An ultra-fast liquid switch for terahertz radiation

At the enormous pressures and temperatures of 300 GPa and 7000 K, molecular dynamics calculations predict that liquid water should be metallic and contribute to the magnetic fields of Uranus and Neptune.¹ More recently, experiments demonstrated that thin layers of liquid water could form a metallic solution for a few seconds, via charge transfer from a sodium potassium alloy.² However, liquid water can also display a metallic-like transient response for an ultra-short amount of time following photoionization. When water molecules in the liquid phase are photoionized via multi-photon optical absorption, the initially excited electron wavefunction can have a radius of^3–5 ∼40 Å. The electron is thus delocalized over 9000 water molecules. This “conduction band electron” is excited when the energy of the optical excitation exceeds the “bandgap of liquid water,” located somewhere between⁶ 10 and 12 eV. The wavefunction of the initially delocalized electron shrinks to less than^7,8 3 Å within ∼0.2 ps, resulting in the familiar absorption of the relaxed, solvated aqueous electron peaking in the near infrared.⁹ 

When electromagnetic radiation propagates from one medium to another with different optical properties, the Fresnel coefficients determine the properties of the reflected and refracted waves at the interface. While the frequency of the electromagnetic radiation is unchanged, the wavevectors of the reflected and transmitted beams change. By analogy with a spatial boundary, reflection and refraction are also possible when the properties of a medium vary abruptly in time, that is, when the variation is much quicker than the duration of a period of the electromagnetic wave. This temporal boundary^10–14 can modify the frequency of the electromagnetic wave rather than its wavevector. Following Morgenthaler’s seminal work,¹⁰ the frequency up-shifting and down-shifting of electromagnetic radiation by a temporal boundary were demonstrated in gas plasmas,^15,16 semiconductors,^17–25 transparent conducting oxides,^26–30 and metamaterials.^31–33 

The Hamm group demonstrated³ that the photoionization of liquid water can be probed in the terahertz (THz) range. A broad, transient absorption feature centered at 1.5 THz decayed within 200 fs and was associated with the delocalized electrons. Previous optical-pump and optical-probe experiments demonstrated that the dissolution in water of iodide anions (I⁻) increases the number of photo-generated electrons.³⁴ Here, we show that a 9M water solution of sodium iodide displays a significant (−20%) and short-lived (∼70 fs) optical-pump terahertz-probe (OPTP) signal at a temperature between 10 and 50 °C. As the optical properties of the liquid are modulated on a timescale that is shorter than the duration of the THz optical cycle, we demonstrate that the THz fields transmitted by a liquid solution are upshifted in frequency from ∼1 to ∼3 THz with an efficiency of 4%.

OPTP measurements, sometimes called time-resolved terahertz spectroscopy (TRTS), were performed on a series of aqueous solutions containing 1, 3, 5, 7, 9, and 11M of sodium iodide (NaI). The samples were prepared by dissolving sodium iodide salt (99.5% purity, supplied by S3 Chemicals) in ultra-pure milli-Q water with a conductivity of 0.055 µS/cm. The initial solution with a concentration of 1 mol/l (or M) was prepared by dissolving 15 g (0.1 mol) in 100 ml of water. After this initial 1M NaI liquid sample was measured, we obtained the 3M solution by dissolving an additional 30 g of NaI in the same solution. This process was repeated until a total of 165 g of NaI was dissolved in 100 ml of pure water, which is close to the solubility limit at room temperature (∼11M). The equilibrium terahertz properties of these solutions were reported previously.³⁵ The experiments were performed in a nitrogen atmosphere with less than 10% humidity and at three temperatures: 10, 30, and 50 °C. A recirculating chiller stabilized the temperature of the reservoir of the liquid within ±0.05 °C. In order to avoid unwanted pump–probe signals from the windows of a static cell or sample holder,³⁶ the measurements were performed on a recirculating liquid jet. We measured a flowing water jet without windows. A water jet is a freestanding sheet of water that is generated by a nozzle; please see Ref. 37 for further details.

