White Paper on THz Coherent Light Source

in Uppsala

Stockholm-Uppsala Centre for

Free Electron Laser Research

Version 1, February 2016

Contents 1. Executive Summary

2. Introduction

3. Science Case

3.1 Quasi particles and collective excitations 3.1.1 Excitons

3.2 Superconductivity 3.3 Magnetism and spin excitations 3.4 Dirac materials

3.4.1 Graphene 3.4.2 Topological insulators

3.5 Surface chemistry 3.6 Phase transitions 3.7 Semiconductors 3.8 Biology

3.8.1 Biophysics 3.8.2 Gas-phase spectroscopy of (bio-)molecules 3.8.3 Biochemistry

3.9 Medicine 3.10 Conclusions from science case

4. Conceptual Design

4.1 Layout of the baseline design 4.2 The accelerator 4.3 Generation of ultra-broadband GV/m THz pulses 4.4 Source 1: broadband THz pump 4.5 Source 2a: narrowband THz pump 4.6 Source 2b: broadband THz probe 4.7 X-ray source: optional 4.8 Conclusion

5. References

3 4 7 7 7 10 13 15 16 17 18 19 21 22 22 23 24 24 25

28 28 29 30 32 35 36 37 40 41

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1. Executive Summary We propose to build a flexible strong-field terahertz (THz) light source that permits a number of

ground-breaking experiments on collective excitations in multi-atomic systems. Such systems comprise of molecular rotations, DNA dynamics, spin waves, Josephson waves and phonons. Strong-field THz pulses allow engineering new dynamic states of matter by selective excitation of the process of interest. One of the non-trivial examples of new physics discovered with intense THz light is the excitation of a transient Josephson plasma wave in superconducting cuprates significantly above the critical temperature of the sample. This phenomenon is indicative of the possibility of room temperature superconductivity.

The energy levels in these type of systems are rather finely spaced such that stimuli with optical photons, which normally have a much too high energy, cause unwanted heating and reduced control. This problem is avoided by using THz radiation having photon energies comparable to the energy levels investigated. It allows targeting the excitation of interest and thus opening the door to controlled manipulation of reactions and processes.

A flexible strong-field THz light source is required for studying fundamental collective excitations. The proposed THz Coherent Light Source in Uppsala will deliver quasi-half-cycle or multi-cycle THz pulses with a field strength in the V/Å range at a multi-kilohertz repetition rate. It makes use of coherent spontaneous radiation from pre-bunched electron beams and a new concept of slippage control between electrons and the radiated field.

With respect to other THz light sources our source in Uppsala has a number of unique features:

• it will be the first source designed specifically for pump-probe experiments; • the broadband THz source will cover the range from 5 to 15 THz, exceeding that of laser-

based THz sources; • the THz source will generate quasi-half-cycle pulses with field strength and repetition rate

that are far beyond any existing or planned source.

The scientific opportunities available with the proposed powerful and flexible THz light source are described in the section ‘Science Case’ followed by the section presenting the conceptual design.

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2. Introduction The terahertz (THz) region of the electromagnetic spectrum covers the frequency range of 0.1-10

THz (3 mm-30 µm in wavelength). This is visualized in Fig. 2.1 together with the conversion of 1 THz into various often used units. Historically there has been a lack of sources producing high-quality radiation in the THz region and it has therefore been called the THz gap. In contrast, efficient lasers have existed in the visible and infrared part of the spectrum, whereas electronic sources have been successfully employed at frequencies below the THz region, in the radiowave and microwave domains. However, with the development of new sources producing THz radiation of high intensity and with various characteristics, the THz gap is being filled, which has led to an increased interest in using THz radiation for scientific and industrial applications.

Figure 2.1. Illustration of the location of the THz region within the electromagnetic spectrum [1]. Also shown is the conversion between different units.

In this White Paper the scientific opportunities (chapter 3) and design (chapter 4) of a highly flexible THz coherent light source based on a superconducting linear accelerator is presented. As illustrated by the scientific examples described in chapter 3, THz radiation is an efficient tool for investigation of a multitude of low-energy excitations existing in the THz region. Examples of such important resonances are plasmons, phonons, spin excitations, intersubband transitions, excitons, and collective molecular vibrations. Here plasmons and phonons are collective electron and lattice vibrations, respectively, intersubbands are electronic energy bands formed in quantum wells, in which the electrons are confined in two directions, and excitons are bound electron-hole pairs. One essential characteristic of the THz wave is that it offers a fine tool for manipulation of systems. This is highly advantageous in comparison with optical photons which often contain excessive energy relative to the type of low-energy resonances given above and therefore provides a blunt tool. The extra energy from the optical photons may for example be distributed as phonon excitations or hot electron distributions, which results in less control and unwanted temperature increase. The THz waves, on the other hand, allow one to specifically target the excitation of interest and thus open the door to controlled manipulation of reactions and processes.

In order to study the need of national users of THz radiation, we organized a workshop on the scientific opportunities of a THz FEL in Sweden, November 24-25, 2014, in Stockholm. The present design of the THz facility complies with the users’ demand and the main target parameters of the THz sources are summarized in Table I.

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Table I: Main design parameters of the THz sources.

Parameter Quasi-half-cycle pulses for

time-resolved experiments Narrowband pulses for

frequency-resolved experiments

Spectral range (THz) 1.5-15 1.5-15 Pulse duration (ps) 0.1-1 1-10 Pulse energy (µJ) 1000 100

Peak electric field (GV/m) 1 0.1 Relative bandwidth FWHM 100% 10%

Repetition rate (kHz) 1-100 1-100

Options for pump-probe experiments provided by the suggested light source:

• Quasi-half-cycle THz pump – optical/IR probe • Narrowband THz pump – broadband THz probe • Narrowband THz pump – optical/IR probe

In order to make the optical probe more versatile we plan to use an optical parametric amplifier for tuning the optical probe in the range from 200 nm to 20 µm. A narrowband collimated soft X-ray source is foreseen as an option and can be implemented upon users’ request.

The proposed THz facility has a number of properties which distinguishes it from other THz sources. Two important advantages of an accelerator-based, compared with a laser-based, THz source, are the potential for narrow bandwidth pulses and the tunability of the frequency, which allows for selective excitation of specific resonances. Such narrow bandwidth, intense pulses are provided by a multicycle-pulse source in our design. Quasi-half-cycle pulses generated by a separate undulator gives access to strong-field transients which are beneficial for investigations requiring a high electric or magnetic field and can, in particular, be utilized for control of molecules or quasi-particles such as magnons, phonons, and excitons. In addition, the short pulses are suitable for time-resolved measurements and the broad bandwidth of these pulses serves well for probing a large frequency range. A highly beneficial feature of the THz light source will be the ability to reach the 5-15 THz region, where present laser-based THz sources normally do not operate because of absorption in crystals, and conventional designs of accelerator-based sources struggle with the need for unrealistically short electron bunches necessary for super-radiant amplification at high frequencies. Access to this fresh frequency window for ultra-short pulses creates the opportunity to investigate new resonances and processes by unique excitation and probing possibilities. Moreover, the variable repetition rate of the proposed THz facility is essential for matching the requirements of different types of studies. For example, pump-probe measurements typically request repetition rates of 1-10 kHz and a reduced repetition frequency is sometimes desired in condensed phase experiments in order to limit the temperature increase. In contrast, the large average power that can be generated with a high repetition rate is required specifically in gas-phase experiments because of the low concentration of particles. Although experiments in condensed phase environments sometimes demand a limited average power of the THz radiation, there are ways to overcome this

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problem, such as using rotating samples, liquid jets, and cooling of the sample. The high average power made available by the superconducting linear accelerator is thus a general asset in many experiments because of the significantly reduced measurement time.

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3. Science Case In this chapter we describe the scientific opportunities available with the type of powerful and

flexible THz source proposed here. Sections 3.1 – 3.9 focus on nine distinct scientific areas where THz studies are expected to be highly beneficial. In these examples investigations of solid state materials are well represented because of the strong impact of THz radiation on e.g. the development of new photonics devices, the understanding of essential phenomena such as superconductivity, and the control of reactions on surfaces. However, as emphasized in sections 3.8 and 3.9, the fields of biology and medicine will also strongly profit from studies in the THz frequency range. In section 3.10 conclusions are drawn from the science case. Here we concentrate on some particularly important areas and in each case we present the THz parameters that will enable the desired experiments.

