The acceleration of charged particles with ultrafast terahertz electromagnetic radiation could enable new, and improve many of aspects of, accelerator applications. These include providing shorter electron bunches for ultrafast time-resolved pump-probe spectroscopy, enabling complex longitudinal profiles to be imparted onto charged particle bunches and significantly improving the ability to synchronise an accelerator to an external laser. In this thesis I present investigations into terahertz radiation sources that enabled the generation of terahertz radiation with attractive properties for accelerator based applications. Specific attention has been paid to temporally tunable sources that generate strong longitudinally polarised electric field components as these enable a free-space co-linear interaction geometry to be implemented. A simulation describing the propagation of radiation from such sources has been developed. Terahertz sources have been designed and the radiation generated characterised via electro optic detection. These include a radially biased photoconductive antenna (PCA) based source of which the longitudinally polarised terahertz electric field component was found to have an amplitude of 2.22 kVcm-1 as well as a near-single cycle temporal profile. This radially biased PCA was used in conjunction with the Accelerators and Lasers in Combined Experiments (ALICE) energy recovery linear accelerator at the Daresbury Laboratory in an electron acceleration experiment. To enable higher longitudinally polarised terahertz electric field strengths to be obtained, as well as the ability to temporally tune the terahertz radiation, generation within non-linear optical crystals was investigated. Magnesium-oxide doped stoichiometric lithium niobate (MgO:SLN) was investigated as a possible candidate due to its high non-linear susceptibility tensor and reported ability to impose temporal tuning directly from the pump laser beam. A scheme consisting of two MgO:SLN crystals each generating a separate linear polarised terahertz pulse which were then combined via a lens was designed and built. Electro optic detection techniques were used to characterise the radiation generated from this source. Peak terahertz electric fields amplitudes of 11.6 kVcm-1 and 47 kVcm-1 were measured for both the longitudinally and transversely polarised field components respectively. Temporal profiles measured from both the longitudinally and transversely polarised electric field components showed electric field periods of approximately 300 fs. This method of generating terahertz radiation employed a pulse-front tilt technique. Allowing for the same scaling as recently reported in the literature for MgO:SLN generation techniques, which will in principle allow this method to scale to longitudinally polarised terahertz electric field profiles in excess of 1 MVcm-1.

Terahertz (THz) spectroscopy is an emerging technology with promising applications in imaging, homeland security, and material detection and quantification. Frequencies in the THz region can be generated by optical rectification of ultrafast near-infrared laser pulses in the presence of a nonlinear optical (NLO) materials such as organic crystals. Non-centrosymmetric organic THz generating crystals such as DAST, HMQ-TMS, and OH1 have received special attention due to the strong generated fields on the order of MV/cm. The cation of these organic salts is designed by connecting electron-donating with electron-accepting groups via a highly planar aromatic system. To improve the performance of organic crystals for THz generation, the molecular hyperpolarizability (β) can be optimized by introducing modifications in the architecture of these push-pull chromophores. However, the large dipole moments associated with molecules that have a large β promote the formation of NLO inactive centrosymmetric molecular alignments in the crystal state. This dissertation provides important insights into the design of new push-pull chromophores that feature a) higher β values compared with state-of-the-art organic crystals, and b) non-centrosymmetric molecular packing in the crystalline state. The first strategy presented on this dissertation relates to the introduction of a triple bond instead of a double bond in the cation of DAST to improve the β parameter. The newly designed 4DEP core was combined with different anions to promote non-centrosymmetric molecular packing with almost ideal arrangements for THz generation. However, large single crystals were difficult to obtain and high THz generation was not achieved. The second strategy presented in this dissertation raises the value of β by extending the π-conjugation length in different cations with dimethylamino and methoxy electron-donating groups. A new molecular cation, 6MNEP, was found to have large β value combined with ideal non-centrosymmetric molecular packing. Combining these two factors, a ~ 75% higher performance for THz generation is expected for 6MNEP compared with DAST. Currently, we are testing different crystallization techniques to grow large single crystals of 6MNEP. In addition to the strategies developed to increase the β parameter value, we also introduce a new molecular modification to induce non-centrosymmetric packing in organic salt THz generating crystals. This is achieved by substituting a methyl by an ethyl group in the quaternary nitrogen of hydrogen-bonded crystals. We showed the applicability of this method for changing molecular packing in the crystal state from centrosymmetric to non-centrosymmetric in two different molecular cations. We also demonstrated the generation of strong THz fields in the novel NLO crystal EHPSI-4NBS.

Unique applications of Terahertz radiation in various fields such as biology and medical sciences, remote sensing, and chemical detection have motivated researchers to develop compact and coherent sources for this least touched region of electromagnetic spectrum. Of the many techniques for generating terahertz signals, difference- frequency generation (DFG) in various crystals is one of the mostly explored methods. Various phase matching methodologies, including phase matching in bulk crystals based on birefringence, and quasi-phase matching have been proposed for this purpose. Although GaAs has an order of magnitude higher second-order nonlinear coefficient in comparison with other crystals, it is one of the least employed crystals for DFG due to phase-matching difficulties. First, it does not provide birefringence in the bulk crystal for birefringence phase matching. Second, GaAs quasi-phase matching has been shown only in few works because patterning the nonlinear susceptibilities in semiconductors is not easily achieved. In this thesis, integration of a GaAs optical waveguide and a terahertz waveguide is proposed as a wide-band phase matching technique for DFG to generate high power coherent terahertz radiation. Using waveguides for both optical and terahertz waves allows for tailoring the phase matching and increasing the interaction length to get high conversion efficiency. Using pump wavelengths between 1.5-1.6 um, where low cost and high optical powers are available, we obtained phase matching for terahertz generation in the range of 0-3.5 THz. We exploit the differences between the GaAs dielectric constant in optical and terahertz range, a high second order nonlinear coefficient, and low terahertz absorption. Simulation results show the appropriate behavior of the proposed devices for both optical and terahertz waves. The proposed waveguide phase matching can be useful for other types of devices using similar nonlinear phenomena, such as coherent detection, electro-optic modulation, and ultra-short pulse generation.

