An Introduction to Terahertz Electromagnetic Waves Generation, Detection, Properties and Applications

Michael R. Boersma, Member IEEE

Abstract –Electromagnetic waves spectrum contains waves containing wavelengths from 30 cm down to .3 nm. Terahertz waves are in the area of 300 m and the terahertz gap is generally considered to be between 300 GHz and 10 THz. What makes terahertz waves interesting is there possible applications because of their interesting properties. They are less harmful then X-rays when used for medical imaging, and when used for spectroscopy they provide information other waves cannot. In this paper the nature of terahertz waves will be examined, focusing on their generation, detection, properties, and their applications.

Index Terms –Applications, Detection Properties, Terahertz waves.

I. INTRODUCTION

Terahertz waves are quickly gaining attention and research funding. These waves are in the 100 GHz to 10 THz frequency range, this range is also know as the “terahertz gap,” as demonstrated in figure 1. This gap exists because until recently effective methods of generating controlled THz waves, and methods for detection of THz waves, were not available. Today there are two basic methods by which terahertz waves are produced. The first method is to use solid-state electronics, but this proves difficult for many reasons. The second method is optical generation, in which high-speed lasers are pulsed as certain semi-conductor surfaces. It is this second method that is receiving the most research attention.

Terahertz waves have found applications in many different fields, such as physics, material science, electrical engineering, chemistry, forensics, and new research potential are being discovered in biology and medicine. The area of focus in this paper will be spectroscopy and medical imaging applications.

The generation and detection of terahertz waves will also be discussed in this paper. The properties of terahertz that make them the focus of current studies will also be presented. Finally, some of the applications for terahertz waves, such as medical imaging, will be discussed.

Figure 1: Electromagnetic spectrum showing the THz band gap.

II. PURPOSEThe need for this kind of study is justified by the

potential benefits terahertz waves poses. The field that is currently receiving the most attention is medical imaging

and spectroscopy. THz waves have different absorption and reflective indices in different tissues. Using terahertz waves abnormalities could be detected sooner then currently possible. THz could also make it possible to distinguish between tissues more effectively. THz waves also provide an advantage over x-rays because they are less harmful to living tissue. This is because they carry less power then x-rays.

The purpose of this paper it to provide an introduction into THz imaging and research possibilities. By giving an overview of the field the goal it to provide a paper which is accessible yet provides a through understanding of the challenges and successes that have come from THz research.

III. GENERATION

Beginning in the early 1990’s two basic techniques for generating THz waves were being developed, solid state and optical methods as mention earlier. Optical generation can be subdivided into photoconduction and optical rectification. The following section provides an overview of these two generation methods.

A. Solid-State Generation

For years, solid-state electronics have generated infrared light by using a layered semiconductor structure, such as in diodes that emit infrared light or lasers that operate in the infrared range. But this principle is not easily extended down to the THz band. Interband diode lasers, which operate at a wavelength of 3 m, operate on the principle that conduction band electrons will recombine with valance band holes across a gap of active material. In doing so light, or electromagnetic waves are emitted. But this type of laser cannot be used to emit THz wave simply because suitable semiconductors for this type of excitation are not available.

A new kind of laser, called the quantum cascade concept has been used in research. Here, the transition between semiconductor layers is used to emit light. The idea is that the thickness of these layers can be changed to manipulate the electrons path. The theory is that it is possible to engineer many different wavelengths using this method. Again, however, a problem arises; the active regions must be very large to accommodate THz frequencies. This is because the active region grows as the square of the wavelength [1]. Below 10 THz the generation of waves becomes impossible for room temperate emitters. However, 4.4 THz has been achieved at cryogenic temperatures. It is these difficulties that have led to the development and excitement about optical techniques for generating THz waves.

B. Optical Generation

The optical generation method does away with the need for a solid-state emitter in the THz band. Instead, optical generation uses a laser that pulses as 10 to 200 fs, which is in the visible or infrared spectrum. This laser is pointed at what is known as a THz generator, often GaSe, GaP, or GaAs. This semiconductor generator will either reflect the pulses or propagate them through itself. What results are THz waves. This is possible because here the semiconductor is no longer emitting the light. Instead they are simply being used to conduct or refract the light. Photoconduction and rectification are the two different variations of optical generation that result from the propagation or reflection of the incident laser pulses.

