹²⁵ (Copyright 2007, Springer-Verlag.)

Fig. 46

Normalized homodyne signal recorded around 310 GHz with a 16.8-mm-thick high resistive silicon sample (dotted line) showing a Pèrot–Fabry effect inside the sample. The solid line is the calculated transmitted Fabry–Pèrot effect.¹²⁵ (Copyright 2007, Springer-Verlag.)

3.4.

Controlled Frequency Sweeping Systems

Based on Eq. (17) changing any of the parameters, path length $\mathrm{\Delta }L$, or THz frequency changes the THz phase.^{106,125–127} Therefore, THz phase can equally be varied by scanning the frequency in small steps. The effect is similar to scanning an interference pattern in frequency. Phase difference is a function of the path difference $\mathrm{\Delta }L$ and frequency. The path difference is

Phase variation in controlled frequency steps can perform as a coherent homodyne spectrometer which is a powerful tool to extract the properties of a sample in the THz region. Using a laser with a large tunability range, accurate measurements at a particular frequency can be obtained at the expense of experiment time to solve the ambiguity of modulo $2\pi$. One advantage of this method compared to the previous approaches is that no further hardware is required, and the main disadvantage is that it needs an accurate frequency control. A frequency step has to be much smaller than the fringe pattern spacing, which in turn should be chosen much smaller than the signature of interest. One solution for high-precision frequency control is using distributed Bragg reflector diode lasers.^{33,58,70,119,128,129} A second challenge arises from the large density of data points, which increases the total measurement time. A 2-THz scan with 40 MHz step size consists of more than 50,000 data points. Completing a scan in a few minutes needs lock-in times in the single-ms range.

The method has been exploited for thickness and distance measurements,¹²⁵ and for spectroscopy of solid-state samples.^58,106 Based on Eq. (17), in the case, THz beam propagates through free space (no sample), the frequency spacing of two subsequent maxima of the receiver photocurrent or zero crossings is $c/\mathrm{\Delta }L$ (Fig. 45). By comparing the maxima or zero crossing position in measurements with and without the sample present in the THz path, we are able to measure the relative phase of the THz beam. In case, we use the maxima information, the effective frequency resolution of the phase data is $c/4\mathrm{\Delta }L$ which is a factor two higher than the resolution of the amplitude data ($c/2\mathrm{\Delta }L$), because only the extrema are used for the amplitude analysis (Fig. 46).

Mouret et al.¹²⁵ described the performance of the coherent homodyne spectrometer and the characterization of dielectric and semiconductor samples. The presence of the sample increases the THz path, and the period of recorded curves is affected. Assuming the refractive index of Teflon is 1.44, a thickness of 109.39 mm is measured with a standard deviation of 0.35 mm from 10 measurements. A value of $109.1\pm 0.1\mathrm{mm}$ has been obtained by using a standard mechanical micrometer. Similar information may be extracted from time-domain analysis but requires the motion of a mechanical delay line and the prior knowledge of the exact position of the zero path difference. The calculated transmission amplitude of this Fabry–Pèrot effect (neglecting the absorption with constant refractive index of 3.4) is superimposed with experimental data. The analysis of the period of the homodyne signal gave a thickness of the silicon sample of 16.7 mm, in good agreement with a classical measurement. To avoid a long frequency scan, it is preferable to perform such measurements with a significant initial difference path. In this example, the period is around 0.4 GHz, the tunability of a diode laser would be sufficient to record several periods to extract the thickness of a sample or measure of distance.

