T-REX (Terahertz Radiation EXperiment):
Coherently controlled THz generation
Sandwiched between the optical and microwave regimes, the far infrared or terahertz (1 THz = 1012 Hz) frequency range has recently drawn special attention due to its ubiquitous nature and board applications (see Fig. 1). The physics of THz generation is also compelling, raising fundamental questions about the interaction of strong electromagnetic fields with atoms and molecules. THz radiation (or T-rays) can easily pass through non-polar materials such as clothing, paper, plastics, wood and ceramics. This property allows many applications in molecular sensing, biomedical imaging and spectroscopy, security scanners, and plasma diagnostics. In particular, THz spectroscopy holds great promise for molecular sensing. Recent work on stem cells shows that T-rays have potential for controlling cellular gene expression.
These applications provide strong motivation to advance the state of the art in THz source development. In particular, high-energy THz generation is vital for application in nonlinear THz optics and spectroscopy. Currently, intense THz radiation pulses exceeding tens of micro-Joules can be obtained from large accelerator facilities such as linear accelerators, synchrotrons, and free electron lasers. However, due to the large cost of building and operating those facilities and limited access, there is a present and growing demand for high-energy, compact THz sources at a tabletop scale.
One approach is to use tabletop ultrafast lasers to produce coherent THz radiation via plasma generation in gases, but the physics of the process is not fully understood and requires detailed understanding of strong field ionization processes in atoms and molecules, especially in the nonperturbative regime. In essence, one must understand the evolution of laser-driven electron wavepackets in a strong electric field and their transition from atomic to plasma states. The generation mechanism also requires a full understanding of collective plasma behaviors and coherent radiation processes at high laser intensities. In addition, there are practical issues to address—Can one control and optimize the process to make compact high-power THz sources? What are the limits on generating and detecting ultra-broadband THz radiation? What interesting nonlinear processes can be driven by powerful THz sources?
Two-color laser mixing (or photoionization) has been widely used as a versatile tool for intense, broadband terahertz (THz) radiation generation [1-11]. In this scheme, an ultrafast pulsed laser’s fundamental and second harmonic fields are mixed in a gas of atoms or molecules, causing them to ionize (see Fig. 2). This phenomenon was first observed by D. J. Cook and R. Hochstrasser at University of Pennsylvania in 2000. Since then, many experiments had followed up for several years without a basic understanding of the process. A four-wave mixing theory was initially proposed to explain the mechanism, but it did not provide any microscopic origin of such nonlinearity. Later Kim et al., proposed a plasma current model to explain the mechanism of THz generation .
In the plasma current model, the laser fields act to suppress the atom’s or molecule’s Coulomb potential barrier, and, via rapid tunneling ionization, bound electrons are freed. The electrons, once liberated, oscillate at the laser frequencies, and also drift away from their parent ions at velocities determined by the laser field amplitudes and the relative phase between the two laser fields. Depending on the relative phase, symmetry can be broken to produce a net directional electron current. As this current occurs on the timescale of photoionization, for sub-picosecond lasers, it can generate electromagnetic radiation at THz frequencies [10-12].
This THz generation mechanism turns out to be closely related to the mechanism used to explain high harmonic generation (HHG) in gases, as both processes originate from a common source, that is, a nonlinear electron current. The electrons re-colliding with the parent ions are responsible for HHG, whereas the electrons drifting away from the ions without experiencing re-scattering ions mostly account for THz generation. As demonstrated experimentally , the generated THz and third-harmonic are strongly correlated in such a way that changing the relative phase can effectively switch the emission between THz and harmonics. This provides the basis to coherently control electromagnetic radiation in a broad spectral range, from THz to extreme ultraviolet. We also demonstrated a high-energy (>5 microjoule), super-broadband (>75 THz), tabletop THz source via ultrafast photoionization in gases .