1. PhotoconductionPhotoconduction is a commonly understood

process and has been used in other applications. Photoconduction is the process by which current is generated from a photoconductive semiconductor. All materials have a valance band of electrons and a conduction band, which is at a higher energy level. The “gap” in between these bands is knows as the forbidden energy gap. In insulators this gab is very large. In conductors it does not exist because the valance electron band and the conduction band overlap. In semiconductors the gap is small. It is possible to over come the gap by applying a sufficient amount of energy, such as electromagnetic energy from the incident waves.

When such a process is applied to certain semiconductors, like GaSE small bursts of current result. This current provides the energy for radiating antennas. This process generally provides higher-powered THz waves then optical rectification [7]. Photoconductive antennas are discussed in detail later in this report.

2. Optical rectification

This is also a simple and well-understood process, which now can be applied to the generation of THz waves because of the availability of suitable semiconductors. Optical rectification is a second-order non-linear process [1]. When the laser pulse hits the semiconductor the semiconductor is polarized. The voltage that results is proportional to the strength of the laser beam. The “envelop” of the laser pulse is all that remains. Figure 2 demonstrates this process. The equation governing this reaction is shown in equation 1.

Eq. 1Where THz = |vis1 – vis2| and is the receptiveness of the semiconductor.

Figure 2: Example of optical rectification: the laser pulse is shown before and after it strikes the semiconductor [11].

The shorter wavelengths of visible or inferred light that are emitted from the pulsing laser are filtered out. The rectified signal of the pulse that remains is in the THz frequency range provided that the laser was pulsed with the appropriate timing.

C. Processes of Semiconductor Sources

The semiconductors that are used as THz generators in conjunction with femtosecond laser pulses use one of two methods to generate THz waves. Bulk electro-optic rectification or ultra fast charge transport.

1. Bulk Electro-Optic Rectification

This is a version of optical rectification. In the rectification process the large electric field from the laser pulses allows the non-linear receptiveness of a semiconductor to generate the THz waves. A polarization in the THz range occurs which is proportional to the intensity of the laser pulses.

Bulk electro-optic rectification differs from simple optical rectification because here two laser pulses are incident on the semiconductor. A special variety of crystals are used, called NLO crystals. NLO crystals either combine or separate incoming electromagnetic waves [8]. The two types of combining NLO crystals are sum frequency generation (SFG) or differential frequency generation (DFG).

Figure 3: Diagram of how waves enter an NLO crystal.

For SFG NLO crystals the resulting wavelength is given in Eq. 2, and Eq. 3 gives the resulting wavelength for a DFG NLO crystal [8].

The efficiency of the conversion from the visible or near infrared spectrum to THz is determined by the effectiveness phase matching (PM) between the pulses entering the NLO crystal and the resulting field [1]. The conversation efficiency depends on phase mismatching. Phase mismatching, k, is described in Eq. 4. From phase mismatching the PM effectiveness can be found. PM effectiveness is shown in Eq. 5.

Where ni is the refractive index, and i is the wavelength.

What is shown from these equations is that the smaller the phase mismatching is, or in other words the closer the refractivity and wavelength of the resulting wave is to the incoming waves the better conversation efficiency is. Figure 4 shows conversion efficiency with respect to phase mismatching.

Figure 4: Graph of conversation efficiency, demonstrating how smaller phase mismatching numbers lead to height conversion efficiency’s.

In other words, for the best result the group velocity of the laser pulse should be matched to the phase velocity of the THz wave pulse [1]. This is difficult to accomplish. Yet this method has been successfully employed in a wide variety of semiconductors, including GaAs, GaP, GaSe, and ZnTe as all as by using certain organic compounds.

2. Ultra-Fast Charge Transport

Ultra-fast charge transport earns its name from electron-hole pairs that are formed on the surface of the semiconductor. Again a laser pulse of around 100 fs in the visible to near infrared wavelength range is used. This

pulse of photon energy is greater then the bandgap of the semiconductor resulting in the creation of the electron-hole pairs on the surface of the semiconductor. The changing dipole moments from an applied electric field cause the generation of THz waves [1].