3.1 Quasi-particles and collective excitations

Many resonances in the THz region are associated with quasi-particles and collective excitations. Prominent examples in this category are excitons, plasmons, phonons, and magnons (collective spin excitations). The proposed THz light source can be tuned to their specific excitations and thus the various processes and effects related to these resonances may be investigated. Moreover, the strong field of the ultra-short THz pulses is very useful for studies in this area. Next we concentrate on excitons while the remaining types of quasi-particles and collective excitations are discussed in other sections. However, we already note that, for example, Josephson plasmon excitations are central in studies of superconductivity, phonon resonances can be utilized for driving various phase transitions, and excitation of magnons is successfully employed for control of spin oscillations.

3.1.1 Excitons

Excitons can be formed by optical excitation of an electron from the highest filled valence band to the empty conduction band, separated by a bandgap of approximately 1 eV. The Coulomb attraction between the created excited electron and the depleted state, the hole, may result in a bound hydrogen-like state. These excitons have an energy structure similar to the hydrogen atom, although the binding energy is scaled down by a factor of 1000 and lies in the THz spectral range.

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Figure 3.1 shows the principle and results of an experiment which demonstrates the formation and monitoring of the exciton by measuring the THz conductivity and the dielectric function as a function of time [2]. Here GaAs quantum wells were excited with a near-infrared pump pulse 21 meV above the bandgap into the unbound electron-hole continuum (Fig. 3.1a). The build-up of the exciton population is probed by broadband THz pulses and is seen by the increasing peak of the conductivity at 7 meV corresponding to the transition from the exciton 1s to 2p level. The shoulder on the high energy side is attributed to transitions to bound higher-energy states and to the continuum. As excitons are formed, the low-frequency conductivity vanishes. The transformation of unbound electron-hole pairs into bound excitons is explained by a combination of Coulomb interactions, such as unbound electron-hole pairs forming excitonic states by transferring energy and momentum to other carriers, and the existence of a phonon bath which accepts the release of binding energy and momentum.

Figure 3.1. a) Optical creation of exciton (blue arrows), scattering of unbound electron-hole pairs into exciton states (green arrow) and transitions between internal exciton states (red arrows). b) Transient spectra of the conductivity ∆σ1 (left panel) and dielectric function ∆ε1 (right panel) demonstrating exciton formation as the increasing peak at 7 meV in the conductivity and an increase of ∆ε1 at low frequencies. [2]

a) b)

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Resonant control over quantum states of excitons can be obtained by intense THz pulses. The two-level system formed by the intra-excitonic 1s and 2p levels has an energy splitting of the order of 10 meV up to 100 meV and is thus accessible with THz frequencies. Tuned to resonance with the 1s-2p energy difference one may stimulate Rabi-oscillations where the two-level system is driven periodically between the two states [3]. Moreover the frequency domain equivalent of this effect, the Autler-Townes effect, has been demonstrated [4]. It is characterized by a THz-frequency and intensity dependent energy splitting of the two levels as illustrated in Fig. 3.2. By tuning the frequency of intense THz fields (1 MV/m) around the 1s-2p resonance one could unambiguously observe this effect. There is also potential for more complicated forms of manipulation on three-level systems [5] where one may carry out state to state control via the so-called stimulated Raman adiabatic passage (STIRAP) process [6].

Figure 3.2. Autler-Townes splitting on resonance (ωTHz= ω2-ω1) where the original states split by the Rabi frequency Ω. [4]

A new phenomenon called high-order-sideband generation (HSG) has been observed from recollisions between electrons and holes in excitons [7]. The mechanism is similar to high-order-harmonic generation in which an intense field removes an electron from the atom or molecule and induces large-amplitude oscillations where the repeated collisions with the charged core results in emission of high-harmonic radiation. The highest-order harmonic is determined by the maximum energy gained by the electron, Emax≈IP+3.2UP, where IP is the ionization potential and UP=e2F2/16π2mef2 is the ponderomotive energy. The latter is the average classical kinetic quiver energy of the electron (mass me, elementary charge e) induced by the field with field strength F and frequency f. Thus, by using low frequency (THz) fields to drive the excitons and cause recollisions between optically excited electron-hole pairs, it was predicted that HSG could be achieved at much lower field strengths (kV/cm to MV/cm) compared with the corresponding high-order-harmonic

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generation in atoms and molecules. This was recently experimentally confirmed by observing sidebands of a near-infrared laser, which was used to create the excitons that were driven by the THz field, up to the eighteenth order, [7] see Fig. 3.3. It shows that recollisions in excitons can be studied at intensities well below the damage threshold of the semiconductor while using quasi-continuous wave sources. HSG may provide a new nonlinear spectroscopy tool for investigating the structure of optical excitations in condensed matter. Furthermore, the new mechanism for ultrafast wavelength conversion has potential applications in terabit-rate optical communications.

Figure 3.3. THz-sideband generation in a semiconductor quantum well from electron-hole collision driven by an intense THz-field. [7]

3.2 Superconductivity

THz spectroscopy is a critical tool for studying low-lying excitations of strongly correlated electron materials and their associated phenomena such as colossal magneto resistance, magnetism, and charge and spin density waves. One of the most important effects emerging from correlated systems is that of superconductivity. Time-domain THz spectroscopy with the ability to directly measure the real and imaginary components of the conductivity (and dielectric function) by recording both the amplitude and phase of the reflectance or transmission, has revolutionized the study of super conductors at THz frequencies. Below, examples of exciting pioneering THz-studies in the field of superconductivity are presented. The use of THz-radiation in this field is just beginning to open up a completely new understanding of the mechanisms of superconductivity and a

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flexible THz-source of the type proposed here would be immensely beneficial for further exploration of this phenomenon.

In some high-temperature superconducting cuprates a connection between one-dimensional modulations of charge and spin, and superconductivity exists [8-10]. At specific doping levels where these stripe orders appear, a significant reduction of the superconducting transition temperature, Tc, is observed. By applying mid-IR pulses to such striped materials, signs of light-induced superconductivity was first demonstrated in 2011 [11] at a temperature of 10 K, just above the Tc. The mid-IR radiation was made resonant with Cu-O vibrations of La1.675Eu0.2Sr0.125CuO4 (LESCO1/8), which perturbed the stripe structure, thus inducing the signatures of superconductivity on an ultrafast time scale. Figure 3.4a displays the measurement of the reflectance spectrum (normalized to the spectrum before the pump pulse) at a time delay of 5 ps after the pump pulse. The appearance of a plasma edge, the drop in reflectivity at ~60 cm-1 (1.8 THz), is related to the formation of a Josephson plasma resonance which is a general feature of cuprate superconductors, and demonstrates the superconducting nature of the photoinduced state. Figure 3.4b shows the temporal evolution of the imaginary conductivity σ2 as a function of frequency. The appearance of a decreasing σ2 with frequency reveals that the system displays superconducting features on the shortest time scales accessible, i.e. shorter than 2 ps. This is significantly faster than expected and may be important for the understanding of the interplay between charge and spin stripe structure, and superconductivity.

Figure 3.4. a) Transient reflectance of the stripe-ordered cuprate LESCO1/8. The drop of reflectivity at ~60 cm-1 indicates photo-induced superconductivity after mid-IR excitation. b) temporal evolution of the imaginary conductivity σ2 as a function of frequency. The appearance of a decreasing σ2 with frequency suggests that the system becomes superconducting on a time scale shorter than 2 ps. [11]

a) b)

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Recently indications of transient light-induced superconductivity were also demonstrated far above Tc for the bilayer cuprate YBa2Cu3O6.5+x [12,13]. In this case the mid-IR pulses were tuned to the coherent excitation of apical oxygen distortions at 15 µm. By comparing parameters such as the THz reflectance and complex conductivity they found strong similarities between the light-generated, and the equilibrium below-Tc properties. For example, they observed a photo-induced plasma-edge very close to the equilibrium Josephson plasma resonance and a photo-induced change in imaginary conductivity, ∆σ2(ω), which corresponded to that generated from a decrease of temperature below Tc. The superconducting signatures could be observed at temperatures up to 300 K. Using femtosecond X-ray diffraction the behavior of the lattice structure was investigated for this exotic state. These studies revealed that the nonlinear excitation of the crystal lattice structure creates a displaced lattice geometry (Fig. 3.5) which cause drastic changes in the electronic structure, and may cause destabilization of the charge-density wave order, of which both may favor superconductivity [14].

