Considerations in upconversion: A practical guide to sum-frequency generation spectrometer design and implementation

A. Light–matter interactions

To start, we must understand the basics of linear and nonlinear light–matter interactions, of which we will only briefly and qualitatively describe. A more comprehensive description of these phenomena can be found in accompanying articles in this tutorial series.1,21. J. D. Pickering, M. Bregnhøj, A. S. Chatterley, M. H. Rasmussen, S. J. Roeters, K. Strunge, and T. Weidner, Biointerphases 17, 011202 (2022). https://doi.org/10.1116/6.00014032. J. D. Pickering, M. Bregnhøj, A. S. Chatterley, M. H. Rasmussen, K. Strunge, and T. Weidner, Biointerphases 17, 011201 (2022). https://doi.org/10.1116/6.0001401 Consider first an electromagnetic field energetically defined by the wavelength of light (or frequency); for the sake of vibrational SFG spectroscopy, we will work in the short-, mid-, and long-infrared (IR) spectral regions (∼2.5 μm to ∼15 μm or ∼4000 cm−1 to ∼667 cm−1) though the concepts are the same regardless of the spectral region. If light from our IR source is resonant with a transition frequency of a molecular target, that is to say, matches the energy gap between the ground and excited vibrational states, one can induce a polarization in the target material (e.g., a nonequilibrium charge distribution, not to be confused with the polarization state of light) that oscillates at the driving frequency of the light. This driven polarization, in turn, can radiate light at the same frequency but out of phase with the incident light field. The radiated light, therefore, destructively interferes with transmitted light resulting in attenuation at the resonant wavelength.3–53. P. Hamm and M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University, Cambridge, 2011).4. L. Velarde and H.-F. Wang, Phys. Chem. Chem. Phys. 15, 19970 (2013). https://doi.org/10.1039/c3cp52577e5. P. Kukura, D. W. McCamant, and R. A. Mathies, Annu. Rev. Phys. Chem. 58, 461 (2007). https://doi.org/10.1146/annurev.physchem.58.032806.104456 This is the phenomenon of linear light absorption. We note however that induced polarization can also contribute to absorption through the generation of heat, but this is not essential to the discussion below.Extending to nonlinear spectroscopies, which arise from multiple light–matter interactions with the same molecular species, we note that an interaction of a single optical field with material creates a coherent superposition between the ground and excited state(s).3–53. P. Hamm and M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University, Cambridge, 2011).4. L. Velarde and H.-F. Wang, Phys. Chem. Chem. Phys. 15, 19970 (2013). https://doi.org/10.1039/c3cp52577e5. P. Kukura, D. W. McCamant, and R. A. Mathies, Annu. Rev. Phys. Chem. 58, 461 (2007). https://doi.org/10.1146/annurev.physchem.58.032806.104456 This superposition is known as a coherence that oscillates and decays (dephases) on a timescale related to the energy difference between the states and the natural linewidth of the transition as plotted in Fig. 1. This decay is known as a free-induction decay (FID), analogous to that commonly found in nuclear magnetic resonance (NMR) spectroscopy. If left alone, the molecules relax to their unperturbed distributions, and the driving optical fields are attenuated in the usual sense for linear spectroscopy. However, if using an intense light source, one can induce a polarization that oscillates, and therefore generates light, at twice the incident frequency.66. K. B. Eisenthal, Chem. Rev. 106, 1462 (2006). https://doi.org/10.1021/cr0403685 This is the phenomenon of second-harmonic generation (SHG).77. K. B. Eisenthal, Annu. Rev. Phys. Chem. 43, 627 (1992). https://doi.org/10.1146/annurev.pc.43.100192.003211 Similarly, third, fourth, and other high-order harmonics can readily be generated through the interaction of a single beam of intense light with molecules and materials.In an analogous way, the introduction of two different optical fields with different frequencies can create a second-order polarization that oscillates at the sum- and difference-frequencies of the input fields.88. Y. R. Shen, Fundamentals of Sum-Frequency Spectroscopy (Cambridge University, Cambridge, 2016). Given these induced polarizations oscillate at different frequencies, new colors of light are generated based on the frequencies chosen for the incident beams. As discussed in other articles in this tutorial series,1,21. J. D. Pickering, M. Bregnhøj, A. S. Chatterley, M. H. Rasmussen, S. J. Roeters, K. Strunge, and T. Weidner, Biointerphases 17, 011202 (2022). https://doi.org/10.1116/6.00014032. J. D. Pickering, M. Bregnhøj, A. S. Chatterley, M. H. Rasmussen, K. Strunge, and T. Weidner, Biointerphases 17, 011201 (2022). https://doi.org/10.1116/6.0001401 SFG and other even order spectroscopies are surface specific since, on average, the radiated light from randomly oriented bulk molecules destructively interferes due to differences in the optical phase. Notably, one can extend the number of light–matter interactions beyond second order to third order (e.g., transient absorption or multidimensional spectroscopies, coherent anti-Stokes Raman scattering, stimulated Raman scattering, etc.), fourth-order (e.g., pump-probe SFG, multidimensional SFG, etc.), and even higher-orders depending on the scientific questions one wants to address. Those of even-order are generally considered to be surface specific due to symmetry, whereas those of odd-order tend to be dominated by the bulk response due to the difference in number densities of surface species vs those in the bulk. The remainder of this review will focus on second-order spectroscopies though concepts of upconversion pulses and associated pulse shaping methods that can be found throughout the diverse field of nonlinear spectroscopy and microscopy, making the ideas presented here apply to a variety of fields beyond SFG.

