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Abstract
A new rotational coherent anti-Stokes Raman spectroscopy (RCARS) concept based on interferometric quantum control (IQC) is demonstrated. Two wavepackets originating from pure rotational states are created by a femtosecond stimulated rotational Raman interaction. The two Raman responses are instantly probed by a single-mode ns pulse generating two interfering RCARS polarizations. The resulting signal is an IQC-RCARS spectrum detected by a streak camera. Here we demonstrate IQC-interferograms of N2 by varying the temporal separation between the two fs pulses within a full rotational revival period, as well as signal amplification and selective detection of nuclear-spin isomers at room conditions and inside a flame.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Quantum control is widely used in fundamental studies such as high-harmonic generation [1], photoionization [2], molecular alignment with strong and weak excitation [3–5], and quantum computing [6,7]. One form of quantum control is achieved by controlling molecular rotations; an approach that has benefitted significantly from modern ultrafast lasers. Most of the recent work on quantum control of molecular rotations is based on non-adiabatic alignment of induced electric dipoles via an intense, non-resonant, and ultrashort electric field [8]. The ultrashort electric field is typically provided by a sub-picosecond laser pulse whose duration is much shorter than the rotational transition periods. Interaction between the laser pulse and the molecules generates rotational Raman coherences, inducing a periodically oscillating macroscopic polarization in the ensemble of molecules. For a particular molecular species, the time period of the oscillation, referred to as the revival time, is given by Trev = 1/(2Bc), where B is the rotational constant of the molecule and c the speed of light. B is species-specific, as is the revival period, enabling concepts for species-selective amplification and annihilation, nuclear spin isomer selection, etc. [9]. Molecular revival dynamics are typically observed using degenerate four-wave mixing [10] or polarization spectroscopy [11] with femtosecond (fs) pulse probing. Although sequential step-by-step probing with a fs pulse provides excellent time resolution, probing with naturally broadband ultrafast pulses limits spectroscopic application and it is not possible to capture an entire scan instantaneously.
Coherent nonlinear spectroscopy is an active field of research as well, including variants based on molecular rotation. Rotational coherent anti-Stokes Raman spectroscopy (RCARS), for example, is a versatile spectroscopic tool providing thermodynamic information in gaseous media, such as temperature, pressure, and species concentration, most often via frequency-domain spectroscopy. More than 40 years of research and development aimed at improving the diagnostic capability of RCARS has established the technique as the gold standard for thermometry and major species detection in reactive flows, specifically in the temperature regime from 300 to ∼1200 K [12]. Among the advancements that support this development, the most significant include the introduction of the dual-broadband RCARS approach [13,14] (providing higher temperature precision and multiple species detection), development of picosecond (ps) and fs concepts [15] (avoiding interference from the non-resonant signal contribution), detection of molecules with complex symmetries [16–18], and reducing the influence of the local and often rapidly fluctuating collisional environment. Regarding the collisional environment, our group recently demonstrated a new RCARS technique (fs/ns-RCARS) which provides the signal decay time, and hence the linewidth, of each rotational-Raman coherence on single-shot basis [19,20]. In addition, the development of powerful ultrafast lasers offers single-shot measurements at kHz rate [21] and single-shot 2-D measurements [22].
In order to extend RCARS further, and to develop entirely new capabilities, we have adapted several concepts from prior work on non-adiabatic alignment, based on interference between rotational wavepackets that is generated during the RCARS interaction. Here, a weak non-resonant field (which falls well below the field strength needed for molecular alignment) generates a nonlinear polarization in the gas via the rotational Raman response to an ultrafast pulse. This distributed material polarization generates a rotational wavepacket exhibiting periodic revivals. The method is implemented using a 2-beam fs/ns-RCARS configuration as shown in Fig. 1(a), in which two broadband fs pulses, referred to as pump and control, with variable delay between them, are used. Note that we apply different nomenclature than what is used in more classic CARS discussions. In Fig. 1, the pump and control pulses both excite
Fig. 1. (a) Schematic of IQC-RCARS in the time domain. (b) Real part of the stimulated Raman response of N2 prepared by the pump or control pulse, where “Trev” indicates rotational revival period. (c) Experimentally recorded IQC signal on N2 at room temperature with pump-control time delay of δt = Trev = 8.38 ps, within a single-shot acquisition. The parameters t, τ, and δt represent the field time, probe time, and pump-control time delay, respectively.