Figure 3.5. Transient lattice structure of YBa2Cu3O6.5 upon 15 µm excitation resonant with apical oxygen (oxygens between the bi-layers) distortions at above Tc. a) shows the simultaneous increase and decrease of the intra-bilayer and inter-bilayer distances, respectively. b) illustrates the increase in Cu-O buckling. [14]

The study of photo-induced superconductivity has also been extended to non-cuprate materials, where in contrast to cuprates, the enhanced superconductivity is not related to melting of an ordered state. Experiments on K3C60 suggest that coherent excitation of the lattice can enhance superconductivity far above Tc, and thus that it may promote superconductivity in a more general way than previously assumed [15].

Superconductivity has furthermore recently been investigated in a cuprate [16] using narrow band (∆ω/ω=1%), 25 ps pulses at a frequency tuned around 2 THz to excite so called Josephson plasma

a) b)

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solitons (JPS). Josephson plasma waves are linear electromagnetic modes that propagate along the planes of cuprate superconductors. The JPSs are slowly propagating waves with a constant shape that are formed via a nonlinear process. By comparison with simulations they [16] could show that the short intense THz pulses tuned to the Josephson plasma resonance at 2 THz generated these solitons. This observation is expected to lead to new strategies for optical control of superconductivity. Furthermore, the demonstration that these flux-carrying JPSs can be driven and detected by THz light open up new opportunities for e.g. information transport and storage. In combination with THz coherent control techniques, light could be used to generate, stop, accelerate or slow down the JPSs.

The examples above show the potential impact of THz radiation on the understanding and control of superconductivity. In particular, broad-band THz pulses covering a wide frequency range will be useful for probing the signatures of superconducting phases. Intense, tunable, narrowband THz pulses will be essential for excitation of plasma and phonon resonances. Furthermore, X-ray pulses will be important for time-resolved measurements of the lattice structure.

3.3 Magnetism and spin excitations

The control of spin and magnetic excitation in solid state materials is highly relevant for the development of data storage and processing with increasing speed. Conventional magnetic switching is accomplished by applying a magnetic field antiparallel or perpendicular to the magnetization of the material. However, experiments [17] suggest a time limit of approximately 2 ps for this type of switching, which has led to the idea of using optical pulses to trigger magnetization reversal.

It has been established that ultrashort optical pulses can be used to control magnetism. For example, 40 fs circularly polarized laser pulses were shown to reverse the magnetization in a reproducible manner [18], although the dynamics proceed on a considerably longer timescale than the pulse duration. In the ultrafast magneto-optical experiments the light field never directly couples to the magnetic order. Here the magnetism is only indirectly affected by the light via the excitation of a non-equilibrium distribution of carriers, which relaxes in energy and momentum as they interact with the lattice and ordered spins [19], and this limits the speed to several tenths of picoseconds.

In contrast, the use of THz pulses may be employed for direct spin manipulation through the time-dependent magnetic field which generates a Zeeman torque on the spins (the torque is proportional to B.S, where B is the magnetic field and S is the spin). This has been demonstrated [20] by coherently controlling collective spin precessions, so-called magnons, using single-cycle intense THz pulses to turn on and off coherent magnons in antiferromagnetic NiO at frequencies as high as 1 THz (Fig. 3.6). They were able to almost completely turn off the spin precession using a second THz pulse arriving at a specific delay after the first. The magnetic dynamics was probed by an 8 fs near-infrared pulse through the induced Faraday rotation of the polarization.

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Figure 3.6. Coherent magnons excited by the magnetic field of an ultrashort THz-pulse. [22]

With these findings of femtosecond coherent control of magnons via pure magnetic coupling, a

new research field in interactions of intense ultrashort pulses of magnetic fields with matter is opened. Possible new experiments involving such coherent magnetic field pulses in the THz range include the coherent manipulation of spins in solids for data storage and quantum processing applications. These experiments were performed with magnetic peak field-strengths of 0.13 T. At even higher fields, approaching 10 T (which corresponds to an electric field of 3 GV/m), a novel regime of THz magnetic nonlinearities in the non-perturbative regime, should be accessible. Using a relativistic electron bunch at the Stanford Linear Accelerator (SLAC) to produce a peak field of 20 T in a 3 ps transient, ultrafast switching of ferromagnetic Co/Pt films was observed [21]. The switching was explained by two contributing components where the initiated precession of the magnetization in the magnetic field was followed by rotation of the magnetization into the direction of the field due to energy dissipation.

The control of magnetization using THz pulses has the essential benefit of a direct coupling to the

spin excitation, free from the generation of a non-equilibrium thermal electron distribution associated with optical excitation. This is highly important, not only because it provides a more direct way of manipulation, but also because of the demand to reduce the temperature in data processing applications. With intense quasi-half-cycle THz pulses we will aim at obtaining a picosecond magnetic switch.

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Another suggested option for triggering magnetic switching is by the electric field of a laser pulse. Here the mechanism would consist of the ultrafast electronic distortion of the valence charge by a sufficiently strong electric field [23]. Suitable pulses would have >1 THz frequency,

3.4.1 Graphene

Graphene is a one-atom thick sheet of carbon atoms formed in a honeycomb 2D crystal lattice. It is the basic building block of other carbon nanomaterials of varying dimensions and properties, such as fullerene (0D), carbon nanotubes (1D), and graphite (3D), see Fig. 3.8. Graphene exhibits exceptional electronic properties [25] exemplified by a remarkable electron mobility due to suppression of back scattering [26] and an unconventional quantum Hall effect [27,28]. Combined with its unique optical, mechanical, and thermal characteristics, as well as the availability of large-area graphene, it is emerging as a highly promising material for future applications in e.g optoelectronic devices and other commercially oriented applications [29-32].

Figure 3.8. Schematic of various carbon nanomaterials with distinct dimensionality in which graphene (top left) is the basic building block. [25]

Graphene is a gapless semiconductor, but for many optoelectronic applications a bandgap is required. For example, in a transistor the electrons should ideally cross an energy barrier provided by a band gap in order to be conducting, otherwise the current cannot be turned off. In graphene the electrons are instead always conducting. However, it has been predicted that circularly polarized infrared and THz waves can be utilized to create a band gap in graphene [33] whose magnitude is

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proportional to the laser intensity and inversely proportional to the frequency of the laser field, and thus THz frequencies are preferable. This provides tremendous opportunities for transistor development and other optoelectronic applications where control of the band gap is required.

3.4.2 Topological insulators

Topological insulators is a relatively new class of materials that have an insulating interior and highly conducting surface states that are protected by time-reversal symmetry. The surface states have electrical properties which are fundamentally different from other 2D conducting states because they do not scatter from ordinary defects and can carry electrical currents even in the presence of large energy barriers.

The detection and control of topological surface states (TSSs) in ambient conditions is crucial for the development of practical applications in fields such as spintronics and topological quantum computation. Electrical and optical techniques have so far suffered from lack of separation between bulk free-carrier states, quantum well states (QWSs), and TSSs in routinely prepared topological insulator samples. Thus, there is a strong request for a method of selectively probing the TSSs and ultimately to control them. By investigating ultrathin Bi2Se3 films of varying thicknesses using THz time-domain spectroscopy (TDS) Park et al. [34] very recently demonstrated such separate detection of the TSSs. They could furthermore monitor the change in topological phase transitions by varying the sample thickness. For example they observed the two-dimensional (2D) trivial insulator at a 2 quintuple layers (QL) thickness, which has zero conductivity. It transformed into a 2D hybrid topological insulator at a 3 QL thickness with the expected conductance of 2G0, where G0 =e2/h (e electric charge, h Planck’s constant) is the single conductance quantum, associated with purely TSS contribution. The factor 2 is related to the TSS contribution from the top and bottom of the TI film. As the thickness was increased up to 8 QL further contribution was added from QWSs and bulk free-carrier states (see Fig. 3.9). Furthermore, they found a strong coupling between an infrared-active phonon mode at 9 meV and the TSSs, revealed by the asymmetric Fano-like lineshape at this energy. It is expected that this coupling will lead to control of the TSSs by manipulation of the lattice with intense THz pulses and may thus generate new applications in THz photonics and plasmonics.

