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Bibliographic review on sub-wavelength terahertz imaging
Introduction to terahertz
Terahertz (THz) radiation is commonly defined as electromagnetic waves whose frequencies spread from 0.1 THz to 10 THz, which corresponds to the wavelength range between 3000 µm and 10 µm [2,3]. One terahertz frequency ( = 1 THz) corresponds to a period ( = 1/ ) of 1 ps, a wavelength ( = / , is the speed of light) of 300 µm, a wavenumber of 33 cm-1 ( = 1/ ) , a photon energy ( = ℎ , ℎ is the Planck constant) of 4.1 meV, and an equivalent temperature ( = ℎ / , is the Boltzmann constant) of 47.6 K. As shown in Figure 1.1, THz radiation bridges the gap between the electronic world (starting from microwave and going to lower frequencies) and the photonics world (starting from infrared and going to higher frequencies), which are defined by the nature of the related sources and detectors. Unfortunately, in the THz range, neither electron based devices nor optical techniques were efficient until the late 1970s and early 1980s. That is why this region is called the ‘THz gap’. However, this gap has been filled over the last three decades with a lot of development in techniques of generation and detection of THz. From the high frequency edge of the THz range, photonic technologies have seen much progress, and the electronic technologies have also developed for the low frequency edge.
After the invention of ultrafast mode-locked lasers, pioneering work came with the study of the response of photoconductive dipole antennas to generate electrical signals with a time resolution of a few picoseconds in 1975 . The first prototype of photoconductive antennas as an emitter and a detector was first used in the late 1980s [5,6]. This led to the development of THz time-domain spectroscopy (THz-TDS) which is a powerful technique for generating and detecting THz pulses [7,8]. After this, different initial mechanisms for the generation and detection of THz radiation have been exploited such as second order nonlinear effect in an electro-optic crystal (LiTaO3) for generating Cerenkov-like THz beams (optical rectification) , complete THz system with optical rectification generation in a nonlinear medium (ZnTe crystal) and detection by electro-optical Pockels effect using the same crystal , and more recently generating THz radiation by the focusing of high-intensity laser pulses into gas (plasma generation)  and detecting the THz signal by a four-wave mixing effect in the photo-induced gas plasma .
As a consequence of growing research in this field, THz radiation now has a wide range of prospective applications: for imaging in the field of security, in biological science, in food industry, in semiconductor technology, in art; for analysing chemical components in the pharmaceutical industry; for communication in wireless technology; for monitoring in the paper and polymer industry and in earth and space science [13–15].
Application of terahertz imaging
There are numerous advantages of using THz radiation to form images. First of all, as terahertz is a given frequency range in the electromagnetic spectrum, THz imaging can provide supplementary information to imaging systems in other frequency ranges, like microwaves, infrared, visible, ultraviolet and X-rays. However, comparing to microwaves, THz has smaller wavelengths so the spatial resolution is better. Also, most of the common materials like paper, clothes, cardboard are transparent, while they are opaque at optical wavelengths. On the other hand, metals are opaque to THz radiation and highly reflective while the plastic is partially transparent. These qualities make it possible to detect the inside of packaging in the THz (cardboard, plastic) to avoid faulty pieces. This can solve the one of the most significant issues in the food industry; there might be some possibly damaging materials in the packaging such as glass, metal, wood. It has been demonstrated that the foreign bodies with a less than 1 mm spatial resolution can be identified in a chocolate bar using THz technology  (see Figure 1.2). There are also other applications in food industry to detect foreign bodies in flour sample , in noddle  , in powdered milk , etc.