Raman coherences, meaning that each of them serves as combined pump and Stokes pulses (in the classical nomenclature). The bandwidth of a fs pulse allows one beam to act as both pump and Stokes beams for RCARS, and so we have changed nomenclature in recognition of that point. Here, we describe excitation of two Raman coherences, not one. Using the new nomenclature now, the pump pulse drives 2-photon rotational Raman transitions, creating a rotational wavepacket, (i.e., a coherent superposition of all rotational transitions reachable within the bandwidth of the fs pulse). The wavepacket exhibits periodic recurrences (revivals), at integer, half-integer and quarter-integer multiples of the rotational time period. Figure 1(b) shows these revivals for the nitrogen molecule, obtained by calculating the real part of the Raman response. The control pulse then creates a second wavepacket, initiated at variable time delay, δt, relative to the pump pulse. In this way two interfering wavepackets are created. This phenomenon is observed here as a RCARS signal by use of a third, single-mode nanosecond pulse-width probe beam, which is aligned according to optimum phase-matching. Using a spectrometer and streak camera, the RCARS signal is both spectrally and temporally resolved within a single-shot acquisition, as shown in the spectrogram in Fig. 1(c).
As demonstrated in this and prior work by our group, interference between the two wavepackets allows manipulation of the shape of the RCARS spectrum for a specific application, controlled by the time delay between the pump and control pulse. In a recent work we successfully demonstrated species-selective annihilation of the RCARS spectrum using a half revival period delay between the pump and control pulses, i.e., δt = 1/2 Trev [23]. Annihilation of spectral lines from a specific species enables detection of spectral lines from other species that otherwise would be obscured and not observable (i.e., the detection selectivity is improved). Since the method is established by carefully engineering the interference of two confined quantum wavepackets, we call it Interferometric Quantum Control RCARS (IQC-RCARS).
This document reports work that further develops the technique, meanwhile deepening understanding of the associated interactions. Here we have explored the use of the IQC-RCARS technique with various pump-control pulse delays for species-selective signal amplification and nuclear-spin isomer selective excitation. The experimental results are predicted well by a theoretical model, described in the next section. In addition, a full interferogram of the IQC-RCARS signal for N2 during a full revival period is presented and the conceptual importance of the result is discussed. Finally, the potential for thermometry at elevated temperatures with the IQC-RCARS technique is investigated, using a theoretically predicted interferogram for N2 at 1500 K and matching data from measurements in a flame.
