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Abstract
Low frequency Raman spectroscopy resolves the slow vibrations resulting from collective motions of molecular structures. This frequency region is extremely challenging to access via other multidimensional methods such as 2D-IR. In this paper, we describe a new scheme which measures 2D Raman spectra in the low frequency regime. We separate the pulse into a spectrally shaped pump and a transform-limited probe, which can be distinguished by their polarization states. Low frequency 2D Raman spectra in liquid tetrabromoethane are presented, revealing coupling dynamics at frequencies as low as 115 cm−1. The experimental results are supported by numerical simulations which replicate the key features of the measurement. This method opens the door for the deeper exploration of vibrational energy surfaces in complex molecular structures.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, low frequency vibrational spectroscopy has opened a window into the collective motions of molecular structures and bonds with heavy atoms [1–3]. These low frequency vibrational modes provide an important insight into the inter molecular potentials of liquids, shedding light on the dynamics of solvation [4,5]. In biomacromolecules, low frequency vibrations are believed to be associated with their function. Specifically, low frequency modes have been shown to play a role in the dynamics of cooperativity in hemoglobin [6], protein-ligand binding [2], and the bending mechanism of lysozyme [7].
One of the primary approaches to resolve vibrational dynamics is coherent Raman spectrometry. [8–16]. Coherent Raman spectroscopy has been successfully applied to resolve high frequency modes, beginning around $4000\;{\textrm {cm}}^{-1}$ with the stretching vibration of strongly bonded light atoms, followed by the fingerprint region ($500-1700 \;{\textrm {cm}}^{-1}$) which describes bending and stretching vibrations [17]. Until recently, vibrational modes in the low frequency regime ($<200\;{\textrm {cm}}^{-1}$) were out of reach for most coherent Raman spectroscopy schemes. The main limitation is imposed by the spectral overlap between the fundamental field and the Raman signal.
While coherent Raman spectroscopy provides a deep insight into the structure of molecular systems, resolving the complete structural dynamics requires the application of more general spectroscopic schemes. 2D spectroscopy provides structural information which cannot be resolved by the one dimensional scheme [18,19]. In 2D spectroscopy schemes, the response of the sample is measured as a function of two driving frequencies instead of the single frequency response traditionally measured in one dimensional vibrational spectroscopy [20]. In the past two decades, 2D-IR spectroscopy has been highly successful in revealing bond structure and ultrafast intramolecular couplings dynamics [21], probing vibrational frequencies above $1000 \;{\textrm {cm}}^{-1}$.
2D Raman spectroscopy in the low frequency regime holds a great potential. 2D Raman spectroscopy can access far lower frequencies, thereby exposing details of the longer range intermolecular potential through the coupling and underlying dynamics between vibrational modes [18,22]. Due to the broad line-widths and abundance of vibrational modes in this region, the additional information gained by additional frequency dimensions is of high importance ([3,23]). Recent developments in multidimensional terahertz spectroscopy [24,25] and hybrid Raman terahertz spectroscopy [3,26,27] have produced spectra in gas and solid phases down to $300 \;{\textrm {cm}}^{-1}$. However, structural information from the liquid phase and at frequencies lower than $300 \;{\textrm {cm}}^{-1}$ is extremely difficult to extract from existing measurement techniques [28].
2D Raman spectroscopy can be described as a fifth order nonlinear light matter interaction [18]. The standard approach to detect this fifth order signal involves five femtosecond pulses arriving from multiple directions at three distinct times, while the detected signal is separated spatially due to phase matching constraints [4,5,10,19,29,30]. Although 2D Raman spectroscopy contains valuable information about the coupling between different vibrational modes, this approach is limited by the cascaded lower-order signals which overwhelm the fifth order effect [9,30,31]. Recently, our group demonstrated a new approach where 2D Raman spectroscopy is performed via a single ultrashort beam [32]. A single shaped ultrashort pulse, imprinted in the frequency domain with the sum of two sinusoidal phase functions, was used to excite the entire fifth-order process. An important advantage to this approach lies in its ability to suppress the lower-order cascaded effects. This scheme exploits optical heterodyne amplification between the input field and the fifth order signal, resolving the spectral shift induced on the spectrometer. Since the cascaded third order signal does not undergo heterodyne amplification, it can be neglected in this measurement scheme.