B. Time vs frequency domain measurements

Although light from any source can be used in a linear absorption experiment, nonlinear light–matter interactions necessitate pulsed light fields with high peak intensities. This has the benefit of providing large signals, but the drawbacks in that classical light sources are subject to time-frequency Fourier relations. Specifically, the time-bandwidth product is given by ΔtΔω ≥ const., where Δω is the spectral bandwidth, Δt is the pulse duration, and the constant depends on the shape of the pulse in time; for a Gaussian pulse shape, this value is taken to be 0.44. This equation simply states that if one wants to obtain high temporal resolution (short pulses) the spectral bandwidths must be correspondingly large. This, on first inspection, might doom aspirations of probing species in a chemically selective manner using pulsed light sources; however, there are tricks one can play regarding how the prepared coherences are “read off” using additional pulses of light.4–54. L. Velarde and H.-F. Wang, Phys. Chem. Chem. Phys. 15, 19970 (2013). https://doi.org/10.1039/c3cp52577e5. P. Kukura, D. W. McCamant, and R. A. Mathies, Annu. Rev. Phys. Chem. 58, 461 (2007). https://doi.org/10.1146/annurev.physchem.58.032806.104456Recall that the IR pulse used in SFG experiments creates coherence in the sample, which undergoes an FID following the first light–matter interaction as sketched in Fig. 1. We note that the use of a broadband, femtosecond IR pulse, which is an increasingly popular approach, can excite many vibrational modes at the same time. This results in an FID that oscillates at many frequencies that decay over different coherence lifetimes. The addition of a second laser pulse can then generate the needed second-order polarization for SFG experiments. This results in the generation of a burst of light (e.g., SFG) that depends on the instantaneous delay between the molecular FID and the upconversion pulse (sketched in Fig. 1, denoted by Δt for a representative pulse shape). At any given delay, assuming the use of femtosecond pulses, the spectral width of the radiated SFG is broad and the temporal width is short. As such, for a single delay between the IR and upconversion pulse, the radiated light only maps part of the FID (Fig. 1) that is temporally overlapped. If instead the FID is mapped in time by scanning the delay between the femtosecond IR and upconversion pulses and detected in a phase-sensitive manner,99. J. E. Laaser, W. Xiong, and M. T. Zanni, J. Phys. Chem. B 115, 2536 (2011). https://doi.org/10.1021/jp200757x the Fourier transform of the time-dependent signal will yield a spectrum. This is because the radiated light at any given delay describes the instantaneous FID response. The frequency resolution of this time-domain spectrum is limited by (1) the time-resolution and (2) the number of delays sampled between the two pulses, in an analogous way to Fourier transform IR (FTIR) spectroscopy. This is known as the time-domain approach to SFG spectroscopy.4,9,104. L. Velarde and H.-F. Wang, Phys. Chem. Chem. Phys. 15, 19970 (2013). https://doi.org/10.1039/c3cp52577e9. J. E. Laaser, W. Xiong, and M. T. Zanni, J. Phys. Chem. B 115, 2536 (2011). https://doi.org/10.1021/jp200757x10. J. A. McGuire, W. Beck, X. Wei, and Y. R. Shen, Opt. Lett. 24, 1877 (1999). https://doi.org/10.1364/OL.24.001877

In time-domain measurements, the shortest possible pulses are desirable and therefore the broadest possible bandwidths are essential to achieve adequate frequency resolution for chemical systems. The drawbacks of this method are that (1) scanning time-delays between pulses is slow, (2) it is difficult to make stable phase-sensitive measurements over the long measurement, (3) making/using temporally compressed (i.e., non-chirped) broadband pulses is tedious and dedicated instrumentation to optimize these parameters at the sample position are often necessary, and (4) spectral overlap of the SFG light with incident laser light frequencies, can make differentiating SFG signals from spurious light difficult using a single-pixel detector. As such, time-domain SFG spectral measurements are not commonly found in the literature; instead, a few convenient tricks discussed below can be played to generate spectra more quickly.