The details of the experimental OPTP setup are given elsewhere.³⁸ In short, the broadband terahertz (THz) probe pulses are generated by two-color plasma filamentation in nitrogen gas. A first, collecting off-axis parabolic mirror (OAPM) collimates the THz radiation. The residual optical radiation is filtered out by a hole in this collecting OAPM and by a high-resistivity silicon slab (Eksma optics) placed after the first OAPM. In order to highlight the effects of pulse shaping and frequency upshifting, paper filters were added to reduce the THz bandwidth. A second OAPM focuses the THz radiation into the sample position, where we placed the flowing, windowless liquid jet sample. A third OAPM collimates the THz beam transmitted by the sample, and a fourth OAPM focuses the THz radiation into the detection crystal. The optical pump pulses at ∼400 nm propagate collinearly with the THz beam via a hole in the middle of the second OAPM. The residual pump energy is filtered out by a hole in the third OAPM and by polyethylene filters placed between the third and fourth OAPM. Examples of the scheme of an optical setup dedicated to non-linear terahertz spectroscopy can be found in Ref. 39.

The THz pulses are detected via electro-optical sampling in a 0.1 mm thick gallium phosphide (GaP) crystal with a temporal resolution of 25 fs. The delay of the sampling beam is the electro-optical sampling delay, t_EOS. In order to avoid spurious contributions by THz reflections, Fourier transformation (FT) is performed after zero padding the THz fields collected between t_EOS = −1 ps and t_EOS = +1 ps to 256 points and with a Hanning window function. This corresponds to a frequency resolution of ∼0.16 THz. The magnitude of the FT of a THz field corresponds to its spectrum. The optical pump pulses are ∼50 fs long and centered at 400 nm, as generated by second harmonic generation. In the following, we will refer to the temporal delay of the pump beam as the pump–probe delay, t_PP. The pump–probe delay was varied in steps of 50 fs. The peak intensity of a single optical pump pulse amounted to ∼1.2 TW/cm². We optimized the laser compression to obtain the fastest and largest transient signals from the liquid samples. The spot sizes of the optical and THz beams were measured with a camera (400 µm). As a wavelength of 400 µm corresponds to 0.75 THz, the optical beam does not excite the probe uniformly for frequencies lower than 0.75 THz. For these reasons, the THz spectra shown here are reliable only above 0.75 THz.

Figure 1 displays the THz fields [Fig. 1(a)] and spectra [Fig. 1(b)] transmitted by an exemplary liquid sample at equilibrium, i.e., when the optical pump pulses are blocked. The reference THz probe field [green in Fig. 1(a)] is obtained by turning off the liquid jet, i.e., by measuring the transmission of the empty path. The duration of the almost single-cycle THz fields is 1 ps. The THz probe field transmitted by the liquid sample is shown in black in Fig. 1(a). The optical properties of the aqueous sample are linked to the delayed arrival of the THz pulse transmitted by the sample and to the reduced amplitude of the transmitted THz field. In the following, the maximum value of the THz field transmitted will be referred to as the “THz peak,” which is marked with E₀ for the liquid sample in Fig. 1(a). The THz spectra transmitted by reference (green curve) and sample (black curve) are shown in Fig. 1(b) with an identical scaling factor, i.e., the absolute quantities can be compared. The maximum magnitude of the FT spectrum transmitted by the liquid will be referred to as M₀ in the following. All the THz probe spectra are centered around 1 THz, which is typical for intense sources, such as table-top-based tilted-front optical rectification in lithium niobate^40–42 and accelerator-based superradiant TELBE⁴³ and TeraFERMI.^44,45 As indicated by the gray area in Fig. 1(b), the noise level of the spectra is lower than 1%.