2. Theoretical model
A theoretical model has been developed for prediction of the temporal and spectral evolution of the IQC-RCARS signal, by extending the modelling framework reported by Miller et al. [24]. For fs/ns rotational CARS, impulsive broadband excitation couples rotational states via purely rotational Raman transitions; J → J + 2 for homonuclear diatomic molecules in the S-branch. Each rotational Raman coherence is driven by multiple photon pairs, creating a macroscopic polarization in the molecular ensemble. The stationary molecular response corresponding to this Raman process is given by:
where ν (= 0, 1, 2, 3,…) is the vibrational quantum number, J is the quantum number corresponding to the total rotational angular momentum, Nνis the fractional population on vibrational level ν, ${g_J}$ is the statistical weight factor due to nuclear spin degeneracy, FJ the Herman-Wallis factor [25], Δρv,J;J + 2the population difference between the rotational levels and ${|{\alpha_0^{(2 )}} |^2}$ the Placzek-Teller invariant, which is represented as: where bJ;J + 2 is the Placzek-Teller coefficient for the S-branch and γ is the polarizability anisotropy of the molecule [26]. In our experiment, the fs-laser pulse energies are kept low, but with sufficient energy to stimulate a Raman response in the free rotors.At higher laser intensities, the projection of the rotors’ angular momenta onto the fixed Z axis (i.e., the M states) breaks the 2J + 1 degeneracy. This phenomenon, which is known as Stark effect [19], arises via an extra Hamiltonian which is proportional to the non-negligible inner product of the induced dipoles and the strong field, ${H_{ind}} ={-} 1/2\left\langle {{{\bar{\mu }}_{ind}} \cdot {{\bar{E}}_{laser}}} \right\rangle$. When using ultrashort laser pulses, the laser field applies a torque on the induced dipoles, ${\bar{\mu }_{ind}}$, towards the laser field, ${\bar{E}_{laser}}$. Therefore, the strength of this effect, commonly known as “non-adiabatic alignment”, is measured by the value of << cos2θ >>t, and is called the degree of alignment, with θ being the angle between the induced dipoles and the laser polarization [27]. Another consequence of using high energy pulses for generation of the Raman coherences is non-thermal population re-distribution over the rotational states [28]. Since neither of these strong-field effects has been observed in our results, we believe that the term “Raman response” reflects the physics of experiments similar to ours more accurately than the descriptors “alignment” or “weak alignment” [5,23].
In a standard RCARS measurement the induced electric dipoles oscillate in phase coherently generating a wavepacket with superposition of all the J → J + 2 coherences. This Raman response, therefore, is a function of time, t:
where $\Delta {\omega _{J \cdot J + 2}}$ is the S-branch transition frequency between rotational level J and J + 2, ΓJ is the linewidth of the transition (calculated here using the energy corrected sudden (ECS) scaling law [29]). It should be noted that Eq. (3) in its general form includes O-branch transitions (J → J – 2) too, which is commonly referred to as coherent Stokes Raman scattering (CSRS). However, since in the current experiment the O-branch is blocked by the short-pass filter (Fig. 2), the minus sign is removed from Eq. (3) for simplicity. For fs/ns RCARS, the pump and Stokes interactions are driven by an ultrashort laser pulse which is considered impulsive compared to the long ns probe pulse. The rotational Raman response function contributes to the non-linear polarization of the gas as follows: where ħ = h /2π is the reduced Planck constant, τ is the probing time (streaking time) [see Fig. 1(c)], and Eprobe (t - τ) is the electric field envelope of the probe pulse. For the thermodynamic conditions that were studied in this work, the Raman coherences decay via collisional dephasing in several hundred picoseconds, meaning that the envelope of the probe pulse can be considered constant during coherence dephasing, i.e., Eprobe (t - τ) = Eprobe. Subsequently, the 3rd order polarization in the frequency domain is obtained by taking the Fourier transform of the polarization. Thus, the 3rd order polarization becomes:Fig. 2. Schematic of the experimental setup; VA- variable attenuator, λ/2- half-wave plate, BS- beam splitter, TS - translational stage, BD- beam dump, P- polarizer, L - lens, M – mirror, SF- short-pass filter, SPECM- spectrometer, SC- streak camera.