While prior implementations of single beam 2D Raman spectroscopy allow the measurement of the coupling between vibrational modes down to 200 ${\textrm {cm}}^{-1}$ [32], their application to the low frequency regime is highly challenging. The small spacing between these low frequency modes (30-50 ${\textrm {cm}}^{-1}$), their broad line shape [33], as well as their weak response to excitation require high spectral resolution and an extremely sensitive signal acquisition scheme. The maximal spectral resolution is limited by the maximal duration of the pulse train. This duration, dictated by the pulse shaper resolution, reaches a maximal value of about 2 ps in our scheme, corresponding to about 16 ${\textrm {cm}}^{-1}$ resolution. In the low frequency region, below 200 ${\textrm {cm}}^{-1}$, improved spectral resolution is highly advantageous in order to separate the spectral peaks. In addition, since both the excitation and the probing are induced within a single pulse, standard methods for noise and background subtraction, such as lock-in detection, are difficult to apply.
In this work, we demonstrate a new approach for 2D Raman spectroscopy, sensitive to off diagonal elements of the fifth order nonlinear susceptibility, in the low frequency regime. We separate the pulse into a spectrally shaped pump and a transform-limited probe, which can be distinguished by their polarization states. The vibrational modes are selectively excited by a pump pulse train which is generated via pulse shaping [17] by applying a sinusoidal spectral phase via pulse shaping. The temporal delay between pulses in the pulse train is given by $T_{mod}=2\pi /\Omega _{mod}$ where $\Omega _{mod}$ represents the frequency of the sinusoidal modulation applied to the spectral phase. A temporally delayed probe pulse interacts with the sample and is phase modulated by the excited vibrational modes. Experimentally, we manipulate two degrees of freedom – the first is the periodicity of the pulse train which dictates the excited modes, while the second is the probe delay. The combination of single beam excitation with delayed probing, enables us to isolate the fifth order signal while providing high spectral resolution. Splitting the excitation pulse into a train of pulses drives the vibrational modes more selectively, compared to other methods which implement amplitude and phase shaping to create a double excitation pulse [34]. Our experiment reveals the vibrational dynamics evidenced by weak low frequency cross-peaks representing the coupling between vibrational modes in the low frequency regime. We apply our method towards observing the coupling between intramolecular vibrational modes at 115 and 175 ${\textrm {cm}}^{-1}$ in liquid tetrabromoethane.
2. Methods
The initial pulse is generated by a Spectra Physics Solstice Ace regenerative amplifier system, which produces 7 mJ pulses with a full width at half max (FWHM) of 40 fs centered at 795 nm at a repetition rate of 1 kHz, horizontally polarized. The beam is split by a thin film beam splitter. The transmitted replica pulse passes through a computer-controlled pulse shaper that imprints a sinusoidal spectral phase upon the spectrum of the pulse. The sinusoidal spectral phase is of the form $\Phi (\omega )=1.2cos[(\omega -\omega _0)T_{mod}]$, where $\omega _0=2\pi c/\lambda _0$ and $\lambda _0=795{\textrm {nm}}$, the central wavelength of the pulse spectrum is held at a fixed phase, and $T_{mod}$ is the period the modulation. In the time domain, such pulse shaping splits the pulse into a train of pulses with a period (T$_{\textrm {mod}}$), defined by the frequency of the applied spectral phase. This pulse train acts as a pump and initiates the vibrational dynamics. The pump intensity is modulated by an optical chopper at 173 Hz. The reflected replica is sent to a computer controlled delay stage which scans the arrival time of the probe pulse (t$_{\textrm {probe}}$). We control the probe’s intensity and its polarization state with a half wave plate and a polarizer. The minimal delay of the probe pulse is set to be 2.6 ps after the temporal center of the pump train, in order to avoid their overlap, as shown in inset to Fig. 1. The maximal delay is limited by the decay time of the vibrational coherence in the sample as well as the sensitivity of the detection apparatus. We were able to scan up to approximately 6 ps, achieving a spectral resolution as high as 5.5 ${\textrm {cm}}^{-1}$.
Fig. 1. Schematic description of the experimental setup for single beam low frequency 2D Raman spectroscopy. The initial laser beam is split into two replicas by a beam splitter (BS1). The reflected beam, which will act as a probe, is temporally delayed by a computer controlled delay stage. The intensity and polarization of the beam are controlled by a half wave plate (HWP) and nanoparticle linear film polarizer (P1). The beam, transmitted by BS1, passes through a computer controlled spatial light modulator (SLM) based pulse shaper, which imprints a sinusoidal phase modulation upon the pulse spectrum (inset schematic shows a representative pulse spectrum and phase modulation function), splitting the single pulse into a train of pulses with period T$_{\textrm {mod}}$. The two beams are recombined on a second beam splitter (BS2) before passing through a computer controlled shutter (S) which opens only during acquisition, reducing damage to the sample during the measurement. The beam is then split once again into two replicas by another beam splitter (BS3). The transmitted beam, which acts as a reference for the "lock-in" detection, passes through a nanoparticle linear film polarizer (P3) to filter out the probe beam, and is then spectrally resolved by a high speed spectrometer. The reflected beam is focused by a 15 cm achromatic doublet (L1) into the sample (S). The scattered light is collected by a 50 cm achromatic doublet (L2). The pump pulse train is filtered out by a nanoparticle linear film polarizer (P2) and then the probe pulse is coupled into a multimode fiber, which guides the light to a second high speed spectrometer. Inset figure shows the final pulse pattern which interacts with the sample. First the pump pulse train of period T$_{\textrm {mod}}$ impinges upon the sample, then a transform-limited probe pulse arrives at the sample at time t$_{\textrm {probe}}$, starting 2.6 ps after the temporal center of the pump pulse sequence. By scanning T$_{\textrm {mod}}$ and t$_{\textrm {probe}}$, we manipulate the two time scales required for 2D spectroscopy.