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Figure 3.9. Measurement of the real conductance in the THz region revealing the increased conductivity with thicker sample (expressed in quintable layers) associated with the added contribution from bulk and quantum well states. [34]

3.5 Surface chemistry

Surface chemistry and catalytic reactions are suitable fields for THz studies because many surface vibrations exist at these frequencies, such as phonons and frustrated vibrations of the molecules bound to the surface. The high-field single-cycle (quasi-half-cycle) THz pulses with electric fields of the order of 1 GV/m, which corresponds to the Coulomb force between the electron and nuclei, provides a handle to manipulate the molecules attached to the surface. It allows for the initiation of a coherent motion of the surface-attached molecules, for which the direction can be controlled by the orientation of the polarization of the incident THz field (see Fig. 3.10). The direct coupling to the vibrations of the adsorbed molecules by the THz pulse provides a crucial advantage compared with previous attempts at controlling femtochemistry on metal surfaces using ultrashort optical pulses. The latter method relies on indirect coupling to the molecules via excitation of phonons and hot electrons and thus allows little control of the reaction pathway. In contrast, the use of THz pulses permits one to target specifically the motion of the adsorbed molecules and thus it provides increased control.

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Figure 3.10. Visualization of the control of the motion of a molecule attached to the surface, enabled by short strong-field THz pulses. [35]

THz-induced control of CO oxidation on Ru(0001) was recently demonstrated [36] using the strong quasi-half-cycle fields of THz transients generated by coherent transition radiation (CTR) from an ultrashort relativistic electron bunch at the Linac Coherent Light Source (LCLS). However, the THz pulses produced from CTR are inherently radially polarized and therefore further control could potentially be achieved by a linearly polarized intense THz transient with rotatable polarization orientation.

3.6 Phase transitions

The interaction between charge, spin, orbital and lattice degrees of freedom in correlated electron systems opens up many pathways for phase transitions. One exciting opportunity accessed by THz radiation is the possibility to photo-induce a phase transition. Moreover, THz probe pulses are especially suited to monitor insulator-to-metal transitions because they provide a direct measure of the conductivity in the THz frequency range. A commonly used testbed for correlated-electron phase-transition dynamics is Vanadium dioxide because both the lattice and on-site Coulomb repulsion contribute to the insulator-to-metal transition at 340 K. In ref. [37] a strong THz electric field (~1 MV/cm) was utilized to induce an insulator-metal transition in Vanadium dioxide (Fig. 3.11) and the phase transition was probed by measuring the transmission of another THz pulse in the 0.3-1 THz range with picosecond resolution. Their experiments indicate a two-step process for the THz-induced phase transition where initially the electric field reduces the Coulomb-induced activation barrier for carrier motion, which is followed by heating through electron-lattice coupling that drives the material into the metallic phase on a picosecond time scale.

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Figure 3.11. Schematic of the structural changes in the THz-induced insulator-metal transition of VO2. [38]

In order to monitor the structural changes during the insulator-to-metal phase transition in VO2, femtosecond X-rays can be used to measure the ultrafast X-ray diffraction. This has been performed at LCLS [39] and a remarkable result of the experiment is that the lattice phase transition occurs ~10 ps after the electronic one. Typically, when one induces a phase transition either via temperature or optical laser pulses, the two sub-systems (the electrons and the lattice) are strongly coupled, and the lattice moves together with the electrons. The fact that THz radiation can be used to potentially drive a purely electronic phase transition opens up for the use of correlated materials in electronics beyond silicon.

One may also control the phase of a solid state material by selectively exciting specific vibrational modes. This has been demonstrated on a manganite [40], a material known to exhibit sensitivity to metal-insulator transitions. Using time-resolved measurements with a 1 µJ, 200-300 fs pump pulse resonant with a Mn-O stretching phonon mode at 17 THz (17.5 µm) and a probe in the visible/nearIR range that measures the reflectivity change, they showed that the system was driven into a high-conductivity phase on a femtosecond time scale. Limitations in generating pulses of frequencies below 12 THz prohibited them from exciting lower frequency modes which would be useful for assessing the specificity of the Mn-O stretching with respect to lower frequency phonon modes.

The formation of a metallic state in a magnetoresistive manganite, where metallicity and ferromagnetism are related (through the double-exchange mechanism [41]), also implies the possibility of generating ferromagnetic domains on ultrafast time scales by specific vibrational excitations. Furthermore, ultrafast vibrational control of correlated-electron phases is likely to be applicable to other interesting cases, such as the nature of high-Tc superconductivity and the role played by lattice vibrations for electronic properties, providing new insight into complex matter.

Insulator Metal

THz

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Perovskite systems are not ferroelectric, but become ferroelectric upon slight doping and below a certain critical temperature Tc. The exact mechanism for the normal-to-ferroelectric transition in these compounds is not yet completely understood, but there is evidence that a soft phonon mode of diverging amplitude as Tc is approached may be the key-player in the transition. SrTiO3 shows no finite Tc (i.e. it never becomes ferroelectric), but there are nonetheless indications of a soft phonon mode of diverging amplitude as the temperature is lowered. At LCLS one has attempted to drive this soft phonon (at ~1 THz) by direct coupling of the THz electric field with the polarization of the perovskite unit cell, i.e. by "dragging" atoms directly, and to observe such atomic displacement in a time-resolved X-ray diffraction signal [42]. They found evidence that the atoms respond to the THz excitation with a characteristic frequency of about 1 THz, consistent with the soft-phonon mode picture.

3.7 Semiconductors

Semiconductors have been immensely important for the development of electronics and optoelectronics. One strong reason for their usefulness is that specific resonances between energy levels can be designed thanks to the ability to engineer semiconductor quantum wells, wires and dots, where the particles are confined to two, one or zero dimensions, respectively. In these structures energy-level splittings are often in the THz range. The high degree of control over the energy levels makes such semiconductor nanostructures suitable for testing advanced applications of quantum optics, coherent control, and high-field physics. For example, engineered semiconductor quantum wells can be utilized for the construction of THz and far-infrared optoelectronic devices such as detectors [43] and lasers [44] based on intersubband transitions (transitions between states created by the confinement of the quantum wells). THz-gain can also be obtained by inducing population inversion between exciton levels of semiconductor wires and wells, which may be of further importance for the development of THz lasers [45]. Moreover, high-order-sideband generation (HSG) has been demonstrated using strong THz fields to drive excitons of a semiconductor quantum well which causes recollisions between optically excited electron-hole pairs [7], as discussed under the section of excitons. This can for example be exploited in the field of terabit-rate optical communications.

In order to reach the full potential with respect to control of processes and quantum states in semiconductor nanostructures it is necessary to characterize the relevant excitations, both in the frequency and time domain, and here a flexible THz radiation source will be an essential tool.

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3.8 Biology

3.8.1 Biophysics 3.8.1.1 Collective modes Theoretical studies indicate that many functionally important structural changes within proteins

proceed along low frequency collective modes [46,47]. These collective modes are believed to play a central part in ligand binding, catalysis, and signal transduction, but solid experimental evidence is largely lacking. Terahertz radiation can be used to excite collective modes within proteins, and the radiation can be used both as a probe for the direct observation of collective modes and as a pump for the selective excitation of certain vibrational modes. Terahertz absorption spectroscopy can directly probe the density of vibrational states in biological samples but due to the large number of modes present in this frequency region and line broadening, the spectra are usually featureless and give no easily accessible structural information [48]. An alternative procedure would be to excite specific collective modes by irradiating the protein or other biomolecules with a small-bandwidth terahertz pulse and then study the excited state using a secondary method, for example X-ray crystallography. The experimental feasibility of this approach has recently been demonstrated [49]. Other results show that orientation-dependent resonances can be detected in a protein crystal, using terahertz microscopy [50]. These observations indicate a new way ahead for the direct observation and manipulation of collective phenomena in biology and are, therefore, of great interest.

A much-debated topic is whether or not collective modes are involved in enzymatic catalysis [51-53]. Enzymatic reactions generally have a turnover in the micro to millisecond time range, which is a result of the combined time scales of the various reaction steps, like substrate binding, chemical transformation, and product release. NMR studies and simulations indicate that picosecond vibrations in proteins can increase the turnover of enzymatic reaction through assisting the substrate binding and the rate limiting product release step [54]. Chemical catalysis can be affected by picosecond vibrations through so called promoting vibrations [51]. Understanding the involvement of such vibrations could offer a way of controlling, and perhaps even synchronising, chemical reactions in enzyme systems, and may transform current views on enzymatic catalysis.

A THz source producing single-cycle THz pulses would be an enabling step for rapid time-resolved studies in a so far largely unexplored area in biology.