What if instead, we map the entire vibrational FID at once? To do that, one needs pulse widths that are much longer than the fs pulses used in time-domain approaches. This is because one needs to temporally overlap with as much of the FID as possible (see Fig. 1) so as to avoid attenuation by inadvertent (or unavoidable) apodization of the FID caused by the use of finite length upconversion pulses. This is to say, upconverting only a portion of the FID response will result in inaccurate and distorted spectral line shapes.4,9,114. L. Velarde and H.-F. Wang, Phys. Chem. Chem. Phys. 15, 19970 (2013). https://doi.org/10.1039/c3cp52577e9. J. E. Laaser, W. Xiong, and M. T. Zanni, J. Phys. Chem. B 115, 2536 (2011). https://doi.org/10.1021/jp200757x11. H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, Int. Rev. Phys. Chem. 24, 191 (2005). https://doi.org/10.1080/01442350500225894 At every point along the FID where the upconversion pulse is temporally overlapped with the FID, light is emitted. This has the effect of smearing out the time-domain response when using a long pulse, thus making the Fourier transformation of the time-domain signal contain very little chemical information—it just maps the cross-correlation between the two pulses. The cross-correlation simply describes the convolution of the two laser pulse widths as they are scanned across one another in time. This approach, however, has the somewhat hidden benefit of being able to use spectrally narrowband light in the upconversion pulse (recall the time-bandwidth product). In this case, the radiated SFG light is temporally broad (defined by the narrow band upconversion pulse width) and spectrally broad (defined by all the colors in the IR pulse)—this, at face value, should be the worst of both worlds: poor time and spectral resolution. However, when dispersed in a spectrometer, the individual frequency components are resolved, and when IR light is resonant, an enhancement in the SFG response is observed. Notably, the spectral resolution is limited in some cases by the upconversion spectral bandwidth as it is used to map the FID. In this way, one can make frequency multiplexed SFG measurements where all the frequency components are measured at once by using a broadband IR pulse, a narrowband upconversion pulse, and a multichannel detector.1212. L. J. Richter, T. P. Petralli-Mallow, and J. C. Stephenson, Opt. Lett. 23, 1594 (1998). https://doi.org/10.1364/OL.23.001594

The only factor limiting the spectral resolution, in this case, is the ability to measure the radiated light and the bandwidth of the upconversion pulses. However, this approach differs from ps-laser scanning systems, where the frequency of the IR light is tuned, and a spectrum is built from measurement at each input IR-frequency. Similarly, broadband systems can provide spectra over much shorter acquisition times as compared to time-domain measurements that rely on scanning a delay. In fact, broadband SFG systems can achieve a comparable spectral resolution to ps-scanning systems while operating at shorter acquisition times and risking less sample damage. Depending on tradeoffs of spectral and temporal resolutions, samples, etc. complete SFG spectra can be taken on the <10’s of ms timescales using conventional CCD cameras. Assuming a typical 1 kHz rep-rate amplified laser system, the complete spectral acquisition time corresponds to only a few tens to hundreds of laser shots. As such, broadband SFG methods provide a means to map chemical and physical changes in a system in real time with arbitrarily high spectral resolution. But again—how one generates the all-important upconversion pulse is key to the chemical and molecular insight one can obtain.

The general rule of thumb is that if one wants to upconvert the entire FID to obtain so called “accurate” line shapes, the pulse duration of the upconversion pulse should be several times longer than the dephasing time of the FID. Noting that maximal signal will arise from the exact temporal overlap of two Gaussian pulses at t = 0 ps, to cover the dephasing from a species with a 2.5 ps dephasing time a time-symmetric pulse of ∼12 ps at full width half maximum (FWHM) is needed (Fig. 1). This is nontrivial to generate with conventional femtosecond laser systems since most of the light in the upconversion pulse bandwidth is discarded in generating the spectrally narrow pulse! Furthermore, such a long pulse has a low peak intensity as compared to temporally shorter pulse widths and correspondingly so necessitates using much higher average laser powers to generate reasonable signal levels. High power upconversion pulses can be damaging to photochemically sensitive systems or limiting in studies of buried interfaces. Additionally, the shape of the upconversion pulse (be it a Gaussian, as shown, or something time asymmetric) has a profound effect on the spectral shapes since the intensity of the upconversion pulse at a given time along the FID has a weighting effect on that part of the FID response (see Fig. 1). As such, and as will be reiterated many times throughout this report, the selection of the upconversion pulse is all about compromises.

C. Selection of upconversion pulses for vibrational SFG spectroscopy

Now that we have motivated the need for careful selection of an upconversion pulse, we note again that the choice of upconversion pulse is system dependent and should be dictated by the scientific questions one wants to answer. For instance, if the interest is in understanding the packing and orientation of amphiphiles at an air/water interface in the context of surfactant research or atmospheric chemistry, measuring accurate line shapes with a high spectral resolution is probably the most important aspect to weigh. If accurate line shapes are essential, custom laser systems or time-domain SFG methods might represent the best choice. This might be important to the studies of gas–solid interfaces for catalysis or photochemical systems where science questions regarding subtle differences in binding need to be resolved. However, if studying species at metallic or semiconducting interfaces is of interest, such as electrode or semiconductor interfaces for energy storage applications then suppressing strong nonresonant contributions from the substrate might be emphasized, with sacrifices in resolution or line shape accuracy being a necessary trade-off. Probing buried interfaces for insight into chemical separations, polymer self-assembly, or applications in molecular electronics often requires flexibility in tuning pulse shapes quickly, reproducibly, and on-the-fly to capture kinetics or other nonequilibrium processes in time. All of these systems and associated questions necessitate different approaches to generating the upconversion pulses.

We begin here by discussing various “fixed modes” of operation, in that the upconversion pulse is designed to address specific types of interfaces or meet certain budgetary considerations. The pros and cons of each method are detailed and some particularly relevant examples of how these approaches yield new insight into specific systems are given. While, in principle, fixed operational modes can be swapped between using different optical pathways or through realignment/rebuilding optical paths, we show how a tunable pulse shaper can provide a means to tune the upconversion pulse on the fly to meet experimental needs for a range of interfaces.