Figure 1.2: THz image of chocolate bar with three different contaminations: a glass splinter (yellow circle), a small stone (red circle) and a metal screw (blue circle). (Image is taken from )
Terahertz technology is also a topic in the field of defence and security. For the detection of exploited materials, terahertz imaging has an excellent ability to detect explosive materials [20,21]. The main concept is that many molecules have different fingerprint in terahertz frequencies so it can be used to distinguish some chemical component and to analyse these materials. For example, terahertz imaging can be used to analyse quantitatively (by measuring water content) the mixture of the petroleum products; one of these products, kerosene, is a serious problem to make illegal fuel with mixing diesel . In additionally, in security application, the illicit drugs can be identified in a packages [23,24] since non-metallic and non-polar materials are transparent to THz. Although the metallic objects are not transparent to THz, dangerous metallic items like guns and knives can be visible because of their shapes .
THz photon energy is lower than X-ray (for 1 THz, the photon energy is 1 million times weaker than X-ray photons). It is a non-ionizing radiation, and it is not hazardous to living tissues in general. Although the depth of penetration into living tissues is small (about 100 µm), various promising diagnostic solutions have been studied. This feature makes it possible to perform medical imaging without any damage to tissues. For instance, we can identify different types of tissues such as muscle, fat, kidney and vein by using terahertz spectral data [26,27]. Other alternative medical imaging techniques are the teeth structure and more specifically identifying dental caries [26,28]. Dentists try to detect patient’s tooth decay by using visual inspection or X-ray radiography. These two methods are difficult to use to identify the early phase of the tooth decay. The tooth decay happens when the dentine is destroyed by acid in the mouth. This result in a reduction of the mineral content of the enamel. Since these regions are absorbent in terahertz, they can be clearly observed by using terahertz-pulse imaging . Figure 1.3 shows two tooth decays (pointed by red squared frames in Figure 1.3(a) and Figure 1.3 (b)) in visible and in terahertz.
THz waves are highly absorbed by water. Therefore, in biology, terahertz radiation can be applied to distinguish between cancerous and healthy cells since the water content in those cells are significantly different [29–31]. One example showing us the comparison between the image of breast tissue in THz and the visible is shown in Figure 1.4. The breast tumor is visible in terahertz region (see Figure 1.4 (b)). In this work, they also studied the absorption coefficient and refractive index of the normal tissues and cancerous tissues . The results show that both properties in THz are higher in cancerous cells than the normal ones.
Terahertz imaging techniques can be applied for imaging and analysing the artworks and the historical objects. Comparing to mid-infrared band, terahertz spectroscopy gives more clear and direct information to identify the compositions of different types of paint layer including the pigments, binders and their mixtures [33,34]. In addition, terahertz reflection imaging can give information on the thickness of the hidden paint layers in painting on a canvas while X-ray and infrared reflectography is limited by the penetration depth to high density pigments such as lead-white paint used commonly in historical paintings . These indicate the potential use of THz imaging for art historians, as well as in restoration of historical objects and paints for conservators and conversation scientists [36,37].
In nanoscale regime, terahertz radiation gives information about biological samples which cannot be easily obtained by other wavelengths. Since a 1 THz corresponds to a period of 1 ps, it can interact with phenomena fluctuating in time scale of picosecond and sub-picosecond. For example, breaking and reforming hydrogen bonds between the water molecules occur in this scale. In addition, vibrational modes of biomolecules which includes DNA modes can be visible in this scale, and the chemical recognition of nanostructured materials can be recognized based on their THz fingerprint. THz spectroscopy techniques can sense the conformational changes in biomolecules . Electrons in nanostructures resonate at THz frequencies, so the dynamic changes in charge carriers can be characterized . In semiconductor industry, the THz microscopy techniques can be used for integrated circuits to detect any fault in the circuit  or for evaluating the performance of solar cells . The opportunities with imaging in THz is limitless.
Classical terahertz microscopy: ‘T-ray imaging’
The lack of sources and detectors in the terahertz region has been one of the biggest challenges to take up. Thanks to the development of far-infrared gas lasers, the first terahertz image was recorded in 1976  by Hartwick et al. They used this gas laser to generate continuous terahertz waves in the wavelength region of 300 – 1000 µm. The THz images were recorded both in the transmission and reflection modes by using a liquid helium cooled GaAs detector. Figure 1.5 shows the visible and the terahertz images of a key, and the key was successfully imaged in the terahertz even when it is enclosed in a small cardboard box filled with foam rubber (see Figure 1.5 (b)).