3.8.1.2 Biological effects of THz radiation

There is an increased use of THz radiation in everyday life where it is exploited in e.g. THz-imaging for detection of skin- [55] and breast cancer [56,57], and public THz security screening [58]. Therefore the biological effects of THz radiation need to be investigated with respect to a variety of parameters, such as intensity, frequency, and duration of exposure. Conclusions have been reported both in support of [59,60], and against [61-65], genetic damage related to THz exposure, but the data seems to indicate that biological function can be affected under conditions of high intensity, long exposure, and at certain THz frequencies. Specifically it was suggested in a theoretical study [66]

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that the THz field may cause localized openings in the DNA double strand above a certain threshold perturbation amplitude of the DNA oscillations determined by the intensity and frequency of the THz wave. However, also here experimental evidence point both in favor [60], and against [63,67], such THz-induced double strand breaks. Hence, further studies of the biological consequences of exposure to THz radiation are required.

3.8.2 Gas-phase spectroscopy of (bio-)molecules With a high average flux it is possible to efficiently study molecules in the gas-phase. The THz

frequencies of molecular collective vibrations, and their sensitivity to the atomic arrangement, may be exploited in gas-phase absorption measurements in order to extract the structure of biologically relevant molecules such as peptides. The gas-phase environment provides measurements free from neighboring particle contributions. An often used method in this environment is action spectroscopy where, due to the low density of the sample which gives a low absorption, the effect of the absorption on some other process is measured. One such technique is THz-UV ion-dip spectroscopy where a UV pulse is tuned to an intermediate state and ionizes the molecule via a two-photon ionization process as illustrated by the blue arrows in Fig. 3.12a. When the THz radiation (red arrows in Fig. 3.12a), which is scanned with respect to its frequency, resonates with a vibrational transition, it depletes the ground state and thus prohibits ionization by the UV light. Consequently an ion dip is created in the THz spectrum. From calculated THz spectra adjusted to match the experimental ones the structure of e.g. a peptide (Fig. 3.12b) can be obtained [68]. In particular THz spectroscopy may serve in recognition of molecular conformers.

Figure 3.12. a) Illustration of the principle of THz-UV ion-dip spectroscopy [69]. b) Extracted structure of the peptide Ac-Phe-Ala-NH2 [68].

Another common technique of IR action spectroscopy is IR multi-photon dissociation (MPD). The MPD action spectroscopy is used to record IR spectra for anions and cations. Although this method is mostly used for IR and mid-IR spectroscopies, it can also be extended to the THz

a) b)

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wavelength range. In such a technique, molecular ions are produced with an electro-spray ionization source which are then mass selected and stored in a trap, where they are irradiated with an intense THz beam. If the wavelength of the THz light corresponds to excitation of a THz vibrational mode, the molecule resonantly absorbs many THz photons which induces molecular fragmentation. By monitoring the production of fragments, for example with a mass spectrometer, versus THz wavelength, the THz absorption spectrum is measured.

3.8.3 Biochemistry

Two light-harvesting mechanisms are responsible for life on Earth, photochemical reaction centers and retinal-activated proton pumps (rhodopsins), and are the subject of numerous unceasing studies [70,71]. Bacteriorhodopsin is a protein that acts as a light-driven proton pump, which captures green light and uses it to move protons across the membrane out of the cell. During this process the protein undergoes a cycle of configurational changes and the resulting proton gradient is subsequently converted into chemical energy. A recent study [70] suggests that the proton pumping mechanism of the bacterial rhodopsin family is a major pathway for harvesting the energy of sunlight within the marine environment. Another recent experimental observation [72] showed that light driven charge phenomena in bacteriorhodopsins are accompanied by emission of THz radiation in the range from 0.1 to 3 THz during the initial structural transformations. This new insight into the ultra-fast phenomena in bacteriorhodopsins introduces the question whether the performance of proteins harvesting the energy of sunlight can be directly controlled or possibly enhanced by external THz radiation. Such a study will require ultra-broadband THz pulses in the range from 0.1 to 5 THz.

3.9 Medicine

THz radiation has great potential for imaging applications in medicine [73,74] but is still at the early stages of development. It has the attractive property of being non-ionizing and therefore less harmful to biological tissue compared with X-rays. Furthermore, the strong absorption of the THz waves in water provides an efficient contrast mechanism for substances of different water content. This can be exploited for detection of tumours which contain higher levels of water than its surrounding. The high absorption in water also limits the penetration depth of THz radiation in tissue and therefore most development has so far targeted surficial treatment and diagnosis, and for water free tissue, such as teeth. Examples of THz imaging applications with high potential for clinical use are detection of skin [75-77] and breast cancer [57], and dental caries [78,79]. Skin cancer detection has been demonstrated using THz pulsed imaging (TPI) [80,81] in reflection mode (see Fig. 3.13) and the studies [82] suggest that the technique could be used to determine affected regions non-invasively. For breast cancer TPI has been shown to provide useful information about the margins of healthy tissue surrounding the removed tumour [83]. In addition to such ex vivo studies, in vivo measurements [57] employing THz transmission imaging have been performed on mice and have successfully detected cancer volumes as small as 0.02 mm3. Here cancer cells were injected into the mouse together with fatty tissue in order to simulate the human conditions.

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Figure 3.13. THz reflection image of skin cancer using TPI. [82]

Many other more developed medical imaging methods exist such as magnetic resonance imaging or techniques using optical, IR, or X-ray wavelengths. However, the high sensitivity to water and the fact that the first few hundred micrometers of depth are difficult to image with other methods motivate further development of THz imaging. Hydration sensing is central to the development of future THz medical imaging techniques [84], but in order to fully exploit the opportunities provided by the THz frequency range it is necessary to obtain a fundamental understanding of THz-living matter interaction. For example, water consists of the ortho and para isomer for which the spin states of the hydrogen nuclei differ. It has been found that the two components have different absorption properties. Specifically it was observed in ref. [85] that the absorption strength of para transitions increases with water humidity while that of ortho transitions increases and then decreases above a specific humidity level. Since the ortho to para water ratio is 3:1 for the human body its absorption properties may be more complicated than presumed. Generally there is a need for a better understanding of tissue scattering and absorption and here THz studies of thin models will be of great help. A suitable technique for further investigations of scattering and absorption characteristics of tissue and water is time-domain spectroscopy using broad-band THz pulses.

3.10 Conclusions from science case The scientific examples presented above reveal the demand for a flexible THz source which can

match the broad range of requested THz-radiation parameters. The desired THz-output characteristics for studies of a few particularly important topics are summarized below.

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Investigations using THz radiation is expected to strongly drive the understanding of superconductivity forward. This is because the THz frequency range is suitable for excitation of lattice vibrational and plasma modes which appear to lead to the formation of superconductive states, and can be used for detection of these states.

Desired THz-radiation parameters, superconductivity: - Narrow-band (1%) pulses, tunable between 0-15 THz for exciting phonons and plasmons. - Broad band (>100%) pulses stretching between 0-15 THz with high average power (~1 W).

The average power is a limiting factor for other broad-band THz sources that may also reach frequencies above 5 THz, such as the plasma-based THz source. Measurements of superconductivity high above Tc would benefit from the increased signal-to-noise using high average power broad-band pulses [13].

- 1-10 kHz repetition rate for pump-probe experiments (THz, IR pump - IR, THz probe). THz pulses provide a tool for direct manipulation of magnetism which is crucial for the

development of high speed data processing and data storage devices. It presents a distinct advantage compared with the previously utilized optical pulses, where magnetism is indirectly controlled via the excitation of a non-equilibrium distribution of electrons and phonons. Specifically this may help to satisfy the need for a reduced temperature in data processing applications.

Desired THz-radiation parameters, magnetism: - High-field (3 GV/m = 10 T) half-cycle THz pulses for B-field induced magnetic switching. - High-field (1 GV/m) single- or multi-cycle THz pulses for E-field induced magnetic

switching. - 1-10 kHz repetition rate for pump-probe experiments (THz pump – optical probe). The importance and technological promise of Dirac materials was highlighted by the discovery

of Graphene and Topological insulators. They possess exceptional electronic properties, such as low scattering, which can be exploited for novel low-energy electronic applications. This development will strongly benefit from studies with low-energy photons in the THz frequency range.