D. Filters and monochromators

The most obvious way to reduce the spectral bandwidth of a broadband pulse is to simply filter out the frequencies one does not want. This can be accomplished by inserting one or more colored filters into one arm of an SFG spectrometer [Fig. 2(a)]. The transmitted light will have frequency components attenuated, making the resulting pulse broaden in time and narrow in frequency. This is by far the most straightforward means to generate narrowband light from a broadband source. Indeed, the development of filters has improved dramatically with the advent of multiphoton microscopies, with spectral edges becoming ever-sharper over an increasingly tunable range. However, these improvements also point out the limitations of a filter-based system: one is at the mercy of the filter bandwidth and central wavelength. For conventional femtosecond Ti: sapphire laser systems, the upconversion pulse is typically centered around 800 nm. To achieve a modest resolution of ∼12.5 cm−1, one needs to generate a pulse with ∼0.8 nm of bandwidth at FWHM. To our knowledge, such a filter does not exist. Instead, one must stack filters to build an effective narrowband filter. Due to variations in the filter cut-on wavelengths, it is not guaranteed that a stacked set of filters would meet bandwidth requirements in a reliable or predictable way. Furthermore, absorptive filters tend to damage easily with the light levels of light sent through them (ideally several watts of average power are dedicated to the upconversion arm). Similarly, the absorptive properties of the filter itself can change due to saturation effects. Reflective filters have an often-hidden side effect forcing one to deal with the rejected light in a safe manner or in negatively impacting beam modes. As such, while convenient to implement and somewhat low cost (high-performance sharp edge filters can cost several thousand USD each), the ambiguity in outcome generally dissuades researchers from using filters beyond the initial setup.Early work on broadband SFG methods used a monochromator to spectrally narrow the output spectrum.1212. L. J. Richter, T. P. Petralli-Mallow, and J. C. Stephenson, Opt. Lett. 23, 1594 (1998). https://doi.org/10.1364/OL.23.001594 Indeed, a monochromator serves to disperse wavelengths in space—selecting one portion of the dispersed light to generate a narrow bandwidth [sketched in Fig. 2(b)]. The limiting factor here is that the monochromator effectively disassembles the pulse in time and spreads frequency components across spatial locations (spatial chirp). This means that the different colors of light transmitted through the slit travel different paths and each wavelength has its own temporal characteristics. As such, a monochromator provides a means to generate narrowband light, but it does so with added challenges related to chirp (spatial and otherwise). Recently, the seemingly deleterious effect of spatial chirp following dispersion has been used to generate narrowband pulses while simultaneously providing spatial information of the sample by imaging the frequency-resolved light onto a CCD camera.1313. H. Li, Y. Zhao, Y. Li, and W.-T. Liu, Opt. Lett. 46, 54 (2021). https://doi.org/10.1364/OL.410335 As we will discuss later, pulse shapers, which bear a resemblance to monochromators, provide a means to carefully adjust the spectral and temporal properties of a broadband light source and reassemble them into well-defined pulses.