CW technique offers the advantages of frequency selectivity and a much higher frequency resolution compared to time-domain techniques. Typical line widths in solid-state samples are of the order of several tens of GHz or broader. Thus, a spectral resolution of a few GHz is usually sufficient. However, a central problem for solid-state spectroscopy is that both the real and the imaginary parts of the complex refractive index $n+ik$ have to be determined reliably using amplitude and the phase of the THz radiation. The refractive index measurement method in Ref. 106 is based on scanning an interference pattern in frequency. It is based on the fact that the period of the interference pattern can be chosen to be much smaller than even the most narrow lines in a solid-state sample. It is shown that this approach is very well suited for solid-state spectroscopy, yielding precise and reliable values of real and imaginary parts of the refractive index without making use of any mechanically moving parts. The measurement setup is shown in Fig. 47.¹⁰⁶ The detected photocurrent $I_{\mathrm{ph}}$ depends on the amplitude of the THz electric field ($E_{\mathrm{THz}}$), and on the phase difference $\mathrm{\Delta }\varphi$ between the THz wave and the laser beat signal [Eq. (17)]. The phase difference is varied by scanning the THz frequency. This method has the significant advantages of avoiding any mechanically moving parts and of a much higher scanning rate (up to 10 Hz, depending on the selected lock-in time, but limited by software overlap). In this case, the detected photocurrent $I_{\mathrm{ph}}$ oscillates with frequency (Fig. 48), and the oscillation period is set by the choice of $\mathrm{\Delta }L$. For reference measurement without a sample, the THz beam travels through air ($n_{\text{air}}\approx 1$) independent of frequency. Thus, $\mathrm{\Delta }{L}^{\mathrm{ref}}$ is constant and the maxima are equally spaced in frequency as

Fig. 47

Setup of the CW THz spectrometer.¹⁰⁶ (Copyright 2010, IOP Institute of Physics.)

Fig. 48

An example of the detected THz photocurrent with and without the lactose sample using setup in Fig. 47. Both amplitude and phase information can be derived. The period $\mathrm{\Delta }\nu$ of the interference pattern depends on the optical path difference $\mathrm{\Delta }L$. Here, $\mathrm{\Delta }\nu \approx 1.5\mathrm{GHz}$ and $\mathrm{\Delta }L\approx 0.2\mathrm{m}$. The suppression of the signal around 557 GHz is due to a water absorption line.¹⁰⁶ (Copyright 2010, IOP Institute of Physics.)

Inserting the sample with refractive index $n$ and thickness $d$ in THz path changes the THz path $L_{\mathrm{THz}}$ by $(n-n_{\text{air}})d$ (neglecting multiple reflections within the sample) which shifts the interference pattern. Figure 48 shows the detected photocurrent in the frequency range just above one of the absorption lines of lactose. The phase information can be gained from both the extrema and the zero crossings of $I_{\mathrm{ph}}$, yielding a frequency resolution of the phase data of 1/4 period of the interference pattern, i.e., $c/(4\times \mathrm{\Delta }L)$. Thus, the spectral resolution of the phase can be adapted easily by varying the optical path difference $\mathrm{\Delta }L$. An enhancement of the spectral resolution, however, requires a larger density of data points, which increases the total measurement time. An interference maximum of order $m$ occurs for $\mathrm{\Delta }L=m\times /\nu$. Comparing reference and sample data, the refractive index can be calculated as

The sample also absorbs the THz light, according to its extinction coefficient $k(\nu )$. The transmittance $T(\nu )$ can be determined by comparing the envelopes of the sample data and of the reference data

With the knowledge of the transmittance and the refractive index, we are able to calculate the extinction coefficient by inverting

Fig. 49

Real part (black, left axis) and imaginary part (blue, right axis) of the dielectric constant of $\alpha$-lactose monohydrate. The red lines depict the results of the Drude–Lorentz model based on fitting $T(\nu )$ and $n(\nu )$.¹⁰⁶ (Copyright 2010, IOP Institute of Physics.)

3.5.

Multimode Laser Mixing Systems

In all the previously mentioned methods, mixing of two independently operating lasers has been used to generate monochromatic THz radiation. The construction of such a spectroscopic system has the advantage of generating THz beam with a narrow spectrum and tunable frequency. Another approach is using two different modes of the same laser to perform the photomixing. However, sophisticated techniques are needed for the stabilization and spatial mode matching of the two lasers. This concept is demonstrated as THz electromagnetic waves are radiated into free space from a PCA by exciting it with a commercially available CW multimode laser diodes.^30,130 In general, a multimode laser holds many different modes and the light intensity fluctuates due to optical beats brought about by the frequency difference between modes. This random fluctuation of the light intensity can be used to produce the THz radiation. Figure 50 shows a setup that mixes modes of a laser diode to generate THz signal.¹³¹ A PCA is irradiated by the multimode laser diode and used as an emitter. The THz radiation is collimated by an off-axial paraboloidal mirror and focused into the detector PCA by another paraboloidal mirror. A part of the multimode laser light is split by a beam splitter and introduced to the detector PCA after a time delay. The signal is modulated in a rectangular wave of 20 kHz through an emitter bias of 20 V and detected by a lock-in amplifier through a current amplifier. The sample was inserted into the THz beam path between two paraboloidal mirrors. The sample was tilted by about 10 deg to avoid the effects of standing waves between the sample surfaces and the optical elements.