Desired THz-radiation parameters, Dirac materials: - Circular polarization for THz bandgap control in graphene. - Single- and multi-cycle intense THz pump pulses tunable between 0-15 THz combined with

broad-band probe pulses. This could be utilized in THz pump – THz probe experiments investigating the control of topological surface states via lattice manipulation by intense THz pulses.

- 1-10 kHz repetition rate for pump-probe experiments (THz pump – THz probe).

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Using THz pulses with peak electric fields on the order of 1 GV/m, which corresponds to the Coulomb force between the electron and nuclei, one may start pulling in a molecule attached to a surface. Intense half-cycle THz-pulses allows for direct control of the surface chemistry by manipulating the motion of the adsorbed molecules through the polarization of the THz wave.

Desired THz-radiation parameters, surface chemistry: - High-field (1 GV/m) half-cycle THz-pulses of linear polarization. - Tunable half-cycle (and multi-cycle) pulses between 0-15 THz resonant with vibrational

modes. - 1-10 kHz repetition rate for pump-probe experiments (THz pump - optical probe). Research on biological systems requires THz radiation of different character. For example, the

biological effects of THz exposure need to be thoroughly investigated within a broad parameter range, especially considering the increasing use of THz radiation in society. Furthermore, the sensitivity of THz waves to collective motions of large molecules can be utilized to extract the structure of biological molecules and to study dynamics of proteins.

Desired THz-radiation parameters, biology: - Average intensity >1 mW/cm2, frequencies >0.01 THz for investigations of biological effects

of THz exposure. - >1 W average power, 1% band width for action spectroscopy of biomolecules in the gas-

phase. - Pump-probe (Optical, THz pump - THz probe) at 1-10 kHz for e.g. induced protein folding

[86] and studies of collective modes in proteins. The X-ray source, which is foreseen as an option in the design, could also be utilized in many of

the above experiments.

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4. Conceptual Design 4.1 Layout of the baseline design

The key part of the design, shown schematically in Fig. 4.1, is two THz sources that can deliver either GV/m quasi-half-cycle or intense narrowband THz pulses. The first source (source 1) makes use of the recently proposed Tanaka scheme [87] for generation of isolated monocycle radiation from a tapered undulator. Tanaka’s scheme was originally proposed for the generation of attosecond X-ray pulses, so in our design it is properly modified for the generation of THz pulses. The basic idea is that a train of electron microbunches emits a train of broadband THz pulses in the tapered undulator, and by a proper choice of the profile of the microbunches one can obtain a wavepacket that has constructive interference of individual pulses at its center whereas at the tails the pulses are cancelled out by destructive interference. The resulting wavepacket can be as short as one cycle with a field strength of GV/m and even more with focusing. A great advantage of such a source over a CTR source is its linear polarization of the field.

The narrowband THz pulses are generated in a regular undulator (source 2a) by a pre-bunched electron beam, whose period of modulation is equal to that of the undulator radiation. Provided that microbunches are sufficiently short, intense coherent spontaneous radiation (often referred to as superradiant) is emitted by each microbunch and the total emitted energy is proportional to the beam charge squared which can be as high as a nC. In such a configuration, there is no need to compress the whole beam to 100 fs scale, which removes constrains on the beam charge pertinent to other facilities using a non-modulated beam. The pre-bunched beam is formed in an RF gun by making use of a train of laser pulses to extract electrons from a photo-cathode.

The regular undulator is followed by a single-period undulator (source 2b) that produces a broadband THz probe in the form of a train of single-cycle pulses, which permits stroboscopic measurements. The narrowband pump and broadband probe are naturally synchronized since they are produced by the same beam. The delay between the pump and probe can be adjusted by the path length travelled by the narrowband pulse.

Figure 4.1. Layout of the THz light source.

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Apart from the pump-probe capabilities of the THz sources, we will also provide users with a powerful optical pump and tunable IR/optical probe. To this end, a combination of a pump laser and an optical parametric amplifier (OPA) will be used. Part of the pump laser pulse will be split out in order to drive the photocathode.

Some applications require an X-ray source for time-resolved diffraction studies. Such a source is not part of the baseline design but can be installed on the users’ request. One of the optimal options for generation of narrowband X-ray radiation is the Compton scattering of laser pulses on electron bunches. The collision of electrons in the energy range from 10 to 20 MeV with a 1 µm laser pulse will result in X-ray scattered photons in the range from 2 to 8 keV (2-7 Å). Upon collision of a train of 50 fs, 100 pC electron bunches with 200 fs, 1 mJ laser pulses, around 5*103 photons will be produced per bunch per shot, with the total number of photons of around 106 per second into 0.1% bandwidth. This is comparable to the synchrotron slicing source with its 105-107 photons per second into 0.1% BW. After the Compton source, electron bunches are sent to one of the THz sources described above.

4.2 The accelerator

The THz light source will be based on a superconducting linear accelerator (linac) to provide a CW mode of operation with a repetition rate from 1 up to 100 kHz with evenly spaced pulses. The spoke cavities are a good choice for such a linac with their small wakefields due to large apertures, weak cavity sensitivity to microphonics and highly efficient solid-state RF sources at low frequencies to drive the cavities. We expect the cavities to be operated at 10 MV/m giving more than 20 MeV energy gain from two cavities. It should be noted that the operation of beta 0.5 spoke cavities at a gradient of 13 MV/m was recently demonstrated at the FREIA laboratory.

The electron gun is the most crucial component of the linac and currently we are considering two options: a low-frequency normal conducting photocathode gun similar to the APEX gun developed for LCLS-II and a superconducting (SC) photocathode gun. The latter gives higher accelerating gradient so that bunches with more charge can be delivered, however, at higher expense and complication in operation. In order to generate a pre-bunched electron beam for further generation of superradiant THz pulses, a train of 200 fs laser pulses with a period of 0.5-1 ps will illuminate the photocathode to drive electrons out of it. Each laser pulse will result in a 100 pC electron bunch with 12-15 bunches in total. The electron beam will have an energy of around 0.5 MeV and 1 µm emittance.

After the gun, the beam enters an emittance compensation line in the form of a drift with properly profiled magnetic field followed by two superconducting cavities, and a bunch compressor. The compression factor is around 5 and 20 MeV electron bunches will be just 50 fs long with 100-200 fs separation. Then, the beam is directed to the Compton source or one of the THz sources.

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4.3 Generation of ultra-broadband GV/m THz pulses

Presently, ultra-short THz pulses are mainly generated via optical rectification of a short intense optical pulse (10-100 fs) that drives a nonlinear polarization through the second order nonlinear susceptibility in crystals such as LiNbO3 or DSTMS. The current record for the generated energy is around 1 mJ [88] but the radiation spectrum is limited to 5 THz and only one pulse per second can be produced. The repetition rate of 1 kHz requires a 30 kW pump laser, which is beyond the state-of-the-art by two orders of magnitude. Moreover there are problems with cooling the crystal. Broadband THz radiation is also available through two-color laser mixing in air plasma. However, the emitted energy is limited to several nJ with a low conversion efficiency of 10-4 from optical to THz energy, and the repetition rate is only up to a kHz [89]. Yet another method for generation of high-energy THz pulses is transition radiation from high-energy charged particles traversing a metallic foil. This method allows generating by far the most intense THz pulses with electric field strength up to 1 GV/m (atomic fields!) that exceeds at least by one order of magnitude all other sources. However, this method can be applied only at large accelerating facilities since it requires multi-GeV electron bunches of a few nC charge. Currently, the only source of that kind producing 1 GV/m THz pulses is available at the FACET facility of SLAC and makes use of the SLAC copper linac to accelerate 2.5 nC bunches to 23 GeV [90]. The repetition rate is limited to around 100 Hz. In order to overcome the deficiency of low conversion rate of the electron beam energy into radiated energy of transition radiation, a multifoil cone radiator [91] was suggested with the promise to boost the emitted energy by one order of magnitude or more. However, the repetition rate is estimated to be limited to a kHz because of heat load on the radiator. None of the conventional methods meets the objective set by the users’ demand. Therefore, in the baseline design we will use a modified version of the recently proposed Tanaka’s method [87] for generation of an isolated monocycle radiation with a tapered undulator.