In IQC-RCARS, there are two femtosecond, 2-photon Raman excitation pulses separated by a variable delay time, δt, each creating a wavepacket with separate revival structures. Since the ns pulse continuously probes the overall Raman response, the CARS polarizations related to each of the wavepackets interfere from time zero, instantaneously. An equivalent experimental approach would be to let the stimulated Raman responses interfere first, then probe the interference by a delayed ps pulse, generating one CARS polarization. Either way, the result is an IQC polarization $\textrm{}P_{total}^{(3 )}$:
The intensity of an IQC-RCARS spectrum evaluated at a probe time τ after the first excitation pulse is given by the square of Eq. (7):
A direct consequence of Eq. (8) is that the IQC-RCARS spectra remain a function of the variable δt. The changes in IQC-RCARS signal with respect to δt are periodic with the period of the rotational revival time. Assuming dephasing is negligible during the first revival, i.e., δt < Trev, using Eqs. (3) and (6) for the third order polarization and squaring the result for temporal homodyne detection, one can write:
Thus, t + τ is canceled out and Eq. (9) is simplified to:
Equation (10) shows that at a certain probe delay τ, each J → J + 2 coherence is periodic with respect to δt, with the angular frequency of the corresponding transition $\Delta {\omega _{J \cdot J + 2}}$ (the Bohr frequency). Experimental evidence for this point will be presented below. Interestingly, the real part of the stimulated Raman response of Eq. (3), also plotted in Fig. 1(c), is very similar to the expression presented in Eq. (10):
One practical significance of the similarities between Eqs. (10) and (11) is that Eq. (10) is achieved via measurement of intensity; by varying the time delay δt one can retrieve the underlying encoded revival structure within the macroscopic CARS polarization shown in Fig. 1(c).
3. Experimental system
Figure 2 depicts the experimental setup. The excitation fields were provided by a Ti:Sapphire laser system (Coherent, Hidra-50), delivering 800 nm transform-limited 125 fs pulses at 10 Hz repetition rate. The fs pulse was divided into two pulses of equal energy by a beam splitter, to create the first excitation (pump) pulse and the second excitation (control) pulse. The required delay between the pump and control pulses was achieved by implementing a motorized high-precision delay stage in the control pulse path. The time calibration of the delay stage (for δt) was done by analyzing the spectral modulation caused by interference of two non-resonant signals. This method of time calibration was outlined in our recent work [23] and is also provided in detail in Supplement 1. The coherences generated by the pump and control pulses were probed continuously by 16-ns pulses with spectral full-width-at-half-maximum (FWHM) of 0.003 cm−1. This probe beam was generated by a frequency-doubled single-mode Nd:YAG laser (Quantel YG:981E) emitting radiation at 532 nm with a pulse repetition rate of 10 Hz. The total energy of the fs pulse was 14 µJ and that of the probe pulse was 11 mJ (averaged over 500 shots). The excitation pulses and the probe pulse were focused into a rectangular gas cell with small open slots on opposite sides, using a lens of focal length f = 200 mm. To achieve optimum phase-matching and consequently larger effective spectral bandwidth for the excitation pulses, the angle between the fs and ns pulses was chosen to be as small as 5° [30].
Since the signal follows the probe beam in this phase-matching scheme, the probe pulse was collimated using a lens with focal length f = 250 mm and separated from the signal by a linear polarizer and a short-pass filter (Semrock, Razor edge, 561 nm). The signal was then guided into a 1-meter Czerny–Turner-type spectrograph fitted with a holographic grating with 2400 grooves/mm, dispersing the signal spectrally, before the spectrum was detected by a streak camera (Optronis, Optoscope). The streak rate was chosen to be 100 ps/mm, resulting in temporal dispersion of 1.4 ps/pixel. The laser pulses and the streak camera were synchronized using pulse/delay generators resulting in 45 ps temporal jitter (root mean square) calculated from 300 single shots.
For flame measurements, the gas cell was replaced by a water-cooled stainless-steel porous plug burner (McKenna). The burner contains a central porous plug of diameter 6 cm, which was fed with a mixture of methane/air with equivalence ratio 1.1 whereas the co-flow was fed with nitrogen. A stabilizer was used above the burner, and the probe volume was placed close to the stabilizer at a height of ∼2.3 cm above the burner at the center.
