Ultrabright THz source

The goal of this project is to create an ultra bright terahertz radiation source, of tabletop dimensions, using coherent transition radiation. The source will emit a pulse of approximately one picosecond, corresponding to a bandwidth of ~ 1 THz, with peak fields of ~ 1 MV/cm. During the project the pulse duration time will be reduced, increasing the bandwidth to ~30 THz and simultaneously increasing the peak fields.

Terahertz science

In spite of the fact that the electromagnetic spectrum (see Figure 1) from 0.3 to 30 THz is scientifically very promising, it never received much attention because a lack of high quality sources.

Figure 1: The electromagnetic spectrum. The THz regime is indicated with red. Diagram from the LBL Advanced Light Source website.

However, recently new sources became available and with them the awareness of the potential of THz radiation. To illustrate this we will give some examples where THz radiation plays a crucial role.

  • Donor impurities in semiconductors, which have a hydrogenic character, have excitations in the THz regime. The corresponding quantum states are interesting because they can serve as model states for quantum bits [1].
  • When the ponderomotive energy (the kinetic energy of a conduction electron oscillating in the THz field) or the electric dipole coupling strength (THz electrical field times dipole moment of a quantum-confined carrier) exceeds the photon energy, nonlinear quantum phenomena can be investigated. At optical frequencies the necessary electrical field is above the damage threshold of most materials. However, at THz frequencies this regime is at a few kV/cm to MV/cm, well below the dielectric breakdown in materials.
  • Small molecules vibrate and rotate at THz frequencies. This can be used to study molecule clusters in gas phases, or the interaction between molecules and a solvent, when molecules are dissolved in a liquid.
    Collective modes in large complex molecules, which lie between the domains of chemistry and biology, manifest themselves on a picosecond timescales. This makes it possible to study them with THz radiation.
  • Difference in absorption of THz radiation of tissue can be used to non-invasively probe the skin of humans, up to a depth of ~ 1 cm. This can e.g. be used for diagnosing skin cancer. Examples of this and other applications can be found on the website of TeraView.
  • THz radiation is absorbed by water and therefore suitable to probe the water content of all sorts of materials or tissues. In Figure 2 an example is given of how THz radiation can be used to measure the water distribution in a leaf.

Figure 2: Because water absorbs THz radiation, it can be used to measure the water distribution in a leaf.  The left picture shows a THz image of a leaf. The middle picture is a THz image of the same leaf 48 hours later, showing a non-uniform evaporation of water from the leaf. The right picture is a color bar indicting the relative concentration of water. Image taken by Nuss and coworkers at Bell labs. Lucent, Technologies.

A less scientific application comes from the ability to look through non metallic substances, which makes THz radiation suitable for security or industrial applications, where it is important to look through the package at the inside.

More information about the research into the fundamental and technological aspects of THz radiation can be found on the websites of P.C.M. Planken and on the website of THz Science and Technology. The website of Hamid R. Tizhoosh contains an overview of several links concerning THz radiation and imaging.

The listed examples are just a small fraction of the potential of THz radiation, and in general one can say that the interesting aspect of THz radiation comes from the fact that the photon energy is too small, to induce individual atomic transitions. Instead the energy quantum is related to larger spatial and time scales, which manifest themselves in all sorts of atom-atom and atom-electron interactions in molecules and solids. Another strong feature is the fact that it is possible to detect the oscillating electrical field of a THz pulse directly, instead of the usual intensity. This makes it possible to detect both phase and amplitude of a spectrum, giving an enormous amount of information in a single measurement.

This is why currently a lot of research is going into new THz radiation sources. The existing sources are either too weak to do the above listed experiments, or too large to be interesting for individual scientific groups. In a workshop of the DOE-NSF-NIH on February 2004 about THz opportunities in science [2], the wish was formulated for table top sources with field strengths of ~ 1 MV/cm or more, either in continuous wave mode or pulsed. With table top dimension it is meant that a small research group can buy and maintain such a facility, making THz radiation widely available in the scientific community.