E. Etalons and time-asymmetric pulse shapes

A Fabry−Pérot etalon is an optical component consisting of parallel windows separated by a medium that is usually air. When light is incident on the etalon the light transmitted through the front face undergoes many reflections between the two air-spaced surfaces, effectively forming a cavity. Depending on the alignment of the etalon with respect to the incident beam, different wavelengths of light will destructively interfere within the cavity whereas light that does not interfere will eventually pass through the second reflector with a time-dependence that is asymmetric, e.g., an exponential like decay. This is shown in Fig. 3, where the multiple round trips and finite probability of transmitting light through the second reflector result in a ring-down like effect depending on spacing. As such, by defining the surface quality of the parallel surfaces, the spacing between the surfaces, and the wavelength range of interest, one can use an etalon to both tune and narrow the central wavelength of a laser source as well as simultaneously generate time-asymmetric pulses with Lorentzian-like spectral line shapes.The use of an etalon in SFG measurements was originally reported by Dlott and co-workers1414. A. Lagutchev, S. A. Hambir, and D. D. Dlott, J. Phys. Chem. C 111, 13645 (2007). https://doi.org/10.1021/jp075391j and revolutionized broadband SFG measurements in that pulse shapers (discussed below) could be avoided in favor of a single optical element. Furthermore, since the time-domain shape of the outgoing pulse is asymmetric (the Fourier transform of a Lorentzian spectral line shape leads to exponential decay in time), one can play tricks with the temporal overlap of the upconversion pulse with the FID to suppress undesirable nonresonant contributions and enhance signatures from molecular species. In this regard, Dlott and co-workers showed how the time-asymmetry in the upconversion pulse could be used to suppress the short-lived nonresonant response of a metallic substrate,1414. A. Lagutchev, S. A. Hambir, and D. D. Dlott, J. Phys. Chem. C 111, 13645 (2007). https://doi.org/10.1021/jp075391j illustrated in Fig. 3(b), which decays on a few tens to hundreds of fs timescales while enhancing signals arising from the longer-lived vibrational coherences of the molecular species. In the case of a time-symmetric pulse, the nonresonant response dominates near t = 0 fs and results in a strong contribution that resembles the spectral shape of the driving IR laser bandwidth with resonances appearing via interference (dips) due to differences in phase [Fig. 3(b), inset].1515. A. G. Lambert, P. B. Davies, and D. J. Neivandt, Appl. Spectrosc. Rev. 40, 103 (2005). https://doi.org/10.1081/ASR-200038326 The use of a delayed time-asymmetric pulse in Fig. 3(b) (red trace), suppresses the electronic coherence contribution of the substrate in favor of generating signals from interfacial species. This has the positive effect of turning signals that appear as dips into positive-going peaks that are generally free from complicating nonresonant contributions.Building on this work, Stolow and co-workers proposed a “reverse” etalon-like pulse shape capable of enhancing signals from the molecular species by providing higher instantaneous peak powers at longer delay times with less power at early times.1616. C. Weeraman, S. A. Mitchell, R. Lausten, L. J. Johnston, and A. Stolow, Opt. Express 18, 11483 (2010). This is sketched in Fig. 4 and shows that by generating a time-asymmetry via frequency doubling in a thick nonlinear optical crystal one should be able to enhance the signals from long-lived FID components and suppress nonresonant contributions. Analysis of the effects on associated line shapes has shown that the use of time-asymmetric pulses, while convenient, inevitably distorts the line shape due to the convolution of the FID with that of the time-asymmetric pulse.9,17,189. J. E. Laaser, W. Xiong, and M. T. Zanni, J. Phys. Chem. B 115, 2536 (2011). https://doi.org/10.1021/jp200757x17. F. Y. Shalhout, S. Malyk, and A. V. Benderskii, J. Phys. Chem. Lett. 3, 3493 (2012). https://doi.org/10.1021/jz301443718. A. D. Curtis, S. R. Burt, A. R. Calchera, and J. E. Patterson, J. Phys. Chem. C 115, 11550 (2011). https://doi.org/10.1021/jp200915z For instance, etalon pulses result in artificially broader line widths than the intrinsic response. Compounding this effect, it was found that for large intrapulse delays, severe differences in spectral phase manifest in the case of multiple resonances—making conclusions that one can draw about orientation potentially incorrect if not considered carefully. On the other hand, the reverse etalon results in intensity dip before and after the central resonance and consequently leads to artificially narrow apparent widths. These differences can complicate fitting and analysis of the resulting spectrum if not considered.While powerful in suppressing nonresonant contributions, this approach has gained a tremendous following in the study of other interfaces as well due to its simplicity. For instance, several groups use etalons in SFG spectrometers to study polymers,1919. U. I. Premadasa, N. M. Adhikari, and K. L. A. Cimatu, J. Phys. Chem. C 123, 28201 (2019). https://doi.org/10.1021/acs.jpcc.9b07816 air/aqueous interfaces,20–2220. L. Lin, J. Husek, S. Biswas, S. M. Baumler, T. Adel, K. C. Ng, L. R. Baker, and H. C. Allen, J. Am. Chem. Soc. 141, 13525 (2019). https://doi.org/10.1021/jacs.9b0523121. S. E. Sanders and P. B. Petersen, J. Chem. Phys. 150, 204708 (2019). https://doi.org/10.1063/1.507858722. S. J. Roeters et al., Nat. Commun. 12, 1183 (2021). https://doi.org/10.1038/s41467-021-21349-3 nanoscopic oil droplets,2323. M. J. Foster, A. P. Carpenter, and G. L. Richmond, J. Phys. Chem. B 125, 9629 (2021). https://doi.org/10.1021/acs.jpcb.1c05508 where nonresonant contributions are already low, but in view of the intermediate cost or simplicity in spectrometer design. The design of the etalon itself has also been shown to allow for multiplexed measurements using two simultaneously selected spectral regions.2424. I. G. Prichett and A. M. Massari, Opt. Lett. 43, 4747 (2018). https://doi.org/10.1364/OL.43.004747 Similarly, stacking etalons can improve spectral resolution in SFG imaging applications.2525. C. M. Lee, K. Kafle, S. Huang, and S. H. Kim, J. Phys. Chem. B 120, 102 (2016). https://doi.org/10.1021/acs.jpcb.5b10290