4. Results and discussion
4.1 Species-selective spectral amplification
As a first step in further development of IQC-RCARS, we demonstrated amplification, which is a complement to the spectral annihilation we demonstrated earlier. The coherent Raman response generated by the pump and control pulses with a delay between them of δt = Trev will be in phase [see Fig. 1(b)] and, hence, their corresponding CARS polarizations interfere constructively, amplifying the signal intensity. This is clear from Eq. (9) where two identical Raman responses lead to an amplification of almost a factor of four, with a small reduction caused by collisional dephasing of the coherences. Figure 3 contains an illustration of this amplification process. The dark blue and dotted green curves are individual RCARS spectra of pure N2 with a delay of δt = 8.38 ps (i.e. full rotational revival period of nitrogen). The spectra were recorded at room temperature and atmospheric pressure and averaged over 100 single shots. Considering the temporal resolution of ∼20 ps, all spectrograms were integrated temporally from t1 = 28 ps to t2 = 120 ps, to avoid the non-resonant signal and the contribution of the single pump pulse excitation before arrival of the second control pulse. The red curve in Fig. 3 is the corresponding IQC-RCARS spectrum of the total CARS signal, which exhibits an amplification of around a factor of four. Both the intensity and shape of the IQC-RCARS spectrum were predicted well by the theoretical model, shown with a dotted-black curve that was normalized by the calculated single-pulse excitation RCARS spectrum. The experimental spectra were also normalized by the first N2 signal (the dark blue curve).
Fig. 3. Experimentally recorded rotational CARS spectra of pure N2 with single excitations at time zero (blue curve) and δt = Trev = 8.38 ps (dashed green curve). The interference of these two signals is constructive resulting in amplification of the IQC spectrum shown by red curve. The theoretically calculated spectrum (dashed-black curve) is in good agreement in both spectral shape and strength.
Owing to the dependence of Trev on molecular mass, signal amplification is species specific. However, amplification of the targeted species perturbs the coherences of other species in the mixture (similar to species-selective signal annihilation demonstrated in our recent work [23]), which emphasizes the importance of a reliable theoretical model.
An important application of species-selective signal amplification with IQC-RCARS is in the field of reacting-flow diagnostics, where the temperature can reach 2000K and more. In such cases, the major remaining species with a significant Raman cross section is usually N2, because it is inert. The CARS signal intensity is proportional to the square of the number density (i.e. N2). Since number density decreases at elevated temperatures, the CARS signal intensity drops considerably for hot media. Increasing the fs-pump-pulse energy to compensate for this signal loss, however, might lead to strong-field perturbations such as ionization [31], AC Stark effects [19], and a laser-induced non-thermal population distribution [28]. Therefore, utilizing a train of low-energy ultrafast pulses with delays corresponding to species-selective amplification is an alternative solution for good amplification while avoiding possible strong-field perturbations. Moreover, it is important to note that the linewidths of RCARS and the corresponding IQC-RCARS transitions were found to be the same, which promises application of IQC-RCARS to linewidth measurements for studying the collisional effects of molecular species in mixtures.
4.2 Spectro-temporal interferogram of IQC-RCARS
It is possible to deepen understanding of the pump/control excitation process and to confirm further the fidelity of the model by studying an experimental spectro-temporal interferogram. The IQC-RCARS signal is a periodic function of the pump-control delay, δt, as shown in Eq. (8). Thus, any delay less than δt = Trev results in a unique IQC spectrum. To investigate this phenomenon, δt was changed from 100 fs to 9.98 ps with a step of 100 fs and the corresponding IQC-RCARS spectra were mapped as a function of variable δt. Here, this map is called an “interferogram”. The theoretical and experimental results of this mapping are depicted in Fig. 4(a) and (b), respectively, where the spectro-temporal interferograms are in very good agreement.
Fig. 4. (a) Theoretically prepared spectro-temporal mapping of IQC-RCARS spectra with respect to pump-control pulse delay, δt, by a step of 100 fs and (b) corresponding experimental data. The red vertical dashed lines indicate special spectra at δt1 ≈ 2.01 ps (1/4 Trev) for selective nuclear-spin-isomer excitation, δt2 = 4.19 ps (1/2 Trev) for species-selective signal annihilation, and δt3 = 8.38 ps (Trev) for species-selective signal amplification.