Fig. 50

Experimental configuration, which is equivalent to the TDS system except for the light source.¹³¹ (Copyright 2000, American Institute of Physics.)

Since the fluctuation of the multimode laser diode light intensity is very rapid, the current meter detects the time averaged value of the photocurrent, or the cross correlation of the electric field and the fluctuating light intensity. The reference signal $J_R(t)$, the photocurrent signal when a sample is not inserted, is expressed as

The complex refractive index at each frequency can be numerically calculated from the $T(\omega )$ and $\mathrm{\Phi }(\omega )$ obtained experimentally. One of the most popular spectroscopic systems at THz frequencies is the Fourier spectrometer which gives optical constants of both real and imaginary parts without resorting to the Kramers–Kronig analysis.¹³² However, they require expensive detectors such as a bolometer cooled with liquid Helium. Time-domain THz systems are very effective but they require an expensive ultrashort-pulsed laser. On the contrary, the quasitime-domain systems are very compact and cheap and also give the equivalent data as that of Fourier spectrometer and the time-domain system. But, the SNR of this system is low compared with that of the time-domain system, which can be improved by changing the structure of the PCA.

Based on the standard photomixing theory⁵³ emitted THz power ($P_{\mathrm{THz}}$), using a multimode laser excitation is⁶⁹

In the detector, the averaged demodulated current flow $I_{\mathrm{THz}}$ is given as⁶⁹

In Ref. 105, two laser modes are emitted from a single or combined laser cavity. The frequency fluctuation in the difference frequency is reduced by the common-mode-noise rejection effect. The frequency fluctuations common to the two modes originating from electrical, thermal, mechanical, or other sources of fluctuation are subtracted from the difference frequency even though the absolute frequencies of the two modes are drifting. One advantage of using DML is easier optical alignment. Because we do not need to align two laser beams, which is critical for photomixing efficiency.

Siebert et al.^83,111 used a dual-wavelength CW Ti:sapphire laser as the photomixing pump source. Two optical waves, with independently tunable wavelengths centered around 800 nm, were generated in the dual-wavelength laser consisting of two unidirectional, single longitudinal-mode ring cavities sharing a single Ti:sapphire gain medium which was pumped by two beams from a 5-W all-solid-state green laser ($\sim 532\mathrm{nm}$). The two laser beams were spatially combined by using a beam-splitter and the beat frequency of the combined beam was tuned from near dc to 10 THz. Since the two beams of this dual-wavelength laser do not share the same cavity, we cannot expect a strong common-mode-rejection effect as in the case of DMLs with a single cavity. However, the dual-cavity laser with single gain media has the obvious advantage in the system simplicity and a wide difference-frequency tunability which is free from the instability due to the mode interaction in close vicinity.

In Ref. 77, a microchip laser with two longitudinal modes is used to pump a PCA to generate an ultranarrowband THz radiation. The microchip laser consisted of a Nd:YVO4 chip (operating wavelength $\sim 1064\mathrm{nm}$) with 0.5 mm length.

The laser mode frequency fluctuates due to the temperature change, power fluctuations of the pump laser, and mechanical vibration. When the two laser modes oscillate in the same cavity, the direction and amplitude of the frequency shift are similar for the two modes. Therefore, the difference beat frequency does not change as much as the original laser modes do. The common-mode rejection ratio (CMRR) as the ratio of frequency shift of the laser mode to the shift in the difference frequency:

External cavity dual-mode semiconductor lasers have been realized in a variety of methods, such as those with a double grating,^56,133 grating-lens,¹³⁴ grating-double-slit,¹³⁴ grating-double-stripe-mirror^73,135 configurations, etc.

The DML excitation for photomixing is preferable to that by two independent lasers since the system can be more compact and the difference frequency stability is improved by the common-mode rejection effect. Although the difference frequency stability of dual-mode semiconductor lasers reported was not good enough (mainly due to the nonoptimized conditions), there is a great potential in THz photomixing systems with dual-mode semiconductor lasers with the external cavity because of the wide-tunability and compactness of the system.