THz radiation sources

In our project we aim for a broadband source, covering the entire spectrum up until ~ 30 THz, with a few µJ per pulse. Radiation pulses with energy of 0.4 µJ are obtained by E. Budiarto et al [3], by switching a photoconductor, which is biased at the highest voltage obtainable without breakdown, with an optical pulse of a few hundred femtoseconds. The photoconductor then serves as an antenna, which is turned on and off very fast, creating a THz radiation pulse. However, the spectrum (see Figure 3) peaks around 0.3 THz and does not contain the entire spectrum up until a few THz’s. So, this approach does produce THz pulses with a high energy and is compact, but does not have the desired broad spectrum.

Figure 3: Spectrum of the THz pulses generated by E. Budiarto et al [3].

A source that does emit a broader spectrum with a few µJ per pulse does exist; G. L. Carr et al [4] reported in Nature that they created high-power THz radiation from relativistic electrons. The electrons are created with photoemission and accelerated in an energy recovering linear accelerator (ERL) up to energies of 40 MeV. The paths of these relativistic electrons are then deflected by a dipole magnet, resulting in radiation emission of the electrons. The radiation pulses have energies of ~ 0.5 µJ, with a spectrum up until a THz (see Figure 4). The used ERL at Jefferson Laboratory can produce electron bunches with a very high repetition rate (37.4 MHz), resulting in a very high average power (~ 20 W), which is unprecedented high. Although this source does have the highest power with a broad spectrum, the bandwidth still needs to be increased if the entire THz gap is to be covered. However, the main disadvantage is that the accelerator is a large and expensive facility, and in no way a suitable option for a small research group.

Figure 4: Measured and calculated spectrum of THz radiation created by G. L. Carr et al [4]. The severe discrepancy between experiment and theory at lower frequencies is ascribed to diffraction effects. These large wavelengths were bigger than the vacuum chamber in which the experiment was conducted.

 
Coherent THz transition radiation

In our project we will use coherent transition radiation as a source. Transition radiation is the light pulse, which is emitted when an electron passes an interface between two media with different electric and magnetic susceptibilities. This is most easily understood in the case of a metal-air interface. Imagine an electron traveling in a metal towards the metal-air interface. This is schematically drawn in Figure 5. As long as the electron is in the metal an observer outside the metal will not notice the electron because its field is screened.

Figure 5: Schematic representation of transition radiation. As long as the electron is traveling in metal, its electromagnetic field is entirely screened and not observable outside the metal (a). The instant the electron passes the metal-air interface its field is no longer screened. However, its field cannot spread out instantaneously since it must propagate with the velocity of light (b).  The radiation pulse travels outwards, “filling” the space with the electromagnetic field of the electron (c).

However, at a certain moment the electron will pass the interface and its field will no longer be screened. The observer outside the metal will not notice this instantaneously, because the field of the electron has to expand outwards first with the speed of light. This expanding shell of light is the transition radiation pulse. The energy in the radiation pulse of 1 electron is in the order of ~ 0.1 eV, which is far too low for interesting applications.

The energy in the pulse can be increased by sending a bunch of electrons through the metal-air interface, instead of one electron. Each individual electron will emit a very short radiation pulse in time, which means that it contains a very broad spectrum of frequencies*. The electrons in the end of the bunch emit radiation with a time delay of ∆t = l/v (v is the speed and l the length of the electron bunch) with respect to electron at the front. This results in a phase difference of ∆Φ = ω∙∆t = ω∙l/v for each frequency component. If we neglect the transverse dimensions of the electron bunch, we can use this to estimate which of the frequency components add up coherently, by stating that the phase difference ∆Φ should be less than 2π in order to be coherent,

(1)

all the frequencies above ωcoherent will interfere destructively. Nowadays (see Figure 6 and ref. [5]) it is possible to create electron bunches that travel almost at the speed of light, v ≈ c, with a bunch length of a picosecond times the velocity of light, b = c∙10-12 m, which means that ωcoherent ≤ 2π THz.

Figure 6: Electro-optic measurement of the field profile of 110 pC electron bunch. The corresponding bunch length is 2.1 ± 0.2 ps. Taken from the PHD thesis of Fred Kiewit [5].