Recently, we have reported macroscopic phase-matching in THz generation (see Fig. 3), which is crucial for efficient frequency conversion . In addition, we have reported two-dimensional plasma currents for optimal THz generation , mechanisms of elliptically polarized THz generation , THz generation in aligned molecule , and THz energy scaling and saturation in extended filamentation . We have recently designed and developed a kHz cryogenically-cooled laser amplifier  for various applications including electron acceleration in collaboration with H. M. Milchberg's group. This laser has been also applied to produce strong THz fields exceeding 8 MV/cm at a 1 kHz repetition rate, along with real-time THz beam profiling .
 K. Y. Kim et al., Opt. Express 15, 4577 (2007).
 K. Y. Kim et al., Nature Photon. 2, 605 (2008).
 K. Y. Kim, Phys. Plasmas 16, 056706 (2009).
 K. Y. Kim et al., IEEE J. Quantum Electron. 48, 797 (2012).
 T. I. Oh et al., Opt. Express 20, 19778 (2012).
 Y. S. You et al., Phys. Rev. Lett. 109, 183902 (2012).
 Y. S. You et al., Opt. Lett. 38, 1034 (2013).
 Y. S. You et al., Phys. Rev. A 87, 035401 (2013).
 T. I. Oh et al., Appl. Phys. Lett. 102, 201113 (2013).
 T. I. Oh et al., New J. Phys. 15, 075002 (2013).
 T. I. Oh et al., Appl. Phys. Lett. 105, 041103 (2014).
The detection of coherent THz pulses is of great importance in THz time domain spectroscopy for material characterization, biomedical imaging, and coherent control. Accurate temporal characterization of THz fields is required in such applications, with electro-optic (EO) sampling and fast photoconductive switching being two widely applied techniques for THz field measurements. In these techniques, the optical-THz pulse delay is successively varied with respect to the optical probe, mapping out the complete THz waveform from a series of time-delayed snapshots. However, measurement of the THz field using a scanned probe often takes from minutes to hours, depending on the THz source power, repetition rate, desired scan step, and field of view. Furthermore, if irreversible processes such as material damage, chemical reactions, or structural phase transformations are being investigated, multi-shot schemes cannot often be used, since these measurements benefit most from a single-shot technique. Single-shot THz detection can be also used to monitor relativistic ultrashort electron bunch profiles in real time. Such demands have inspired the development of various ultrafast single-shot THz diagnostic methodologies.
One single-shot THz diagnostic, previously demonstrated by Jiang et al., adopts a temporally chirped optical probe pulse to map out the entire THz field in a single shot. In this scheme, each temporal slice of the THz field is projected onto a different frequency component of the chirped pulse, allowing the entire THz field to be reconstructed from a direct mapping of frequency to time. While this so-called spectral encoding technique has been applied to many experiments, it has also been shown that the temporal resolution is ultimately limited by the extent of the chirp applied to the probe pulse. However, we recently proposed and demonstrated a novel THz retrieval algorithm which can significantly enhance the temporal resolution of the spectral encoding technique . In fact, with the technique, the temporal resolution is ideally limited only by the spectral bandwidth of the chirped probe pulse.
Another THz diagnostic developed is two-dimensional electro-optic imaging with dual echelons . An echelon itself consists of a right-angle prism with a stepwise structure on the hypotenuse surface which can split an incoming single laser pulse into incrementally time-delayed multiple small beamlets, either thru transmission or reflection. With the addition of a second orthogonally-oriented echelon whose single step size matches the overall step height of the first echelon.