The fs-pulse energy was monitored during 500 single shots, in which a maximum variation of ±7% was observed. This intensity variation had a negligible effect on the IQC-RCARS spectrogram and thus, was not compensated for in preparing Fig. 4(b). As evident in Fig. 4, each transition plotted vs δt is periodic with a certain frequency. This behavior was predicted and explained in the discussion following Eq. (9). The frequency of each transition in the IQC-RCARS interferogram should reflect the actual frequency of the induced transition dipole moments. This is shown in Fig. 5(a), where three transitions (integrated across the spectral line shape) from the IQC-RCARS interferogram in Fig. 4(b) are selected and shown by blue, red, and green curves for transitions FJ4→6, FJ5→7, and FJ6→8, respectively. The dashed black curves are the best first-order sinusoidal fit functions to each of the curves. The derived wavenumbers from the fits are 43.8126 (±0.20) cm-1, 51.719 (±0.21) cm-1, and 59.6947 (±0.13) cm-1, respectively. These values are strikingly close to the theoretically calculated transition wavenumbers (Bohr frequencies) of 43.7386 cm-1, 51.619 cm-1, and 59.6663 cm-1, respectively. However, even higher accuracy might be achieved by choosing shorter pump-control delay than δt = 100 fs in this experiment.
Fig. 5. (a) Spectrally integrated transitions from the IQC map in Fig. 4(b) showing temporal oscillations of the coherent transitions FJ4→6 (blue curve), FJ5→7 (red curve), and FJ6→8 (green curve). The dashed black curves are the best first order-sinusoidal fit functions to each of the curves. (b) Spectral integration of the IQC interferogram in Fig. 4(b) (blue curve), and real part of the theoretically calculated stimulated Raman response by one-pulse excitation (dashed black curve).
To further investigate the periodic nature of the IQC-RCARS coherences, the interferogram of Fig. 4(b) was spectrally integrated and depicted in Fig. 5(b) with the blue curve. The result is also compared with the theoretical prediction by Eq. (10), shown by the dashed-black curve. Interestingly, as apparent from Fig. 1(c), the 20-ps temporal resolution of the detection system is not high enough to resolve the rotational recurrences during the decays of the coherences captured by the streak camera. However, Fig. 5(b) and Eq. (10) demonstrate that the revival pattern of the Raman response [Fig. 1(b)] can be retrieved from the interferogram of Fig. 4(b).
One significance of the IQC-RCARS interferogram presented in Fig. 4 is that it suggests the possibility to shape spectra favoring a specific application. For instance, by choosing a specific δt, a spectrum can be generated that does not include contributions from a specific transition. This ability could enable a variety of applications for diagnostics in reacting flows, and in quantum information technology. One example would be to choose a pump-control delay of δt1 at around 1/4 Trev indicated with vertical dashed line in Fig. 4(a). This line does not cross transitions with an odd rotational ground state. Thus, the resulting spectrum includes only the even transitions, as shown in Fig. 6, which is in very good agreement with the theoretical prediction.
Fig. 6. Experimentally recorded IQC spectrum of N2 at pump-control pulse delay time of δt1 ≈ 2.1 ps (blue curve), and the theoretical calculation (black dashed curve).
In nitrogen, odd and even transitions have different nuclear-spin degeneracies of 3 and 6, respectively. Thus, such a spectral selection process has been referred to as nuclear-spin-isomer selective excitation [32].
In reacting-flow diagnostics, this particular IQC-spectral selection could be very useful for studies of high-pressure media. In hybrid fs/ps RCARS (a standard laser-based method for temperature measurements in reacting flows), the spectral resolution is often limited by the bandwidth of the transform-limited ps-probe pulse. In these experiments, probing at delays shorter than the mean-free-time of molecules (few ps), allows detection in a collision-free regime, hence simplifying interpretation of the recorded spectra. However, at elevated pressures, the mean-free time becomes shorter, requiring shorter probe pulses for collision-free detection. In addition, it is desirable to avoid temporal overlap of the excitation and probe pulses to circumvent contribution of the non-resonant signal. Utilizing short transform-limited ps pulses for probing also degrades the spectral resolution and thus, increases the uncertainties for quantified evaluations [33]. Therefore, by doubling the line spacing to ΔF = 8B, the IQC-RCARS spectrum in Fig. 6 offers a practical solution to challenges caused by low-spectral resolution, especially, for detection of heavier molecules with smaller B constants and, consequently, shorter line spacing such as CO2.