The transition radiation pulse created by such a bunch thus contains the entire spectrum up until the THz regime and is approximately 1 picosecond long in time. Because the electromagnetic fields of the transition pulse add up coherently they scale with the number of electrons, N, in the bunch. This means that the intensity scales with N2, resulting in a very bright source. To illustrate this, the number of electron in the aforementioned bunches are in the order N ≈ 109 which means that the energy in the total transition radiation pulse is approximately ~ N 2∙0.1 eV = 10 mJ. If we would focus this transition pulse in a spot of 1 mm diameter, the electrical field strengths would be in the order of ~ 20 MV/cm. In reality the energy per pulse is lower because only a part of the spectrum adds up coherently. To illustrate this we have calculate the spectrum of a transition pulse of a realistic electron bunch. The electron bunch length is 1 ps and the width is 200 µm, the kinetic energy is 5 MeV per electron and the charge is 100 pC. The spectrum is shown in Figure 7.

Figure 7: Calculated spectrum of transition radiation pulse. The electron bunch length is 1 ps and the width is 200 µm, the kinetic energy is 5 MeV per electron and the charge is 100 pC.

 

The shown spectrum is flat up until ~ 1 THz, which agrees well with the rough estimation made with equation 1. The bandwidth and energy per pulse of the source based on coherent transition radiation is thus comparable with the ERL at Jefferson Laboratory, however with the advantage of compactness. This opens the road to some very interesting experiments, e.g. those listed in the previous part.

The mentioned bunches have already been created in a Radio Frequency (RF) accelerator [5] in our group. However, this still requires a femtosecond laser for photoemission of electrons and a klystron for producing the electromagnetic waves. So the question is, is this table top? The answer is yes, because these facilities can be bought and maintained by a small research group. Especially if one compares it with the large acceleration facilities, currently necessary to produce THz radiation pulses with comparable electrical fields.

Smaller electron bunches, larger bandwidth

From equation (1) it is clear that the bandwidth of the pulse can be increased by decreasing the size of the electron bunch. This is a challenge in itself because the electron-electron interaction in the bunch tends to increase the size of the electron bunch. However, if the bunch is a homogenously filled ellipse it is possible to reduce the size of the bunch with relative ease, because the self fields inside the bunch are linear. Creating a bunch with such a distribution is another goal of this group.

Radiation reaction on electron bunch

All literature on transition radiation assumes that the loss in kinetic energy of the electron passing the metal-air interface is negligible. We can give some realistic number to show that this is perfectly valid for the single electron case. The kinetic energy of an electron accelerator by the aforementioned RF accelerator is ~ 5 MeV, which is much more than the ~ 0.1 eV emitted in the transition radiation pulse. However, in the case of an electron bunch this assumption might be violated, because the kinetic energy scales with N and the emitted energy with N2. Let’s assume we have a bunch with N ≈ 1∙108 electrons, accelerated by the RF cavity to a kinetic energy of ~ N ∙5 MeV. We furthermore assume that the bunch can regarded as a point particle. The ratio between the emitted energy in the pulse and the total kinetic energy is then,

which clearly shows the assumption is incorrect. This estimation shows that there is more energy in the transition pulse than initially available in kinetic energy. The main reason for this is that we regarded the bunch as a point particle, in reality only a part of the spectrum adds up coherently because of the finite extent of the bunch. Still, it clearly demonstrates that the known theory of transition radiation is not sufficient to describe coherent processes. If one truly wants to understand the process of transition radiation the effect of the radiation on the bunch should be taken into account properly.

* The width of the spectrum is determined by the electric susceptibility of metal. At very high frequencies the metal cannot respond and the difference in electric susceptibility between metal and air disappears.

Literature

  1. Cole, B. E., Williams, J.B., King B.T., Sherwin, M.S. & Stanley, C. Nature 410, 60-63 (2001)
  2.  M.S. Sherwin, A. Schmuttenmaer, P.H. Bucksmaum, Report of DOE-NSF-NIH workshop   opportunities in THz sience held on 12-14 February 2004, Arlington, VA. http://www.sc.doe.gov/bes/reports/list.html
  3. E. Budiarto, J. Margolies, S. Jeong, J. Son, and J. Bokor, IEEE J. Quantum Electron. 32, 1839 (1996) 
  4. G.L. Carr, M.C. Martin, W.R. McKinney, K. Jordan, G. Neil and G.P. Willliams, Nature (London) 420, 153 (2002)
  5. PhD thesis Fred Kiewiet