 K. Y. Kim et al, Appl. Phys. Lett. 88, 041123 (2006).
 K. Y. Kim et al., Opt. Lett. 32, 1968 (2007).
LUX (Laser-driven Ultrafast X-rays):
Femtosecond (10-15 s) to attosecond (10-18 s) x-ray generation is of great current interest owing to its potential to study ultrafast dynamics at the atomic and molecular level. Femtosecond x-rays can image atomic structure and dynamics of materials undergoing chemical/biochemical reactions with extremely short time resolution. On even shorter timescales, attosecond x-rays can provide unprecedented precision in studying atomic inner-shell dynamics. These ultrafast x-rays can be used for applications in time-resolved x-ray diffraction and absorption spectroscopy, ultrafast x-ray interactions with matter, and attosecond science. Currently, intense femtosecond/picosecond (10-12 s) x-ray pulses can be obtained from large accelerator facilities such as synchrotrons and free electron lasers (FELs). In particular, x-ray FELs can produce ultra-bright femtosecond x-ray pulses with several orders of magnitude higher flux. In parallel, there is a strong interest in generating such intense x-rays on a tabletop setting. In this direction, high-intensity, tabletop femtosecond lasers continue to receive considerable attention due to their capability of producing ultrafast x-rays via various frequency up conversion techniques.
One method is relying on high harmonic generation (HHG) in gases. This process, however, exhibits an extremely poor soft X-ray (<keV) conversion efficiency (10-8 ~ 10-5). Moreover, due to its subtle nature of HHG, such scheme is not scalable with laser energy. One emerging approach to dramatically increase the conversion efficiency is relying on HHG from overdense solid plasmas, including nanostructured solid targets. One of our research efforts will be directed to seek such scheme to produce high-flux, ultrafast x-ray pulses. With these sources, we can excite and probe inner-shell electron dynamics with unprecedented spatio-temporal resolution. Moreover, femtosecond x-ray source can be used to study time-resolved dynamics of shock waves and structural phase transitions, as well as warm dense plasmas.
Warm Dense Matter (WDM):
Upon heating, metals typically exhibit decreasing electrical conductivity due to enhanced electron-phonon scattering. However, if heated far beyond melting, it places the metal into a low-density hot plasma state where the conductivity then increases with temperature due to its lowered Coulomb collision rate between the electrons and ions. In between these two extremes, where the conductivity slope changes sign, a state of warm (0.1~10 eV) and dense (0.1~10 times the solid density) matter exists, which can be created in intense laser-produced laboratory plasmas, and is also thought to exist in a variety of extreme natural environments including brown dwarfs and the interiors of giant gaseous planets like Jupiter. In this so-called warm dense matter (WDM) regime, the ion-ion interaction is strongly correlated and the electrons are degenerate. Lying between a solid state and an ideal plasma state, WDM is considered too dense to be depicted by classical plasma theory and too hot to be described by solid-state physics. Due to this complexity, it is generally difficult to determine the equation of state (EOS) for WDM. Thus, it is extremely useful if one can characterize WDM through measurements of its transport properties such as electrical and thermal conductivities.
Previous studies of electrical conductivities have been performed by employing electrically exploding wires or foils and measuring the current and voltage change across the formed WDM plasma, or by using optical probe reflectivity measurements from laser-heated solids. In the latter case, the measurements provide the AC electrical conductivity because the probe is at optical frequencies. However, since knowledge of the DC component is actually desired, the DC electrical conductivity is obtained by applying a free-electron Drude mode. To further complicate matters, recent theoretical models predict non-Drude behavior for WDM at low frequencies even for relatively simple metals such as aluminum, making the general applicability of a Drude model based analysis questionable.
To address this issue, we have applied ultrafast terahertz (THz) spectroscopic techniques to directly measure the quasi-DC electrical conductivity , which in principle, does not require any extrapolation based upon a Drude model. In addition, by using a broadband THz electromagnetic probe pulse approach, we are able, for the first time, to critically evaluate the validity of a Drude model analysis for WDM at low (THz) frequencies . This THz spectroscopic method can be a powerful quantitative characterization tool applicable to a variety of WDM creation methods, including x-ray heating, thin foil explosion, and ion beam heating to create a single-state WDM necessary for EOS characterization.
 Kim et al., Phys. Rev. Lett. 100, 135002 (2008).