Tanaka’s idea is as follows: consider a tapered undulator such that the period of the EM pulse emitted by a test electron traversing the undulator monotonically changes along the pulse, i.e. the pulse is frequency-chirped. Suppose we generated a pre-bunched electron beam whose period changes in the same way as that of the EM pulse. Then, the combined pulse is a wavepacket composed of identical wavefronts shifted by one period with respect to each other and interfering constructively at the center of the wavepacket and destructively at the tails, see the illustration of the idea in Fig. 4.2. It is shown in [87] that the resulting field, which is the convolution of the field emitted by one electron and the current density, is 𝐸𝐸(𝑡𝑡) = 𝑏𝑏𝑛𝑛0𝐸𝐸0 ℱ−1[|𝑓𝑓𝜔𝜔|2], where ℱ−1 stands for the inverse Fourier transform, 𝑓𝑓𝜔𝜔 is the Fourier transform of the temporal profile 𝑓𝑓(𝑡𝑡) of the EM pulse of magnitude 𝐸𝐸0 emitted by a test electron; 𝑏𝑏 and 𝑛𝑛0 are the bunching factor and average electron density, respectively. By employing an undulator with a large taper amplitude one can obtain broadband undulator emission and, therefore, short pulses from a pre-bunched electron beam.

In order to form the required pre-bunched beam, Tanaka suggested using a modulator-undulator

that is an undulator identical to the one used for generation of broadband radiation but with reversed tapering. In the original scheme a seed is provided by an external laser but at THz frequencies it is more efficient to use a seed electron bunch that follows the main bunch and is sufficiently short to generate coherent spontaneous radiation in the modulator, which is further downstream used to imprint the required temporal modulation to the main bunch. One more option of forming the pre-

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bunched beam is via direct laser shaping of the beam at a cathode. It has great potential and will be given further careful consideration.

Figure 4.2. To the explanation of the generation of isolated monocycle radiation (adopted from [87]).

Figure 4.3. Modified configuration of Tanaka’s scheme.

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4.4 Source 1: broadband THz pump

In order to generate quasi-half-cycle pulses as depicted in Fig. 4.4, the spectral distribution of the undulator radiation must match that of the quasi-half-cycle pulse. A test electron traversing an undulator with a varying field envelope 𝑓𝑓𝑢𝑢(𝑧𝑧) emits a frequency chirped pulse, whose spectral distribution is determined by the profile of 𝑓𝑓𝑢𝑢(𝑧𝑧). An analysis shows that the required profile of 𝑓𝑓𝑢𝑢(𝑧𝑧) is given by

𝒦𝒦𝑓𝑓𝑢𝑢(𝑧𝑧) = 10.8 �𝜁𝜁𝑧𝑧𝐿𝐿𝑢𝑢�3

+ 10 �𝜁𝜁𝑧𝑧𝐿𝐿𝑢𝑢�2

+ 4.8 �𝜁𝜁𝑧𝑧𝐿𝐿𝑢𝑢�, (1)

where 𝒦𝒦 is the conventional undulator parameter and the parameter 𝜁𝜁 is equal to 0.65. In numerical simulations 𝜁𝜁 can be adjusted to improve the spectral distribution and we found that the optimum value of 𝜁𝜁 is 0.7.

In order to check how efficient the obtained optimal profile is, we developed a quasi-1D self-consistent simulation code that solves the equations of charged slices and calculates the field from the 1D wave equation. First, we applied the code to the case of a short bunch traversing a linearly tapered undulator. The results are very close to those obtained by Tanaka [87] and are depicted in Fig. 4.5 by dotted black curves. The main parameters are summarized in Table II. The spectrum of emission from such an undulator is quite broad but not uniform and the field resulting from the superposition of waves emitted by an ideally pre-bunched beam is roughly 2 cycles long with long oscillating tails. In the first order approximation, the total field produced by a train of bunches is the superposition of wavefronts of individual bunches; hence, the simulation results for one bunch are used to find the resulting wavepacket assuming properly positioned bunches.

The use of the optimal tapering found analytically and represented by the solid blue curve in Fig. 4.5 makes the spectrum more Gaussian-like and reduces the number of cycles to 1.5 while simultaneously reducing ringing, see the middle and bottom plots in Fig. 4.5. The peak electric field of the combined pulse produced by a train of 15 bunches is a bit more than 1 GV/m and the emitted energy is around 3 mJ.

Figure 4.4. The temporal profile and spectrum of ideal quasi-half-cycle pulses.

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Figure 4.5. The results of 1D simulations. From the top to bottom: profile (envelope) of the undulator field; spectrum; the combined electric field as a function of time. The solid blue curves stand for an optimally tapered undulator whereas the dotted black curves are for a linearly tapered undulator.

Being convinced by the results of the 1D self-consistent simulation that the relative motion of charged slices caused by the radiation field is negligible and has no impact on the field itself, we developed a 3D simulation code that solves directly the 3D wave equation with a source in the form of a collection of charged slices whose shape and dynamics are governed by external magnetic fields. The results of 3D simulations are illustrated in Fig. 4.6. The on-axis electric field calculated with the help of the 3D model at the end of the optimally tapered undulator is almost identical to the field calculated within the 1D model despite quite strong diffraction. However, at a distance of 1 meter away from the undulator, the field profile is changed significantly by diffraction and the combined field from a perfectly pre-bunched beam is not a quasi-half-cycle pulse since the undulator profile was optimized for the desired pulse shape at the end of undulator. Further optimization is needed to ensure the required field profile at a detector.

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Table II: Main parameters of single-bunch broadband emission.

Parameter Symbol Value Units

bunch charge 𝑄𝑄𝑏𝑏 100 pC bunch duration 𝜎𝜎𝜏𝜏 50 fs bunch radius 𝑟𝑟𝑏𝑏 1 mm bunch energy 𝑈𝑈𝑏𝑏 20 MeV undulator period 𝜎𝜎𝑢𝑢 6 cm number of periods 𝑁𝑁𝑢𝑢 15 undulator parameter 𝒦𝒦 2 peak electric field 𝐸𝐸peak 80 MV/m

linear taper emitted energy ℰ𝑟𝑟 26 µJ central frequency 𝑓𝑓 𝑐𝑐 7.25 THz relative bandwidth Δω/ω 95%

optimal taper emitted energy ℰ𝑟𝑟 25 µJ central frequency 𝑓𝑓 𝑐𝑐 9 THz relative bandwidth Δω/ω 105%

Figure 4.6. The results of 3D simulations at the output of the optimally-profiled undulator. The left plot shows the electric field produced by a single microbunch as a function of time and normalized radial distance. Although the diffraction effect is strong, the combined pulse produced by a train of bunches preserves its quasi-half-cycle shape very well as it is depicted in the right plot.

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4.5 Source 2a: narrowband THz pump

Narrowband radiation needed as a pump pulse can be obtained by using a regular undulator and a pre-bunched electron beam. The spectrum calculated with the 3D code is depicted in Fig. 4.7. As an example, we considered a 15-period undulator with the parameters summarized in the Table III. The spectrum is shown at the end of the undulator. The peak electric field and total emitted energy from a beam composed of 15 bunches are around 0.9 GV/m and 4 mJ, respectively. Note that the total kinetic energy of the beam is 30 mJ, which implies the energy conversion of 13%. The field pattern of THz pulses can be quite well described by the fundamental optical beam with a Rayleigh length of around 45 cm.

Figure 4.7. The spectrum of radiation from a regular undulator as a function of frequency and normalized radial distance. The result is presented at the output of the undulator.

Table III: Main parameters of single-bunch emission from a regular undulator.

Parameter Symbol Value Units

bunch charge 𝑄𝑄𝑏𝑏 100 pC bunch duration 𝜎𝜎𝜏𝜏 50 fs bunch radius 𝑟𝑟𝑏𝑏 1 mm bunch energy 𝑈𝑈𝑏𝑏 20 MeV undulator period 𝜎𝜎𝑢𝑢 6 cm number of periods 𝑁𝑁𝑢𝑢 15 undulator parameter 𝒦𝒦 1 peak electric field 𝐸𝐸peak 70 MV/m emitted energy ℰ𝑟𝑟 29 µJ central frequency 𝑓𝑓 𝑐𝑐 10.52 THz relative bandwidth FWHM Δω/ω 10%

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4.6 Source 2b: broadband THz probe

There is great interest in THz pump - THz probe experiments and in order to provide users with such type of capability there will be a single-period undulator installed next to the long one described above. The short undulator will produce 1.5 cycle 100 fs pulses in the spectral range from 3.4 to 15.6 THz (FWHM) at the central frequency of 8.5 THz. The main characteristics of the bunch, short undulator and resulting radiation are given in the Table IV. It should be stressed that the bandwidth of radiation is almost 150%. The graphic illustration of the spectrum is presented in Fig. 4.8.