F. Bespoke laser systems

Long time-symmetric pulses do a surprisingly good job at reproducing the spectral line shapes, with only a slight broadening in the profile.99. J. E. Laaser, W. Xiong, and M. T. Zanni, J. Phys. Chem. B 115, 2536 (2011). https://doi.org/10.1021/jp200757x Given the discussion of filters above, we recall that selecting a narrow bandwidth of light from a broadband laser pulse necessarily results in throwing away much of the power available for upconversion. This sets a limit on how a narrow band pulse can be while still being able to generate SFG at reasonable count rates. What if instead, one used separate laser systems to generate the broadband IR pulse and the narrowband upconversion pulse?This approach was pioneered by Velarde and co-workers,2626. L. Velarde, X.-Y. Zhang, Z. Lu, A. G. Joly, Z. Wang, and H.-f Wang, J. Chem. Phys. 135, 241102 (2011). https://doi.org/10.1063/1.3675629Y. where they used a custom synchronized and seeded laser system to independently generate broadband IR and very narrow band upconversion pulses. Their first report demonstrated a means to resolve different local chemical environments for “identical” functional groups on the same molecule at an air/dimethyl sulfoxide (DMSO) interface using a ∼87 ps upconversion pulse (spectral bandwidth of 0.6 cm−1).2626. L. Velarde, X.-Y. Zhang, Z. Lu, A. G. Joly, Z. Wang, and H.-f Wang, J. Chem. Phys. 135, 241102 (2011). https://doi.org/10.1063/1.3675629Y. Through the interference of resonances that were fit in the SFG spectrum, which can only be resolved at sub-cm−1 resolution, they were able to infer how one methyl group on DMSO pointed more into the subphase, whereas the other “identical” methyl group pointed more into the air. The subtle difference in the local chemical environment resulted in a small spectral shift of 2.78 ± 0.07 cm−1. This work has been built upon in the studies of interfaces, both idealized and complex,2727. R. Zhang, X. Peng, Z. Jiao, T. Luo, C. Zhou, X. Yang, and Z. Ren, J. Chem. Phys. 150, 074702 (2019). https://doi.org/10.1063/1.5066580 and in the development of heterodyne-detected high-resolution broadband SFG systems capable of directly probing up vs down orientations of molecular chromophores,2828. L. Fu, S.-L. Chen, and H.-F. Wang, J. Phys. Chem. B 120, 1579 (2016). https://doi.org/10.1021/acs.jpcb.5b07780 and chiral SFG responses,2929. X.-H. Hu, L. Fu, J. Hou, Y.-N. Zhang, Z. Zhang, and H.-F. Wang, J. Phys. Chem. Lett. 11, 1282 (2020). https://doi.org/10.1021/acs.jpclett.9b03470 to name a few examples. This approach has been adopted by other groups as well seeking to push the limit of spectral resolution to obtain accurate line shapes in the context of catalysis.30,3130. R. Zhang, J. Dong, T. Luo, F. Tang, X. Peng, C. Zhou, X. Yang, L. Xu, and Z. Ren, J. Phys. Chem. C 123, 17915 (2019). https://doi.org/10.1021/acs.jpcc.9b0591631. T. Luo, R. Zhang, W.-W. Zeng, C. Zhou, X. Yang, and Z. Ren, J. Phys. Chem. C 125, 8638 (2021). https://doi.org/10.1021/acs.jpcc.1c02418 Recent reports also combine the dual-laser method with further spectral narrowing and time-asymmetry using etalons.2727. R. Zhang, X. Peng, Z. Jiao, T. Luo, C. Zhou, X. Yang, and Z. Ren, J. Chem. Phys. 150, 074702 (2019). https://doi.org/10.1063/1.5066580 Similar concepts have been reported using compact fiber laser sources.3232. K. Madeikis, R. Kananavicius, R. Danilevicius, A. Zaukevicius, R. Januskevicius, and A. Michailovas, Opt. Express 29, 25344 (2021). https://doi.org/10.1364/OE.433617The high resolution afforded by this approach allows one to obtain “accurate” line shapes, in that the widths are better represented by a Voigt profile, which is the convolution of a Lorentzian natural line shape with that of a Gaussian profile arising from inhomogeneous broadening. From these measurements, it is possible to extract the natural line shape of the resonance through fitting to provide an estimate of inhomogeneous broadening and the lifetime of the associated vibrational transition (the so called natural or homogeneous line shape).3333. S.-L. Chen, L. Fu, W. Gan, and H.-F. Wang, J. Chem. Phys. 144, 034704 (2016). https://doi.org/10.1063/1.4940145 While powerful and capable of providing the best possible spectral resolution at the highest light levels possible, this approach is correspondingly so extremely expensive. As such, at the time of writing this article, the authors are aware of only three such instruments in the world. Furthermore, one must ask what is gained in probing spectra with such high resolution? In some cases, insight into broadening or assignments can be gleaned from the high spectral resolution that would not otherwise be possible;33,3433. S.-L. Chen, L. Fu, W. Gan, and H.-F. Wang, J. Chem. Phys. 144, 034704 (2016). https://doi.org/10.1063/1.494014534. M. A. Upshur, H. M. Chase, B. F. Strick, C. J. Ebben, L. Fu, H. Wang, R. J. Thomson, and F. M. Geiger, J. Phys. Chem. A 120, 2684 (2016). https://doi.org/10.1021/acs.jpca.6b01995 however, for most chemical interfaces, there is already sufficient broadening that the inhomogeneous contribution to the Voigt profile tends to dominate. In fact, two-dimensional (2D) IR spectroscopy35,3635. C. Yan, J. E. Thomaz, Y.-L. Wang, J. Nishida, R. Yuan, J. P. Breen, and M. D. Fayer, J. Am. Chem. Soc. 139, 16518 (2017). https://doi.org/10.1021/jacs.7b0660236. D. E. Rosenfeld, Z. Gengeliczki, B. J. Smith, T. D. P. Stack, and M. D. Fayer, Science 334, 634 (2011). https://doi.org/10.1126/science.1211350 and 2D-SFG work37–3937. W. Xiong, J. E. Laaser, R. D. Mehlenbacher, and M. T. Zanni, Proc. Natl. Acad. Sci. U.S.A. 108, 20902 (2011). https://doi.org/10.1073/pnas.111505510838. H. Vanselous, A. M. Stingel, and P. B. Petersen, J. Phys. Chem. Lett. 8, 825 (2017). https://doi.org/10.1021/acs.jpclett.6b0302539. K.-i Inoue, S. Nihonyanagi, and T. Tahara, “Ultrafast vibrational dynamics at aqueous interfaces studied by 2D heterodyne-detected vibrational sum frequency generation spectroscopy,” in Coherent Multidimensional Spectroscopy, edited by Cho M. (Springer Singapore, Singapore, 2019), pp. 215–236. have shown that inhomogeneous broadening dominates the line shape in most cases, meaning that the complexities of the interface itself ultimately limit the spectral information one can obtain using second-order spectroscopy. While there is certainly a need for these custom systems in advancing SFG methods and in cases where such a high spectral resolution is essential, for many interfaces, especially liquids, other means of generating narrowband light are typically sufficient.