In order to achieve a high contrast measurement, we rotate the polarization of the probe pulse to be perpendicular to the pump before the sample. The pulses are then recombined on a beam splitter before passing through a computer controlled shutter which opens only during data acquisition and reduces the thermal damage to the sample. An additional beam splitter transmits a replica of the beam before the sample, which passes through a polarizer aligned along the shaped beam’s polarization. This beam is then coupled into a high speed spectrometer (Avantes Avaspec-ULS2048L-EVO), acting as the reference signal for the "lock-in" detection. The reflected beam is focused onto the sample by a 15cm achromatic lens. Dispersion was compensated separately for the probe and pump paths, adjusting the compressor which is built into the Solstice Ace for the former and then compensating for residual dispersion with the pulse shaper for the latter. Optimal compression at the sample plane was found by measuring the total intensity of non-resonant four wave mixing as a probe of the instantaneous intensity at the focus. The compressed pulses were evaluated using a commercially available frequency-resolved optical gating (FROG) [35] device (MesaPhotonics FROGScan) confirming a pulse duration of 40 fs, with time-bandwidth product of 0.5. After the sample, the beam is collected by a 50 cm achromatic lens and the pump pulse is filtered out by a polarizer. The remaining probe is then coupled into a second high speed spectrometer (Avantes Avaspec-ULS2048L-EVO) with which allows for shot by shot spectral measurements at the laser’s repetition rate. The pump-probe scheme, combined with the high speed acquisition of the probe spectrum, enables us to implement a "lock-in" measurement scheme, which significantly reduces the noise level in the measurement.
We resolve the Raman signal by measuring shifts in the center of mass of the spectrum as a function of the two time delays [32]. Specifically, the full spectrum of the probe is acquired for each shot, while the shifts in the center of mass of the spectrum are calculated in a "lock-in" method, by subtracting the center of mass of the acquired spectra in each chopper state, and then averaging over the data collected in a given time window. Using polarization discrimination to filter the pump as well as "lock-in" detection for the probe, we are able to reach a signal to noise ratio larger than 50:1. By scanning the pump pulse train period, T$_{\textrm {mod}}$, and the probe pulse arrival time, t$_{\textrm {probe}}$, we measure the 2D vibrational dynamics. Through Fourier analysis, we extract the 2D spectrum.
3. Experimental results
We demonstrated the measurement of the low frequency 2D spectrum on Tetrabromoethane (Sigma Aldrich 86760) in a quartz cuvette. Since this sample is isotropic and has no birefringence, the polarization discrimination scheme can be applied. Figure 2 describes the time dependent spectral shift in tetrabromoethane. The vertical axis represents the period of the pump pulse train, while the horizontal axis represents the delay of the probe pulse. Clear modulations are observed in both the vertical and horizontal directions representing the spectral shift induced by the dominant vibrational mode at 220 ${\textrm {cm}}^{-1}$. The modulations induced by other vibrational modes are not visible in the time domain data without further data processing.
Fig. 2. Experimentally resolved spectral shift as a function of pump pulse train period (T$_{\textrm {mod}}$) and probe delay (t$_{\textrm {probe}}$). Note that the initial probe delay (t$_{\textrm {probe}} = 0$) was set to 2.6 ps, such that the probe pulse did not temporally overlap at the sample with the most intense pulses in the pump pulse train. Color bar represents differentially detected shift in center of mass of the probe pulse spectrum in arbitrary units. The image is saturated to reveal weak oscillations at large delays.
By applying a 2D Fourier transform we present the 2D vibrational spectrum in Fig. 3. Since our pump and probe pulses are not identical in their intensity, as well as their scanning resolution, or scanning range, we find that the spectrum has features which are not symmetrical about the diagonal. The most apparent features are the vertical and horizontal ridges along 220 ${\textrm {cm}}^{-1}$. These features are associated with the strong Raman response of the 220 ${\textrm {cm}}^{-1}$ mode. Along these ridges, the observation of the off-diagonal components is very challenging. For a sample with different response and lifetime ratios between the Raman modes, these ridges would be reduced significantly. The weak peaks along the diagonal correspond to the vibrational modes at 115 and 178 ${\textrm {cm}}^{-1}$[36]. The low intensities of these peaks result from damping of the modes on the time scale of the probe pulse arrival time.