4.3 IQC-RCARS measurement at elevated temperatures
At elevated temperatures, higher angular momentum states are thermally occupied, leading to a more prominent effect of the centrifugal distortion constant D (∼10−5 cm-1) on the rotational energies F, where F = BJ(J + 1) - DJ2(J + 1)2. This affects the frequency of the transitions ΔωJ;J + 2 and perturbs the periodicity of the Raman response in Eq. (3), which in turn might affect efficiency of IQC-RCARS signal annihilation corresponding to δt2, and amplification at δt3 in Fig. 4. Therefore, to investigate this effect, the IQC-RCARS interferogram of N2 was theoretically calculated at a relatively high temperature of T = 1500 K, as presented in Fig. 7(a), in addition to an IQC spectrum cut out at δt3 = Trev (red curve in Fig. 7(b)), and a single-excitation RCARS spectrum at the same temperature (black curve) for comparison. However, to quantify the effects of the D constant over wide range of high temperatures, rigorous experimental investigation under controlled condition utilizing fs pulses with broader spectral bandwidths is required.
Fig. 7. (a) Theoretically calculated IQC-RCARS interferogram of N2 at T = 1500 K, and (b) spectrum cut out at δt3 = Trev for signal amplification (red curve) compared to a single-excitation RCARS spectrum (dashed black curve) at the same temperature.
As shown in Fig. 7(a), the vertical dashed line at δt2 associated with signal annihilation still does not cross the transitions. Moreover, from Fig. 7(b), the amplification factor at δt3 is close to four, i.e., similar to the result displayed in Fig. 3 for room temperature. However, a closer look at Raman shifts higher than 225 cm-1 reveals a minor effect of centrifugal distortion on IQC amplification efficiency, at this particular temperature.
Furthermore, to demonstrate the potential of IQC-RCARS amplification for temperature evaluation in reacting flows, spectra were recorded in a one-dimensional air/methane flame. The probe volume was placed above a McKenna burner at a height of ∼2.3 cm, close to a flame stabilizer. The recorded spectra were averaged over 300 single shots and integrated temporally between 28 ps and 120 ps.
The blue and green-dotted curves in Fig. 8 are recorded RCARS spectra with single-pulse excitation. The excitation pulses had a relative time separation of δt = 8.38 ps, corresponding to the IQC-signal amplification of N2, shown by the red curve. The measurement was performed in the product gases with N2, CO2, H2, and H2O expected to be the major species of which, only the N2 lines were observed in all the three recoded spectra. The amplification factor for the amplified spectrum in Fig. 8 is less than what was predicted theoretically in Fig. 7(b). The reason for this discrepancy lies in collisional dephasing of the coherences. Rotational coherences of particular species decay at different rates depending on the energy of transition, pressure, temperature, and the composition of the collider species. These decay rates are inversely proportional to the Raman linewidths, ΓJ in Eq. (3) [19]. The spectrum in Fig. 7(b) is prepared considering only self-broadening of N2 molecules, i.e., ΓN2-N2. However, N2 molecules in Fig. 8 interact with other collider partners increasing the collision rate, especially collisions with H2O and H2 [34]. Thus, N2 coherences dephase faster in the flame relative to pure N2, lowering the efficiency of amplification.
Fig. 8. Experimentally recorded rotational CARS spectra of pure N2 with single excitations at time zero (blue curve) and δt = Trev = 8.38 ps (dashed green curve). The amplified spectrum from the flame (red curve) and the best theoretical fit (dashed black curve) gives a temperature of 1563 K.
