The effect of the Gouy phase in optical-pump-THz-probe spectroscopy

Gouy phase of Bessel-Gaussian beams: theory vs. experiment

It is well-known that the wave of a freely propagating Gaussian beam experiences an additional π phase shift compared to a plane wave. This phase shift, known as the Gouy phase, has significant consequences in, e.g., nonlinear optics, since the nonlinear processes require high peak intensity and phase matching of the focused beams. Hence, determining and controlling the Gouy phase is crucial in many fields of modern optics and photonics. Here, we develop an analytical model for the Gouy phase of long-range Bessel-Gaussian beams obtained by annihilating highly charged optical vortices. The model accounts for the influence of the relevant experimental parameters (topological charge, radius-to-width ratio of the initial ring-shaped beam, and focal length of the Fourier-transforming lens). We find an evolution of the Gouy phase varying nearly linearly with propagation distance and confirm this result experimentally.

Terahertz Kerr Effect of Liquids

In recent years, tremendous advancements have been made in various technologies such as far-infrared, low-frequency Raman, and two-dimensional (2D) Raman terahertz (THz) spectroscopies. A coherent method has emerged from numerous experimental and theoretical investigations of molecular dynamics in liquids by comparing linear and non-linear spectroscopic techniques. Intermolecular hydrogen bond vibration, molecular reorientation motion, and interaction between molecule/ionic solute and hydrogen bonds have been demonstrated to occur in the THz region, which are closely related to their physical/chemical properties and structural dynamics. However, precise probing of various modes of motion is difficult because of the complexity of the collective and cooperative motion of molecules and spectral overlap of related modes. With the development of THz science and technology, current state-of-the-art THz sources can generate pulsed electric fields with peak intensities of the order of microvolts per centimeter (MV/cm). Such strong fields enable the use of THz waves as the light source for non-linear polarization of the medium and in turn leads to the development of the emerging THz Kerr effect (TKE) technique. Many low-frequency molecular motions, such as the collective directional motion of molecules and cooperative motion under the constraint of weak intermolecular interactions, are resonantly excited by an intense THz electric field. Thus, the TKE technique provides an interesting prospect for investigating low-frequency dynamics of different media. In view of this, this paper first summarizes the research work on TKE spectroscopy by taking a solid material without low-frequency molecular motions as an example. Starting from the principle of TKE technology and its application in investigating the properties of solid matter, we have explored the low-frequency molecular dynamics of liquid water and aqueous solutions using TKE. Liquid water is a core of life and possesses many extraordinary physical and biochemical properties. The hydrogen bond network plays a crucial role in these properties and is the main reason for its various kinetic and thermodynamic properties, which differ from those of other liquids. However, the structure of the hydrogen bond network between water and solutes is not well known. Therefore, evaluating the hydrogen bond-related kinetic properties of liquid water is important.

Molecular Orientation-Induced Second-Harmonic Generation: Deciphering Different Contributions Apart

We demonstrate and explore an all-optical technique for direct monitoring of the orientation dynamics in gas-phase molecular ensembles. The technique termed “MOISH” utilizes the transiently lifted inversion symmetry of polar gas media and provides a sensitive and spatially localized probing of the second-harmonic generation signal that is directly correlated with the orientation of the gas. Our experimental results reveal selective electronic and nuclear dynamical contributions to the overall nonlinear optical signal and decipher them apart using the “reporter gas” approach. “MOISH” provides new crucial means for implementing advanced coherent rotational control via concerted excitation by both terahertz and optical fields.

Low-frequency anharmonic couplings in bromoform revealed from 2D Raman-THz spectroscopy: from the liquid to the crystalline phase

Two-dimensional (2D) Raman-THz spectroscopy in the frequency up to 7 THz has been applied to study the crystalline beta-phase of bromoform (CHBr3). As for liquid CHBr3, cross peaks are observed, which however sharpen up in the crystalline sample and split into assignable sub-contributions. In the Raman dimension, the frequency positions of these cross peaks coincide with the intramolecular bending modes of the CHBr3 molecules, and in the THz dimension with the IR active lattice modes of the crystal. This work expands the applicability of this new 2D spectroscopic technique to solid samples at cryogenic temperatures. Furthermore, it provides new experimental evidence that the cross peaks indeed originate from the coupling between intra- and intermolecular vibrational modes.

Molecular dynamic investigation of ethanol-water mixture by terahertz-induced Kerr effect

The terahertz Kerr effect (TKE) spectroscopy provides time-resolved measurement of low-frequency molecular motions of liquids. Here, the intense broadband terahertz (THz) pulses resonantly excite multiple molecular modes in pure ethanol and ethanol-water mixtures. For pure ethanol, the obtained unipolar TKE response contains the molecular relaxation information extending over tens of picoseconds, which originates from the coupling between the permanent molecular dipole moment of ethanol and the THz electric field. For ethanol-water mixtures with different molar proportions, the results observed on the sub-picosecond time scale can always be divided into the linear superposition of the TKE signals of pure ethanol and water. Under the observation time window over tens of picoseconds (after 1 picosecond), the relative molecular contribution of ethanol in the mixture changes nonlinearly with the increase of water molecules, implying the complex structural perturbation of ethanol hydrogen bond network in the mixture. This work provides a new perspective for further investigation on the hydrogen bond network structure and dynamics in aqueous amphiphilic solutions.

Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced transient birefringence

The fundamental properties of water molecules, such as their molecular polarizability, have not yet been clarified. The hydrogen bond network is generally considered to play an important role in the thermodynamic properties of water. The terahertz (THz) Kerr effect technique, as a novel tool, is expected to be useful in exploring the low-frequency molecular dynamics of liquid water. Here, we use an intense and ultrabroadband THz pulse (peak electric field strength of 14.9 MV/cm, centre frequency of 3.9 THz, and bandwidth of 1-10 THz) to resonantly excite intermolecular modes of liquid water. Bipolar THz field-induced transient birefringence signals are observed in a free-flowing water film. We propose a hydrogen bond harmonic oscillator model associated with the dielectric susceptibility and combine it with the Lorentz dynamic equation to investigate the intermolecular structure and dynamics of liquid water. We mainly decompose the bipolar signals into a positive signal caused by hydrogen bond stretching vibration and a negative signal caused by hydrogen bond bending vibration, indicating that the polarizability perturbation of water presents competing contributions under bending and stretching conditions. A Kerr coefficient equation related to the intermolecular modes of water is established. The ultrafast intermolecular hydrogen bond dynamics of water revealed by an ultrabroadband THz pump pulse can provide further insights into the transient structure of liquid water corresponding to the pertinent modes.

Periodic sampling errors in terahertz time-domain measurements

An extensive investigation of the origin and the impact of periodic sampling errors of terahertz time-domain spectroscopy systems is given. We present experimental findings and compare them to a theoretical model which is developed in this work. Special attention is given to the influence on the extraction of the refractive index from measurements. It can be shown that even distortions of the spectrum at frequencies higher than the used bandwidth can have a significant impact on the extracted refractive index.