G. Second-harmonic bandwidth compression

In some cases, the central wavelength of the upconversion light needs to be very different from the fundamental beam.4040. Y. Rao, D. Song, N. J. Turro, and K. B. Eisenthal, J. Phys. Chem. B 112, 13572 (2008). https://doi.org/10.1021/jp802499w This can also provide a means to tune to electronic resonances for double resonance spectroscopies,4141. M. Raab, J. C. Becca, J. Heo, C.-K. Lim, A. Baev, L. Jensen, P. N. Prasad, and L. Velarde, J. Chem. Phys. 150, 114704 (2019). https://doi.org/10.1063/1.5081726 etc., where enhancements and additional information can be extracted from the SFG response. This is particularly important to high repetition rate laser systems (100 s of kHz)42,4342. Z. Heiner, V. Petrov, and M. Mero, APL Photonics 2, 066102 (2017). https://doi.org/10.1063/1.498369143. F. Yesudas, M. Mero, J. Kneipp, and Z. Heiner, J. Chem. Phys. 148, 104702 (2018). https://doi.org/10.1063/1.5016629 where the peak laser powers are lower than those in conventional 1–10 kHz amplifiers. Losses in the upconversion step from filtering or otherwise from these systems could lead to weak optical responses, despite the improved averaging from the higher repetition rate.Conceptually, spectral narrowing by frequency doubling in a thick nonlinear crystal (analogous to the reverse etalon-like line shape mentioned above) should result in narrowband outputs. In this simple case, phase-matching conditions for second-harmonic generation limit the output bandwidth that can be supported and therefore narrows the pulse in frequency. However, in practice, to achieve narrow enough bandwidths, one runs into limitations in damage thresholds and the emergence of other nonlinear phenomena that arise when focusing ultrashort pulses into a material. As such, researchers have developed a means to select a bandwidth of incident light for doubling using highly chirped broadband pulses.4444. F. Raoult, A. C. L. Boscheron, D. Husson, C. Sauteret, A. Modena, V. Malka, F. Dorchies, and A. Migus, Opt. Lett. 23, 1117 (1998). https://doi.org/10.1364/OL.23.001117 By mixing one pulse with a positive chirp with a second pulse having the same, but negative, chirp at a small angle in a nonlinear crystal [Fig. 5(a)], one can use the instantaneous bandwidth that is temporally overlapped [Fig. 5(b)] for the two pulses to gate the generation of second-harmonic light to a small portion of the bandwidth. Given the bandwidth that is doubled is small as determined by the temporal overlap in the crystal, phase matching conditions are easily satisfied and conversion efficiencies of the temporally overlapped bandwidths as high as 90% can be achieved while providing a bandwidth reduction as much as a factor of 120.4545. T. L. Courtney, N. T. Mecker, B. D. Patterson, M. Linne, and C. J. Kliewer, Opt. Lett. 44, 835 (2019). https://doi.org/10.1364/OL.44.000835 As such, the light radiated in the phase-matched direction is narrowband, time-symmetric, and frequency doubled relative to the original beam. These methods can readily be combined with etalon methods and further amplification schemes to generate time asymmetric pulse shapes with high efficiencies.4646. X. Liu, B.-H. Li, Y. Liang, W. Zeng, H. Li, C. Zhou, Z. Ren, and X. Yang, Rev. Sci. Instrum. 92, 083001 (2021). https://doi.org/10.1063/5.0056050The benefit of this approach is that a spectral bandwidth as narrow as ∼3 cm−1 can be achieved.4545. T. L. Courtney, N. T. Mecker, B. D. Patterson, M. Linne, and C. J. Kliewer, Opt. Lett. 44, 835 (2019). https://doi.org/10.1364/OL.44.000835 By adjusting the delays between the pulses, one can select the central wavelength of the doubled light, thereby providing some spectral tunability of the upconversion pulse. The fact that the narrowband light is higher frequency due to the doubling process makes this approach appealing to those seeking to perform double resonance SFG experiments or work in different detection windows. These bluer upconversion wavelengths also mean that the radiated SFG is correspondingly blue-shifted. This has the potentially negative side effect of making detection more difficult since optics designed to work in the UV (e.g., lenses, filters, polarizers, waveplates, gratings, etc.) are typically fewer, more expensive, and have reduced throughputs. Similarly, CCD cameras and other detector efficiencies tend to drop off quickly in the UV region unless specialized coatings or compositions are specified.