The difference between the arrival times of the THz peak transmitted by the empty path and the THz peak transmitted by the sample varied between about 50 and 80 fs for all the water samples studied here. By assuming, for simplicity, an index of refraction equal to 2, this temporal delay corresponds to a thickness of the liquid jet between 15 and 24 µm for all the samples. The ratio between the amplitude of the THz peak transmitted by the liquid sample and the THz peak transmitted by the empty path varied between about 60% and 65% in all the investigated solutions. Our setup is designed to perform high-resolution transient and relative measurements, but is not equally suited to quantify the absolute optical properties of the samples in the THz range because the thickness of the liquid jet is affected by the temperature and salt concentration. The equilibrium optical properties of these liquids can be obtained with THz time-domain spectroscopy and a static cell, as reported earlier.³⁵ 

The overall pump-induced response can be quantified by performing a “pump scan” or “fixed-gate scan.” In this experiment, the electro-optical sampling beam is kept at the fixed time delay corresponding to the maximum field transmission (E₀), while the pump–probe delay (t_PP) is varied. The relative variation of the THz peak field (ΔE/E₀ = E_0,pumpON/E_0,pumpOFF − 1) is measured as a function of the pump–probe delay. The result is shown in Fig. 2(a) for the 9M NaI sample at three temperatures. The transient change of the THz peak drops by 20% at zero pump–probe delay (t_PP = 0 ps) and depends weakly on the temperature. To our knowledge, this is the largest OPTP signal ever reported on a liquid sample. After the maximum transient response is reached, the relative variation of the THz transmission decays. This decay can be fit to a bi-exponential function, which is shown with the black curve in Fig. 2(a). The fastest component has a decay constant of τ₁ = (70 ± 30) fs and accounts for most of the size of the transient signal. The transient THz signal and its decay constants are similar in all the investigated samples, but the amplitude varies with the salt concentration. As shown in Fig. 2(b), the size of the transient THz signal is roughly proportional to the concentration of sodium iodide in water, thus proving the crucial role of this salt in the processes measured here. A maximum signal of −24% is found for the 11M NaI solution at 50 °C. In this case, however, we have data only at 30 and 50 °C because the salt came out of solution at 10 °C. For these reasons, we highlight in Figs. 2(a) and 3 the results of the 9M NaI water sample, which is stable between 10 and 50 °C. As a further control, we note that similar measurements on pure water revealed much smaller pump–probe signals, about ΔE/E₀ ∼ −10⁻⁴ at the pump–probe overlap, t_PP = 0. The experimental results on pure water will be included in a separate publication.

The results in Fig. 2 prove that the optical-pump excitation strongly perturbs the THz properties of NaI water solutions. The pump-induced effect is the largest over a timescale τ₁ ∼ 70 fs, which is much shorter than the duration of an optical cycle of the THz field (∼1 ps, see Fig. 1). As this liquid sample could slice or clip the THz field with sub-cycle resolution, we can use it as a temporal boundary for THz radiation.

In a “probe scan” or “fixed-pump scan” experiment, the THz field is fully recorded by delaying the electro-optical sampling beam (t_EOS). When the optical pump is blocked, we obtain the THz transmission of the liquid at equilibrium, which is shown with the black trace in Fig. 3(a). When the optical pump is turned on at t_PP = 0 [black arrow in Fig. 3(a)], the transmitted THz field is perturbed—see the red trace in Fig. 3(a). It is evident from the raw data that the pump pulse induces a strong asymmetry in the THz pulse, which implies that the pump interaction changes the frequency components of the THz field. The THz spectra obtained by FT are shown in Fig. 3(b). As expected, the spectra are different for pump on [red in Fig. 3(b)] and pump off [black in Fig. 3(b)]. Please note that the THz spectra are shown with the same scaling factor and can be quantitatively compared. When the optical pump pulses perturb the liquid, the transmitted THz magnitude is weaker at ∼2 THz and stronger above ∼3 THz. The purple curve in Fig. 3(c) is equal to the difference between the red and black curves in Fig. 3(a), thus showing the relative change of the THz field transmission. Similarly, Fig. 3(d) shows the relative change of the magnitude of the FT, which highlights the redistribution of THz energy induced by the optical pump pulses. The THz magnitude decreases by about −10% between 1 and 2 THz and increases by about +4% at 3 THz, +1% at 4 THz, and +0.5% at 5 THz. The efficiency of the upshifting from a frequency range at around 1 THz to frequencies close to 3 THz amounts to 4%. We calculate this efficiency from the area of the increased magnitude of the FT between 2.5 and 5.5 THz when the pump pulse is on [purple shaded area in Fig. 3(d)] and divide it by the area of the FT magnitude between 0 and 4 THz when the pump is off [gray shaded area in Fig. 3(b)].