One method for applying the electric field was developed by D. H. Auston. Auston’s method was to imbed two electrodes into the semiconductor surface. Which applied a large electric field and accelerated the electron-hole pairs.

Ultra-fast charge transport is receiving considerable attention. It is allowing the development of many new applications of THz technology.

D. Semiconductor Sources Properties

As mentioned earlier, some of the common semiconductors used in terahertz generation are GaSe, GaAs, GaP, and ZnTe. By far the most common are the Ga crystal varieties. Experiments that have been conduction on Ga crystals and the properties that have been demonstrated are presented here.

1. GaSe Semiconductor Sources

Experiments conducted, such as that described in [5], have demonstrated the properties of tunable terahertz waves generated with GaSe. The waves were generated using optical rectification. The laser used as a 1.064 m YAG laser. The crystals used were 2 mm thick of undoped GaSe. Because this was intended for spectroscopy use over a wide range these short crystals where used because power would not be limited. Long crystals would also have made the setup more difficult because displacement of the THz signals caused by the orientation of the crystals could not be neglected as with the short crystals.

The experiment in [5] was done using a DFG NLO. The efficiency of which for GaSe can be found by a different method then the one described above. Taking the cosine squared of PM () and the cosine of the azimuthal () angle, as shown in Eq. 6.

This means that NLO conversation efficiency is optimized at any particular PM when |cos(3)| = 1. In [5] they held the azimuthal angle such that that condition was met, allowing them to study the effect of changing PM on maximum power and frequencies generated.

Using 2 mm GaSe crystals frequencies from 0.3 to 4.9 THz could be generated that produced at least 3% of the maximum power possible. The highest power wave was found at 3 THz. The lowest power was at 0.48 mW at the lower side of the spectrum. The power was maintained at about 15 mW over 2.4 to 3.1 THz. The power dropped back off to 0.48 mW at 4.9 THz, and no signal could be detected at 5.1 THz [5].

2. GaP Semiconductor SourcesExperiments done on GaP, using the same general

set up as those conducted with GaSe have shown that they are tunable over a 0.5 to 7 THz range [6]. The differences included using 2.6, 5, and 20 mm crystal but again used DFG and a 1.064 m YAG laser.

It was shown that the power ranges greatly over the tunable spectrum. At 0.5 THz the power was 10mW. This increased all the way up to 300 mW at 2.5 THz for the 20 mm crystal. The semiconductor showed a power of 67 mW at 1.3 THz, which rose to 100 mW at 2.5 THz. Interestingly the power maximum occurred at the same frequency as the 20 mm crystal. Unlike the 20 mm crystal the 5 mm crystal held that 100 mW over a wide range, 2.5 – 4.5 THz. The smallest crystal size was able to maintain a higher power level at frequencies above 7 THz then the 5 mm crystal [6].

Overall, GaP was tunable over a larger then GaSe, as well as provides higher-powered waves. But there are advantages to GaSe because the configuration for GaSe is easier for spectrometer applications [5].

3. GaAs and InAs Semiconductor Sources

GaAs and InAs are being compared together because of there seminaries, and because [13] used the same experimental setup for each of these semiconductors in their experiments. The process by which the THz waves were generated was bulk electro-optic rectification. A 140 fs pump laser was used. The experiments in [13] were done to compare the response of GaAs and InAs to differing magnetic fields. A summery of their findings is presented in figure 5. For both GaAs and InAs the highest power around or just below 2 THz.

Figure 5: Power vs. frequency for GaAs and InAs semiconductor THz generation.

IV. DETECTION

It is obvious that the generation of THz waves is pointless without an effective means of detection. The general process by which THz waves are detection follows four steps. First the waves are focused onto a detection medium or photoconductive antenna, which will be discussed later. Second, the birefringence can be read using a visible or inferred pulse, usually split off of the laser used to generate the waves. Third, the probe beam is measured with a quarter wavelength plate. Finally, the time delay between the probe pulse and the THz signal can be measured to obtain the electric field in the time domain.

A. Photoconductive Antennas

Photoconductive antennas were the first key to effective THz detection, as well as emissions. They are commonly made from either Si or GaAs. Laser pluses split off from the pump laser pulses probe the antenna. The time delay from pump and probe pulses are measured, as well as the chance in DC current form the antenna to determine the THz waveform [12].