Fig. 3. 2D Raman spectrum of tetrabromoethane. Diagonal peaks (blue arrows) correspond to the vibrational modes at 115, 178, and 220 ${\textrm {cm}}^{-1}$[36], slightly shifted due to the limited spectral resolution of our measurement. Off diagonal cross peak is visible below the diagonal, between the 178 ${\textrm {cm}}^{-1}$ vibrational mode and 115 ${\textrm {cm}}^{-1}$ mode (red arrows). An artifact appears along the diagonal at 90 ${\textrm {cm}}^{-1}$ (green arrow) which we believe to be caused by errors induced by the spatial light modulator. Color bar represents Fourier transform magnitude in arbitrary units.
The off-diagonal signal at the intersection of the 178${\textrm {cm}}^{-1}$ and 115 ${\textrm {cm}}^{-1}$ represents the coupling signal between these two vibrational modes. These peaks are slightly shifted and broadened considerably by the limited spectral resolution along the pump axis.
4. Simulations
In the following stage, we simulated the third and fifth order nonlinear response of tetrabromoethane using the induced dipole-dipole interaction [19] to describe the coupling between vibrational modes. As in the experiment, the simulation scans two parameters, the pump pulse train period (T$_{\textrm {mod}}$) and the probe delay (t$_{\textrm {probe}}$), calculating the spectral response of the material for each temporal configuration, and isolating the heterodyne amplified spectral shift induced upon the pump. Once the spectral shift for all temporal configurations was calculated, the simulated data was processed by the same Fourier analysis as the experimental data.
In Fig. 4, we can identify diagonal peaks which represent the 115, 151, 178, and 220 ${\textrm {cm}}^{-1}$ vibrational modes (blue arrows). In this simulation, the 151 ${\textrm {cm}}^{-1}$ vibrational mode appears above the background, while in the experimental data, this peak was below the noise threshold. The simulation was calculated either with or without the matrix element associated with the fifth order coupling dynamics taken into account. As we can see in Fig. 4(a.), in the case of no coupling, the spectrum is composed of diagonal terms only. When these coupling coefficients are introduced in Fig. 4(b.) a cross peak clearly appears above the background signal (red arrow). Comparison of the simulation in Fig. 4(b.) with the experimental results in Fig. 3 shows good agreement in the intensities and positions of all peaks in the 2D spectra.
Fig. 4. Simulated 2D Raman spectrum of tetrabromoethane. In (a.), the fifth order coupling coefficients were set to zero to remove coupling dynamics from the simulation, while in (b.) these coefficients were introduced. Diagonal peaks (blue arrows) correspond to the vibrational modes at 115, 151, 178, and 220 ${\textrm {cm}}^{-1}$[36]. The red arrow in both figures points to the position where a cross peak between the 178 and 115 ${\textrm {cm}}^{-1}$ modes would be expected. Color bars represent Fourier transform magnitude in arbitrary units.
5. Conclusion
We have presented the first experimental scheme capable of measuring 2D Raman spectra in the low frequency regime. By combining a shaped pump and a transform-limited probe, this method provides the spectral resolution required to distinguish the coupling between low frequency vibrational modes. This experimental setup, separating the pump and the probe beams via their polarizations, opens the door to a broad range of applications. Shot-by-shot acquisition of the probe spectrum and the "lock-in" detection scheme enhances the signal to noise ratio and enables the detection of the weak, fifth order signal. In addition, the coupling dynamics of tetrabromoethane were simulated, and the key features of the experimental spectra were reproduced.
The single beam geometry at the sample plane allows for a direct integration of this approach in standard microscopy schemes. The Raman interaction is advantageous due to the short wavelength and deep penetration depth of the applied frequencies, relative to terahertz schemes. In addition, the availability of high intensity sources and sensitive detectors for visible wavelengths allows for future implementation in liquid and biological samples. Applications to more complex molecular structures, together with molecular dynamics simulations, hold the potential to reveal the energy transfer dynamics in a broad range of molecules.
Funding
Crown Photonics Center; Israeli Centers for Research Excellence.
Acknowledgments
We would like to thank Prof. Dan Oron for his contribution to all aspects of this work, which proved crucial to the development and success of our research. Dr. Omer Yaffe provided many fruitful discussions, as well as unhindered access to his research group and their acquired knowledge base. Mr. Maor Asher provided a wealth of insight on an-harmonic processes in low frequencies. Dr. Miri Kazes assisted greatly with sample preparation.
Disclosures
The authors declare no conflicts of interest.
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