Two main processes could contribute to the experimental observations reported here: absorption by delocalized electrons and the impulsive response of the photo-excited solute. As suggested by the increasing value for increasing NaI content [Fig. 2(b)], the transient THz signal is related to the photoionization of I⁻, which results in the generation of a precursor to the solvated aqueous electron³ and the neutral iodine atom,³⁴ I. The precursor to the solvated aqueous electron was described before as a large, delocalized electron, with a radius of up to 40 Å that decays within ∼200 fs. According to a particle in a box model,³ a delocalized electron with a radius of 40 Å absorbs THz radiation at around 1.5 THz. Thus, the generation of short-lived delocalized electrons is expected to reduce the THz transmission within 200 fs, which is consistent with the experimental observations reported here. A second process involving the THz field emitted by a photo-excited solute in water was described by Ahmed et al.⁴⁶ They performed OPTP experiments on a free-flowing liquid jet of water containing a photo-absorbing dye (Coumarin). The pump pulse resonantly excites a molecular state of the solute while THz radiation probes the transient response. They found a fast and negative signal most prominent at pump–probe overlap, ΔE/E₀ ∼ −6 · 10⁻³ at t_PP = 0. They also performed non-equilibrium molecular dynamics simulations and explained this negative signal as the THz field emitted by the solute and its surrounding water upon photoexcitation of the solute molecule. By extension, also in our case, the photoionization of I⁻ results in a charge redistribution in liquid water, for which the emission of a THz field with the opposite phase is expected, thus resulting in a decreased transmission of the THz signal. Further theory and experimental works are required to pinpoint the role of the THz emission triggered by the photoionization of water.

In summary, this Letter demonstrates that water solutions containing sodium iodide display very large and very fast optical-pump terahertz-probe signals at the temperature of 10, 30, and 50 °C. The relative variation of the transmitted THz field decreases by up to −20% at the pump–probe overlap and recovers with a fast time constant of ∼70 fs. Moreover, the spectral content of the THz radiation was manipulated by recording the THz fields at a temporally fixed pump excitation. The sub-cycle slicing of the THz field redistributes its spectral component, resulting in the frequency upshifting to ∼3 THz with an efficiency of 4% in the 9M NaI solution. The results presented here could have significant consequences. In the shorter term, we propose that solutions of sodium iodide should be used as reference samples in the alignment and optimization of OPTP or TRTS experiments on liquids. In addition, this technique could be used to tailor THz fields at low frequency.^40–45 In the long term, especially if combined with suitable window materials, this work could open the door to “water electronics.” The advantage could be the fast decay time of the THz photo-switch, τ₁ ∼ 70 fs. For example, to our knowledge, the fastest decay time of an OPTP modulation in a typical semiconductor is larger than^47–49 >150 fs. The liquid switches reported here could be used at a faster rate or, equivalently, have a larger bandwidth (1/70 fs⁻¹ > 1/150 fs⁻¹).

We acknowledge support from the Cluster of Excellence RESOLV (Grant No. EXC 2033 – 390677874) funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), by the ERC Advanced Grant No. 695437 (THz Calorimetry) and by the DFG Project No. 509442914. We acknowledge support by the Open Access Publication Funds of the Ruhr-Universität Bochum. We are particularly grateful to Thorsten Ockelmann, Sashary Ramos and Martina Havenith. This work was dedicated to my late father.