The common structure is shown in figure 6. It is shown with a GaAs substrate, but other semiconductors such as GaSe may be used. The whole in the middle, labeled D on the diagram, is biased by a DC voltage, A, and is probed by laser pulses slit off from the laser pump in the case of detection. It is normally on the order of 5 to 10 m. The over all size of the antenna is generally 10-20 (W) m by 30-50 (L) m [12].

Figure 6: Photoconductive antenna structure [12].

The THz waves strike the antenna they cause slight transient current changes. These current changes J(t) describe the incident electromagnetic field by the simple relation shown below:

The maximum THz wave that is capable of being measured by the photoconductive antenna is:

In eq. 8, is the mobility of the carriers, R is the reflectance of the substrate, hv is the photon energy form the laser, P in is the average laser power, and Vb is the biasing voltage [12].

The bandwidth of the antenna is affected by several factors. The key factors are the physical structure of the antenna, the carrier scattering time, the THz beam optics. However, what is the key factor according to [12] is the duration of the laser pulse.

B. Electro-Optic Sampling

Electro-Optic sampling was first presented in 1995 and offers several benefits over a single photoconductive antenna. It is able to provide a higher bandwidth and has parallel imaging capabilities.

The birefringence caused by the electric field applied will polarize an optical probe beam that is passed through the crystal. This polarization can be analyzed to determine the amplitude and phase of the THz field. If a thinker crystal is used the sensitivity of the system is increased because the length of the interaction between the field and electro-optic probe is increased. To image a sample, the sample is placed in-between the THz. Wave source and the sensing crystals. The interaction of the THz waves with the sample is measured by recording the waveform of the THz wave.

V. APPLICATIONS

The study of terahertz waves applies to many areas, from forensics to 3D imaging, medical imaging and spectroscopy. Medical imaging however presents many areas of study. Terahertz wave poses many properties that make them perfect for such imaging, but also contain many challenges.

A. THz Imaging and Tomography

Just As other electromagnetic waves are used in imaging so can THz waves. This is the single most important application of THz waves and most other applications draw from THz imaging. THz imaging has been demonstrated on leaves, semiconductors, IC packages, floppy disks, biological material, and teeth. THz imaging possibilities has been demonstrated on such a wide range of material because THz waves penetrate almost all non-metallic or polarizing substances [12].

What is the benefit of THz waves over X-rays though? X-rays are capable of penetrating nearly all materials, and the technology is well developed. X-rays are limited however in what they can image. If the material as a low index materials x-rays cannot provide clear images.

THz waves could be used to supplement x-rays in this case [12].

There are other properties of THz waves that have clear benefits over other imaging techniques. One benefit of using THz time-domain spectroscopy (THz-TDI) is that THz-TDI provides a measurement of the electric field produced by THz waves, of the intensity of the wave [9]. Through this phase information is maintained and a Fourier transform can reveal the imaginary and real components of the THz wave. When THz waves are applied to a sample the structure of the sample can be determined.

Another benefit of THz imaging is that is it also possible to gain spectroscopic information along with the structural information. This is because THz waves contain all the necessary frequency information [9]. Other benefits include improved safety and non ionizing radiation [12].

A disadvantage of THz imaging however is the resolution. Because THz waves have large wavelengths then visible light or x-rays they cannot provide as high was a resolution [12]. This will be discussed more in depth later.

1. Relevant Wave Equations for THz Imaging

When a THz passes through, or is reflected off it, the waves amplitude and phase is altered and scattered. This is a result of the refractive indexes of the samples. Maxwell’s equations may be used to describe this process [9,10]. Eq. 8 is an extension of Maxwell’s electric field equation shown in eq 7.

Here c is the speed of light, r is a point in space, (r) is dielectric constant, and (r) is the magnetic permeability of the sample [9].

Assuming that and are changing slowly a simplification may be made. If it is indeed the case that and are changing slowly then del natural log of and will be approximately 0, as shown is eq. 9.

Applying this to eq. 8 we are left with

Going one step further and neglecting polarization effects eq. 10 can be shown to be the scalar Helmholtz equation [9].