H. Pulse shaping

What if we wanted to have arbitrary control over the pulse to specify any of the time-domain waveforms discussed above? To do so, we need to be able to independently manipulate the phase and amplitude of each spectral component in the broadband upconversion laser pulse. This necessitates separating the pulse into wavelength components, modifying them individually, and reassembling the pulse in time.4747. A. M. Weiner, Opt. Commun. 284, 3669 (2011). https://doi.org/10.1016/j.optcom.2011.03.084 This, as alluded to above, has an analogy to the way a monochromator works where we resolve the pulse into frequency components over a spatial coordinate. However, instead of simply filtering the output with a slit and using the transmitted light as is, we want to reassemble the pulse in space and time by traversing the same optical components, only in reverse.To apply a phase or amplitude mask, one needs the individual frequency components focused on what is known as the Fourier plane. This is a unique location where the individual frequency components in the upconversion pulse can be manipulated without affecting others. This is typically accomplished with what is known as a 4f-pulse shaper.4747. A. M. Weiner, Opt. Commun. 284, 3669 (2011). https://doi.org/10.1016/j.optcom.2011.03.084 The 4f-refers to the fact that the distances between four key optics described below are separated by a focal length, f. A basic 4f-pulse shaper consists of a dispersive element(s) (e.g., a grating) and a focusing element(s) (e.g., a lens or a curved mirror), as sketched in Fig. 6. The incident beam is diffracted by the grating into various orders—the first-order diffraction should be the most intense to carry the majority of the light. The dispersed light then is focused onto the Fourier plane with a focal element of one’s choosing. The distance between the grating and the focusing elements is f and the distance from the focusing elements to the Fourier plans is also f. At the Fourier plane, one can adjust the amplitude (intensity of light at a given wavelength), or phase (discussed more below) using a range of approaches. The light can then either propagate through a matching arm in a transmission geometry (as shown in Fig. 6) or back reflect through the same optics in reflection geometry. The choice of transmission or reflection is often dictated by the optical elements placed at the Fourier plane.A basic 4f-pulse shaper is sketched in Fig. 6; the first portion of this sketch parallels the monochromator approach discussed above. The difference in a 4f-shaper is that the light is then either returned through the same optics (back-reflected) or transmitted through a matching focusing element and grating places at distances given by f. This key step of reassembling the pulse back to the time-domain after spectral manipulation, provides well-defined pulses, quality beam modes, and pulses free from chirp (spatial or otherwise). The most basic form of pulse shaping is achieved by applying a mechanical slit at the Fourier plane to select a small region of the bandwidth (e.g., amplitude shaping). This has been used to great effect to generate ps laser pulses from broadband fs laser pulses to study a range of interfaces.48–5248. J. F. D. Liljeblad and E. Tyrode, J. Phys. Chem. C 116, 22893 (2012). https://doi.org/10.1021/jp306838a49. B. Doughty, P. Yin, and Y.-Z. Ma, Langmuir 32, 8116 (2016). https://doi.org/10.1021/acs.langmuir.6b0164350. B. Xu, Y. Wu, D. Sun, H.-L. Dai, and Y. Rao, Opt. Lett. 40, 4472 (2015). https://doi.org/10.1364/OL.40.00447251. Y. Rao, M. Comstock, and K. B. Eisenthal, J. Phys. Chem. B 110, 1727 (2006). https://doi.org/10.1021/jp055340r52. L. Fu, J. Liu, and E. C. Y. Yan, J. Am. Chem. Soc. 133, 8094 (2011). https://doi.org/10.1021/ja201575e Using this approach, researchers have made improvements to select multiple spectral windows at once to perform polarization-resolved measurements more quickly.5353. P. M. Kearns, Z. Sohrabpour, and A. M. Massari, Opt. Express 24, 19863 (2016). https://doi.org/10.1364/OE.24.019863 The main drawback in using slits as the shaping medium is that the reproducibility is governed by the ability to adjust the slit width and position, which is then limited by a micrometer and the skill of the researcher or motors that manipulate the slit width and position. In most cases, this is done manually, so swapping between broadband higher power pulses and narrowband pulses is slow and requires pulse characterization before and after tuning to accurately retrieve the SFG spectrum. Additionally, pulse shaping with a slit provides only amplitude control over the light, meaning one can only generate time-symmetric upconversion pulses with approximately Gaussian temporal characteristics. Furthermore, ruled diffraction gratings typically used in these systems are lossy and the choice of blaze angle and groove density, which are key to maximizing both throughput and dispersion, are somewhat limited by those available from a handful of manufacturers.

What if we want to manipulate more than just the amplitudes? To do this, we need a way to adjust the phase of individual frequencies of light by forcing them to interact differently with a medium at the Fourier plane. As an example, placing a material such as glass in the Fourier plane but as only interact with a part of the pulse bandwidth causes light to travel at a different speed on both ends of the spectrum. This introduces a linear phase that translates into a time-delay between the interacted and un-interacted parts of the pulse when re-assembled. Controlling this interaction variably across the spectrum can be done in a variety of ways using optical modulators placed at the Fourier plane where the phases can be adjuste

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