For successful modelling of IQC-RCARS spectra, prior knowledge of the variables affecting the linewidths is necessary, such as the composition of the collider species and their molar fractions [26,34]. However, simultaneous access to both temporal and spectral domain in hybrid-fs/ns approach for detection, allows extraction of linewidth information experimentally, without a priori knowledge of mixture composition. Thus, temperature evaluation of the IQC spectrum in Fig. 8 (red curve) was done using this unique advantage of the technique based on spectral fitting explained in detail elsewhere [20]. The best theoretical fit is shown in Fig. 8 by the dashed-black curve, and the evaluated temperature was 1563 K. Figure 8 is a demonstration of thermometry using fs/ns IQC-RCARS amplification. More thorough quantified investigation of such thermometry and species detection is needed to compare the accuracy and precision of the technique to alternative approaches. Such investigations will be presented in a forthcoming paper.
5. Conclusion
In this work, using theoretical and experimental evidence, we have demonstrated a new generation of non-linear ultrafast laser spectroscopy for diagnostics in practical environments such as reacting flows. The technique is based on engineered interference of two quantum wavepackets generated by the RCARS process. The wavepackets are coherent rotational Raman responses to two transform-limited fs pulses, here called pump and control, with variable relative time delay, δt, and they are probed by a single-mode ns laser. The signal is dispersed by a spectrometer and detected by a streak camera; a combination that resolves the signal, simultaneously, in the spectral and temporal domains. Thus, by exploiting the time domain while varying the delay between the pump and control pulses, similar to a Mach–Zehnder interferometer, the shape of the resulting spectra can be controlled and manipulated, optimizing the diagnostic for a specific application.
A theoretical model, which predicts the experimental IQC-RCARS spectra very well was presented in detail. Moreover, a spectro-temporal IQC interferogram of N2 was measured experimentally by varying the pump-control pulse delay at room temperature, and the result is in excellent agreement with the theoretical prediction. The importance of preparing the IQC-RCARS interferogram is that it shows that unique spectra can be generated by varying the pump-control time delay to meet the needs of a specific application. Three important examples were demonstrated, namely species-selective signal annihilation (δt = 1/2 Trev) and amplification (δt = Trev), and nuclear-spin isomer selection (δt ≈ 1/4 Trev). It was shown experimentally and theoretically that a pump-control delay of 1/4 Trev results in an IQC-spectrum including only the rotational transitions corresponding to even rotational states. For such spectra, the distance between adjacent spectral lines is doubled, facilitating experiments with degraded spectral resolution, such as studies in high-pressure environments.
IQC-RCARS, amplification of N2 coherences was demonstrated at a pump-control delay of δt = Trev for both room temperature and inside a one-dimensional flame (a practical and more complex flow), where the temperature was evaluated to be around 1500 K. The amplification factor was found to be about four, with slightly less efficiency inside the flame owing to extra collisional dephasing of N2 coherences interacting with other colliding partners such as H2O and H2. An advantage of IQC amplification is the low pulse energy requirement for excitation pulses, avoiding possible signal perturbations caused by strong-field effects such as Stark splitting, ionization, and non-equilibrium population re-distribution over the rotational states, induced by the fs-laser field. Moreover, although this work was based on hybrid fs/ns RCARS detection, as it was explained in the discussion followed by Eq. (6), similar results can be achieved by utilizing a fs/ps RCARS approach. The promising results presented in this work motivate further investigation to determine the accuracy and precision of IQC-RCARS for temperature evaluation and species detection in real time, as well as possible applications in quantum information technology.
Funding
Laserlab-Europe (871124); Stiftelsen för Strategisk Forskning (ITM17-0309); Vetenskapsrådet (2019-03601, 2022-06155).
Acknowledgments
The authors would like to thank the funding agencies mentioned above for financial support and Dr. Andreas Ehn and Prof. Stefan Kröll for helpful discussions.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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