Here, n is the refractive index, u(r) is the amplitude function, and k0 is the wavenumber. Eq. 11 is the basis of imaging techniques [9]. The general goal in THz imaging is to determine the n(,r) and u(r) functions from the measured THz wave.

B. THz Tomography

As said previously, in order to obtain valid tomography the diffraction and scattering of the THz waves needs to be resolved by finding the n(,r) and u(r) functions. Max Born solved this problem in 1925 [9]. The resulting equation is

G(r-r`) represents the Green function, and u(r) = us(r) + u0(r). Figure 7 shows the general method of tomographic measurements. The waves are measured by a wave that by a plate perpendicular to the incoming waves [9]. By performing a Fourier transform the sample can be reconstructed.

Once the waves have been measured this data must be handled. One of the factors that limits the amount of data that must be recorded in order to reconstruct the sample are the Nyquist criterion. Nyquist criterion, often applied to digital sampling, says that in order to reconstruct the sample the sampling rate must be at least twice that of the highest frequency being sampled. [2] provides an example, if the area of the sample is 400 mm2, then no less than 128 x 128 (rounded to the nearest power of two) samples should be taken. And this is just for the special dimensions. In order to represent spectral

Figure 7: Standard tomography measurement setup [9].

information many more points are need in the time domain. If the emitter is putting out 3 THz waves then the sampling rate in the time domain is about 100 fs. In all at least 10 6

points are needed. Since it is a mechanical system that scans across the sample data taking can be a lengthy process [2].

C. Capabilities and Difficulties

Many difficulties have arisen in the THz imaging process. Not the least of which is image resolution.

Figure 8: THz image of a melanoma sample under different conditions. a) Transmittance at .5 THz b) Transmittance at 2 THz c) Phase angle at 1 THz d) e) dispersion at 1 THz f) dual frequency image, 1 THz and 1.5 THz. There images were interpolated to cut down on pixelation [2].

B. Medical Imaging

The need and desire for medical imaging is clear, there is always a desire for earlier detection and improved, non-invasive imaging. Currently, in the detection of cancer medical professionals look for tumors or anatomic location, but if instead doctors could detect pre-malignant cell growth, tumor cell markers, or genetic alterations cancer detection, treatment, and survival would greatly increase [7].

With THz imaging technology diagnoses could occur much earlier then current technology allows. It could provide a multi-spectral 3D image of the tissue or living abnormal tissue. This would lead to a better understanding of diseases and how they spread [7]. Indeed, the potential for THz imaging and spectroscopy technology is nearly endless in the medical field.

An example of what is possible with THz medical imaging is shown in Figure 8. From each of the six different images something unique can be learned. The sample was prepared according to standard practices; it was dehydrated, formalin fixed, and then wax embedded. The difference between pictures (a) and (b) is due to the higher absorption rates are higher frequencies. Image (c) demonstrates a time delay. It points to the refraction differences between the melanoma and the normal skin, giving a very clear indicator to the nature of the sample. The final two images, (e) and (f) also show that the absorption rate of THZ waves is higher in the melanoma then he surrounding tissue [2]. Again, demonstrating how THz imaging could be employed to gain faster and earlier diagnosis of diseases such as melanoma.

In the next section the current technology for medical imaging is presented. As well as the current

challenges. This is the main application focus for this paper.

1. Medical Imaging Systems

A typical medical imaging system is shown in figure 9. The laser beam is split into two; one beam is for the THz generation, the other is for detection. THz waves are optically generated by either photoconduction or optical rectification. From the generator, parabolic mirrors focus the THz waves onto the sample. The detection beam crosses a detector and acts as a time indicator for the THz waves being detected [2]. The data can be handled in several waves as described in the imaging section.