Terahertz (THz) spectroscopy is a powerful tool that uses ultrashort pulses of light to study the properties of materials on picosecond time scales. THz light can be generated through a variety of methods. In our lab, we generate THz through the process of optical rectification in nonlinear optical (NLO) organic crystals. THz light can be used to study several phenomena in materials, such as spin precession, electron acceleration, vibrational and rotational motion. The work presented in this dissertation is divided into two parts: (1) the generation of THz light and (2) applications of THz light. The first portion of this work shows how THz light is generated, with an emphasis on the generation through optical rectification. We also show how to improve the generation of THz light by creating heterogenous multi-layer structures with yellow organic THz generation crystals. Additionally, we show that crystals used for THz generation can also be used to generate second-harmonic light. In the second half of this work, we show that THz light can be used to study the vibrational motion of molecular systems. We model how resonant vibrational modes in a fluorobenzene molecule can be excited with a multi-THz pump to transfer energy anharmonically to non-resonant modes. We also show that we can use two-dimensional (2D) THz spectroscopy to excite infrared-active vibrational modes and probe Raman-active modes in a CdWO4 crystal to obtain a nonlinear response. We show that the nonlinear response is due to anharmonic coupling between vibrational modes and we can quantify the relative strengths of these anharmonic couplings, which previously was only accessible through first-principles calculations.

Die vorliegende Dissertation behandelt Grundlagen und Anwendungen der nichtlinearen Terahertzspektrospie (THz). Diese Arbeit zeigt erstmalig, dass sich die Inversion des Quantenkaskadenlasers nach einer Störung schon innerhalb von hundert Femtosekunden wieder erholt. Außerdem wurde der exakte Generationsprozess von THz Impulsen in einem Laser-induzierten zwei-Farben Plasma untersucht. Durch Vergleich mit Simulationen wird eindeutig der Ionisationsstrom im Plasma als Quelle der THz Strahlung identifiziert. Neue Spektroskopiemethoden in ein und zwei Zeitdimensionen werden entwickelt und auf verschiedene Halbleiterstrukturen angewendet. So wird das elektrische Feld des THz-Impulses für Hochfeld-Transportexperimente genutzt. Im quanten-kinetischen Regime entkoppelt die Elektronbewegung von den Phononmoden des Kristalls, und quasi-ballistischer Transport wird möglich. Wir entwickeln ein dynamisches Polaronmodell, welches sowohl die experimentellen Ergebnisse auf kurzen Zeitskalen als auch Literaturwerte auf langen Zeitskalen zuverlässig reproduziert. Bei niedrigen Temperaturen von 80 K tritt zusätzlich THz-induziertes Interbandtunneln in GaAs auf. Die temperaturabhängige Tunnelrate hängt dabei wesentlich von der Dekohärenzrate des induzierten Prozesses ab. Desweiteren wird eine kollineare 2D THz Spektroskopiemethode entwickelt und erstmals an Quantentrogstrukturen angewendet. Eine komplizierte, nichtkollineare Strahlgeometrie ist prinzipiell nicht notwendig. Die eingeführten Frequenzvektoren erklären das zugrundeliegende N-Wellen Mischen analog zum Raum auch in der Zeit. So werden mit einer kollinearen Strahlgeometrie alle nichtlinearen Signale simultan gemessen werden. Mit diesem Konzept wurden Rabi-Oszillationen an Intersubbandübergängen in Signale verschiedener nichtlinearer Ordnung zerlegt. Die ersten 2D Korrelationsspektren im THz-Bereich demonstrieren die energetischen Kopplungen zwischen verschiedenen polaronischen Zuständen in einer Doppel-Quantentrogstruktur. / The presented thesis concerns fundamentals and applications of nonlinear terahertz (THz) spectroscopy. It is demonstrates that the a gain recovery time of a quantum cascade laser (QCL) amounts only to several hundred femtoseconds. We explored the generation process of THz pulses within a laser-induced two-color plasma and identified the ionisation current as the origin of the THz radiation. Novel methods of THz spectroscopy in one and in two dimensions are developed and applied to different semiconductor heterostructures. We use the electric field of THz pulses for high-field transport experiments. Within this quantum-kinetic regime, the electron velocity decouples from phonon modes of the crystal lattice and quasi-ballistic transport becomes feasible during the first hundreds of femtoseconds. We develop a dynamic polaron model, which reproduces the experimental results on short time scales as well as the published values on long time scales. At low temperatures of 80 K, we find additional THz-induced interband tunneling in GaAs. The temperature dependent tunneling rate depends essentially on the decoherence time of the induced process. Furthermore, a novel method of collinear 2D THz spectroscopy is developed and applied to quantum well structures. Frequency vectors are introduced to explain the underlying process of N-wave mixing not in space, but in time. This allows for a collinear beam geometry to measure all nonlinear signals simultaneously. We used this new method to decompose Rabi oscillations on intersubband transitions into nonlinear signals of different order. The first 2D correlation spectra in the THz frequency range demonstrate energetic couplings between polaronic states within an asymmetric double quantum well structure. Another experiment displays for the first time the 2D correlation spectrum of a 2pi Rabi flop on the intersubband transition of a multiple quantum well structure.