Figure 1.5: (a) Image of a key in the visible region and (b) image of a key enclosed in a box using a wavelength of 300 µm – 1000 µm created by using far infrared gas laser (image taken from ) One of the reasons for the interest in terahertz imaging is related to the terahertz time-domain spectroscopy, or THz-TDS . The key components of a THz-TDS system are a femtosecond laser, an emitter, a detector and a delay-producing stage. Ultra-fast optical pulses can generate sub-ps terahertz pulses in the emitter, which can be detected by the detector whose integration time is longer than the terahertz pulse length, because the THz signal is read only when the receiver is triggered by the laser probe pulse. The obtained information is in the time domain and can be converted to frequency domain by Fourier transform. The first image produced by using THz-TDS was obtained by Hu and Nuss in 1995 . In their setup, they used photoconductive antennas: one for THz emission and the other for THz detector, and they obtained transmission THz images by raster scanning. Figure 1.6 (a) shows the THz image of a semiconductor integrated circuit in a package which shows that terahertz imaging can be used for package inspection in industry. The next two images were obtained from a fresh leaf just after it was cut and the same leaf after 48 hours (see Figure 1.6 (b)). The leaf image changed after 48 hours because the water concentration decreased gradually due to the evaporation, and THz waves are strongly absorbed by watery materials. This is also quite a useful property of terahertz to examine chemical compositions in the materials. Hu and Nuss named this method as ‘T-ray’ imaging . These first terahertz images made a huge impact on the scientific communities working on terahertz imaging systems and lead to subsequent development of terahertz microscopy techniques.
Sub-wavelength terahertz microscopy
Limitations of sub-wavelength Terahertz microscopy
Terahertz imaging has evolved differently in many fields. As a consequence, the developments in macroscopic imaging have made possible performing microscopy at THz wavelength, and the interest to image microscopic objects using THz waves has increased as well. However, there are some difficulties which limit the performance of terahertz imaging of microscopic objects . The major problem for THz sub-wavelength microscopy is diffraction, because the long THz wavelength limits the spatial resolution to 100’s of µm when employing classical microscopy techniques.
The diffraction limit
When light passes through a circular aperture of any size, it diffracts, bends around the corner of the hole and interferes constructively and destructively. Instead of a sharp edge spot, the image becomes a center bright spot surrounded with less intense concentric rings. This diffraction limited spot is the Airy disk. In Figure 1.7, light passes through a hole with a diameter of D and the diffraction pattern appears on a screen at a distance from the hole marked as L. The first minimum in the pattern occurs at an angle =1.22 / (the angle is defined as regards to the optical axis, and thus it corresponds to the radius of the first minimum circle), i.e. at a position 1.22 / from the center if the distance between the hole and the screen is .
The problem when resolving two neighbouring objects (assuming here two circular light sources) comes from the distance between them. If they are too close, their diffraction patterns overlap and the image becomes unresolved. If the maxima of the diffraction patterns are separated, they can be resolved as shown in Figure 1.8. But what can be the minimum opening angle between these object to resolve? The criterion was proposed by Rayleigh in the 19th century which states that two objects can be distinguished if the maximum of one diffraction pattern falls onto the first minimum of other one. This is known as Rayleigh criterion for diffraction-limited imaging systems. So the minimum resolvable angle is = 1.22 / . Figure 1.8: Resolved: two images are resolved because the airy disks do not overlap. Rayleigh criterion: the images are just resolvable because the minimum separation between them is the radius of their airy disk. Unresolved: the images are not resolved because their airy disks overlap.
The same criterion can be applied for a focused laser beam; whose profile is a Gaussian one. At the focal plane of a lens, which is supposed to be big enough to neglect diffraction by the lens aperture, two parallel laser beams of equal intensity are focused down a waist of radius . The two spots can be distinguished if the two Gaussian shapes cross at half their maxima. It corresponds to distance from the centre of the first spot equal to √ 2 and thus to a lateral resolution = 2 √ 2. Let us notice that both resolutions (Airy disks and focused Gaussian beams) are rigorously not exactly the same, since the Rayleigh criterion corresponds to Airy disk curves crossing at ~0.37 instead of 0.5.