2. Concerns and Challenges

In developing imaging technology for medical purposes there are additional challenges above the challenges presented by generating and detecting THz waves. Foremost is safety, which involves signal power. In addition to safety concerns there are challenges presented by absorption rates, size, and cost

Figure 9: Layout for a typical THz imaging system [2].

a. Safety

When THz waves are used for medical imaging it is very important that that radiation levels to not exceed safety protocols. Electromagnetic radiation levels are given in terms of the maximum permissible exposure, or MPE. This is calculated from the root mean square value of the

peak electric and magnetic fields [2]. Factors that effect the MPE value are pulse repetition frequency, exposure length, total number of pulses, the area of the incident beam, and the duration of the pulse itself. As recommended by the American National Standard Institute the maximum average power for a pulsed THz imaging system is

Where MPEPW is the maximum average power, A is the area of the incident beam, MPECW is the maximum allowed continues exposure power level, F is the pulse frequency, and t is the pulse duration [2].

Using standard values from other pulsed imaging technologies MPEPW is 94 W. As discussed in the generation section earlier, current power in THz wave systems are on the order of mW, well below what safety regulations require. It should be noted however, that these values are typically used for shorter wavelengths. As will be discussed THz waves have high absorption rates with water and this could lead to more tissue damage then expected [2].

b. Absorption rates

This is perhaps the most challenging hurdle to medical imaging. Water and other polar liquids present a high absorption rate for THz waves, on the order of 150cm-1

at 1 THz [7]. This limits the depth at which THz waves can be effective because most THz applications rely on THz passing though the samples. Therefore, most current applications in medical imaging rely on skin conditions [7].

The impressions, however, should not be that absorption of THz waves is a complete limiting factor and something that needs to be completely resolved. As mentioned at the beginning of this section, melanoma absorbs more THz radiation then the surrounding tissue. This is due to the composition of melanoma. If it were not for differences in absorption rates some of the effectiveness of THz imaging would be lost.

c. Size and Cost

A THz wave imaging set up requires a few square meters. One possible simplification of the process is that the same semiconductor could be used to both generation and detection. This is because of the inverse relationship between optic rectification and electro-optic detection. This would allow transceivers to be made that are much smaller [7].

Currently THz systems cost up to $300,000 total, this is for sensing and imaging of THz waves. Before THz imaging can be adopted by the mainstream medical community the cost my have to reduce. Currently THz imaging systems are limited to research application [7].

d. Specific Medical Applications

The process of THz imaging and medical imaging processes and concerns have been presented. In order to clearly demonstrate the need for this technology, presented are a few specific applications for medical imaging.

Dermatology is the first and obvious application. Skin is not only the most accessible part of the human body for observation but some of the difficulties having to due with THz absorption rates are removed from the picture. It is already well known that using ultrasound for MRI reveals differences between normal healthy skin and diseased skin. THz imaging offers the potential to gain further understanding into skin diseases, and provide a way to monitor them more effectively then with large MRI machines [2].

Specific applications within dermatology include, monitoring healing, measuring scar tissue, and perhaps most important, cancer detection. This could lead to a better understanding of the healing process. It could also be used to test the effectiveness of drugs designed to suppress the formation of scar tissue.

Dentistry also has a lot to gain from THz imaging. There are fewer options currently for dental imaging. Primarily the introductory relies on x-ray imaging. A new imaging technique that is emerging besides THz imagining is optical coherence tomography. It has been shown however that THz imaging can detect caries in the tooth’s enamel layer earlier then the other techniques [2].

VI. SUMMARY PROPERTIES IN SPECTOSCOPY

SYSTEMS

When used for biomedical purposes, several properties of THz waves are important. These include power, wavelength, signal to noise rations, signal absorption, and bandwidth.

The typical power for a THz wave is from 0.1 W to 100W. For real time applications however, a higher power is required. Amplifiers are used to boost the output to the mA range and in some cases as high as kW.

A key factor in determining the usefulness of medical imaging is the resolution that can be obtained. The resolution is limited by the wavelength of the wave, which is around 300 m. This means that imaging cellular structure is not possible. However, research is being done in order to improve the resolution of THz waves.

VII. CONCLUSTIONMore research is needed to continue developing

THz wave applications. As the equipment become more readily available and lower in cost they systems are likely to become more available. Particularly, in the medical field great potential exists. Once some of the challenges are met THz will become a true, practical benefit.

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Michael R Boersma( M’03) was born in Grand Rapids, MI, on March 10, 1982. He attended Calvin College in Grand Rapids in 2000. He graduated with a BS in engineering with a concentration in electrical engineering in 2004. He is currently seeking employment in the west Michigan area.