Figure 4.8. The spectrum of radiation from a one-period undulator as a function of frequency and normalized radial distance. The result is presented at the output of the undulator.

Table IV: Main parameters of single-bunch emission from a one-period undulator.

Parameter Symbol Value Units

bunch charge 𝑄𝑄𝑏𝑏 100 pC bunch duration 𝜎𝜎𝜏𝜏 50 fs bunch radius 𝑟𝑟𝑏𝑏 1 mm bunch energy 𝑈𝑈𝑏𝑏 20 MeV undulator period 𝜎𝜎𝑢𝑢 1.5 cm number of periods 𝑁𝑁𝑢𝑢 1 undulator parameter 𝒦𝒦 0.75 peak electric field 𝐸𝐸peak 48 MV/m emitted energy ℰ𝑟𝑟 1 µJ central frequency 𝑓𝑓 𝑐𝑐 8.53 THz relative bandwidth FWHM Δω/ω 143%

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4.7 X-ray source: optional

There is no X-ray source in the baseline design, but a narrowband emitter suitable for X-ray diffraction can be installed upon users’ request. Therefore, here we describe the parameters of the X-ray source that can be built in for studying the atomic structures of the samples in question and complementing the results obtained with THz and/or optical probing. We studied several options for the generation of narrowband X-ray radiation with as high brilliance as possible while keeping the size feasible for a small scale facility. Specifically, we looked into the generation of X-rays with channeling and parametric radiation, bremsstrahlung with filtering and Compton backscattering. The characteristics of the latter turned out to be superior and are discussed in some details below.

The scattering of 1 µm laser radiation on an electron bunch with an energy tunable from 10 to 20 MeV results in X-ray photons in the range from 1.8 to 7.5 keV, which is suitable for X-ray diffraction studies, see Fig. 4.9.

Figure 4.9. The energy of scattered photons vs electron beam energy for a pump laser with a wavelength of 1 µm. The beam-laser collision is head-on.

The total number of scattered photons and on-axis average flux into 0.1% bandwidth is [92,93]

𝑁𝑁𝑝𝑝ℎ =𝑁𝑁𝑒𝑒𝑁𝑁𝐿𝐿𝜎𝜎𝑇𝑇

2𝜋𝜋(𝜎𝜎𝐿𝐿2 + 𝜎𝜎𝑒𝑒2)𝐹𝐹𝐹𝐹, ℱ = 1.5 × 10−3𝑓𝑓𝐿𝐿𝑁𝑁𝑝𝑝ℎ. (2)

Here, 𝜎𝜎𝑇𝑇 = (8𝜋𝜋/3)𝑟𝑟𝑒𝑒2 is the Thompson scattering cross-section, other symbols are defined in Table V. The term FF is a form factor less than unity that depends on rms pulse durations of laser and electron beams, beam spot sizes at the interaction point for the laser and electron beams. It represents the degradation of the interaction efficiency for cases where the pulse durations exceed the diffraction lengths of the laser and electron beams. In what follows FF is taken as unity. A large geometric emittance of the electron bunch is the main dominant degradation factor of the spectral brilliance, so the formulas for the average and peak on-axis brilliance can be simplified to [92]

𝐵𝐵𝑎𝑎𝑎𝑎𝑒𝑒𝑟𝑟 =ℱ 𝛾𝛾2

4𝜋𝜋𝜖𝜖𝑛𝑛2, 𝐵𝐵𝑝𝑝𝑒𝑒𝑎𝑎𝑝𝑝 =

ℱ 𝛾𝛾2

4𝜋𝜋𝜖𝜖𝑛𝑛21𝜏𝜏𝑏𝑏𝑓𝑓𝐿𝐿

.

(3)

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Table V: Parameters of the Compton backscattering source.

Parameter Symbol Value Units

bunch charge 𝑄𝑄𝑏𝑏 100 pC number of electrons 𝑁𝑁𝑒𝑒 6.24 10

8 bunch duration 𝜏𝜏𝑏𝑏 100 fs e-bunch emittance 𝜖𝜖𝑛𝑛 2 mm mrad rms e-bunch size 𝜎𝜎𝑒𝑒 60 µm geometrical beta-function 𝛽𝛽𝑔𝑔 3.5 cm laser wavelength 𝜆𝜆𝐿𝐿 1 µm rms laser beam size 𝜎𝜎𝐿𝐿 57 µm Rayleigh length 𝑧𝑧𝑅𝑅 1 cm laser pulse energy ℰ𝐿𝐿 1 mJ laser rep. rate 𝑓𝑓𝐿𝐿 5 kHz average power of the laser 6 W number of scattered photons at all angles/per shot

𝑁𝑁𝑝𝑝ℎ 5 103

total number of photons per second

2.5 107

peak brilliance 𝐵𝐵𝑝𝑝 3.6 1014 ph/s/mm2/mrad2/0.1%BW

average brilliance 𝐵𝐵𝑎𝑎𝑎𝑎 3.6 105 ph/s/mm2/mrad2/0.1%BW

For estimates we use the parameters of an off-the-shelf laser called PHAROS [94]. It is quite suitable as a pump for the Compton source. The minimum pulse duration is 190 fs, which is a bit too long for pump-probe experiments but good enough for estimates. The dependence of the pulse energy on the repetition rate for this laser is given in Fig. 4.10. The detailed quantitative description can be found in the Table VI. It is interesting to note that several laser systems can be combined to deliver up to 60 W of average power.

Figure 4.10. Pulse energy vs. repetition rate for the commercial lasers from ‘Light Conversion.’

38

Table VI: Parameters of the PHAROS lasers

The basic sources of energy spread in scattered photons are energy spread in an electron bunch, laser bandwidth and divergence of the laser and electron beams at the collision point. For a head-on collision, the total energy spread reads [95]

(4)

Here, Δ𝛾𝛾 is the bunch energy spread, Δ𝜔𝜔 is the laser bandwidth, Δ𝜉𝜉 is the angular divergence of a laser or electron beam. Let us estimate each term one by one. The relative laser bandwidth can be re-written as Δ𝜔𝜔/𝜔𝜔 = 𝜆𝜆/𝜋𝜋𝑙𝑙𝐿𝐿 and for the PHAROS laser is 0.0056.

The maximum energy spread of the electron is planned to be limited to 1%, so it will give 2% of energy spread of photons. The divergence of a laser beam is Δ𝜉𝜉 = 𝜆𝜆/𝜋𝜋𝑤𝑤0, where 𝑤𝑤0 = 2𝜎𝜎𝐿𝐿 is the laser spot size at the waist, and for the parameters above Δ𝜉𝜉 = 0.0028. The divergence of an electron beam is Δ𝜉𝜉 = 2𝜖𝜖/𝜎𝜎, where 𝜖𝜖 is the geometric emittance and 𝜎𝜎 is the beam size at the waist. For a 10 MeV e-bunch, the bunch divergence is 0.0067.

Plugging all the numbers into (4) gives the total energy spread of scattered photons of 2.1%. Therefore, the total number of photons scattered per second into 0.1% BW is 1.2*106.

39

One should keep in mind that there is a need for an optical laser for optical pump – THz probe experiments, and it is also advantageous to have an optical parametric amplifier (OPA) so one can cover some frequency range. The tuning range of the possible OPA is shown in Fig. 4.11, and it uses the same PHAROS laser mentioned above. Thus, the same laser can be used as a pump for the Compton source and OPA.

Figure 4.11. An example of the tuning curve of an OPA.

4.8 Conclusion

The THz Coherent Light Source in Uppsala is a novel coherent THz light emitter delivering quasi-half-cycle or multi-cycle THz pulses with a field strength in the V/Å range at a multi-kilohertz repetition rate. The proposed THz light source is flexible and has a number of unique features:

• with respect to other accelerator-based THz light sources, it will be the first machine designed specifically for pump-probe experiments;

• the broadband THz source will cover the range from 5 to 15 THz where laser-based THz sources fail to work;

• the THz source will generate quasi-half-cycle pulses with field strength and repetition rate that are far beyond any existing or planned source.

40

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http://www.lightcon.com/products/product.php?ID=28

Figure 3.7. Energy dispersion of a) a typical 2D semiconductor and b) that of graphene with its cone-type band structure. [24]3.4.1 Graphene