Spatial resolution is one of the limitations of all kind of microscopic techniques. For example, in classical optical THz microscopy, lenses and objectives are limited by construction to a numerical aperture = ⁄2 = ⁄2 ≈ 1~1.5 (in microscopes, the distance between the lens and the sample is equal to the focal length ). Therefore the best resolution restrained by diffraction is 1.22 / = 1.22 /2 ≈ /2 , i.e. half of the wavelength (for example 150 μm for 1 THz). Although this spatial resolution is adequate in some applications [47,48], it restrains the application of THz imaging to large objects. For example, terahertz has a unique property to excite low-frequency internal molecular motions including the weakest hydrogen bonds and other weak interactions. The weakest hydrogen bonds are quite essential for biological cell processes and are required for the function of DNA, enzymes, proteins and others . They can be directly detected by terahertz radiation and not by IR, UV and visible radiation. Therefore, a terahertz absorption spectrum plays an important role in cancer diagnoses. The imaging of these vibrational resonances in micrometre-size biological cells is only possible by achieving a sub-wavelength terahertz resolution.
There have been different techniques developed to reach the sub-wavelength resolution in terahertz. To image a sub-wavelength object, it is necessary to collect not only the propagating waves but also the evanescent waves. This can be possible when the distance between the object and the source (or the detector in some cases) is smaller than the wavelength. This technique is called near-field imaging. There have been a variety of techniques developed for near-field imaging. The first terahertz near-field imaging was demonstrated in 1998  and since then this technique became a very popular research area. Some of the cases just implemented the optical techniques to the terahertz domain while others were only developed particularly for terahertz imaging. The other approach is to use a sub-wavelength aperture. A smaller aperture results in weaker transmission. However, there has been some research showing that special design of holes can enhance the transmission through the hole. The detailed studies for near-field techniques and sub-wavelength aperture is discussed in the next section.
Table of contents :
1.1 Introduction to terahertz
1.2 Application of terahertz imaging
1.3 Classical terahertz microscopy: ‘T-ray imaging’
1.4 Sub-wavelength terahertz microscopy
1.4.1 Limitations of sub-wavelength Terahertz microscopy
1.4.2 Different sub-wavelength terahertz microscopy techniques
1.5 Thesis Objectives and Primary Results
1.5.1 Primary Results of ORTI technique
2.1 Generation of terahertz pulses
2.1.1 Optical rectification
2.1.2 Photoconductive (PC) antenna
2.2 Detection of terahertz pulses
2.2.1 Electro-optic sampling
2.2.2 Photoconductive antenna
2.2.3 Intensity measuring detectors
2.3 Terahertz time-domain technique
3.1 Superconducting detectors
3.2 Kinetic inductance detectors
3.2.1 Kinetic Inductance Detector Properties
3.3 Interest of using KIDs for THz microscopy/imaging
3.4 Results for detection of weak THz –TDS signals using KIDs
3.4.1 Experiment setup
4.1 Simulation Model
4.1.1 Tapered hole device for THz microscopy
4.2 Experimental Results
4.2.1 Experimental Setup
4.2.2 Imaging with using KIDs
5.1 Imaging results using the first experimental setup
5.1.1 Imaging with LiNbO3
5.2 Imaging results done by second experimental setup
5.2.1 Imaging the ZnTe slivers
5.2.2 Imaging with PPKTP
5.2.3 Polycrystalline sample
5.3 Performance and limit of ORTI
5.3.1 Correspondence between the recorded image and the actual sample properties
5.3.2 Estimation of the best achievable spatial resolution
6.1 General conclusion
6.2 Future work
Appendix A: Horn antenna simulation
Appendix B: THz generation in LGT through optical rectification
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