We demonstrate that broadband electronic optical activity can be measured with supercontinuum light pulse generated by a femtosecond pump (800 nm). It is the self-heterodyned detection technique that enables us to selectively measure the real (optical rotatory dispersion, ORD) or imaginary (circular dichroism, CD) part of the chiroptical susceptibility by controlling the incident polarization state. The single-shot-based measurement that is capable of correcting power fluctuations of the continuum light is realized by using a fast CCD detector and a polarizing beam splitter. Particularly, non-differential scheme used does not rely on any polarization-switching components. We anticipate that this broadband CD/ORD spectrometry with intrinsically ultrafast time-resolution will be applied to a variety of ultrafast chiroptical dynamics studies.
© 2011 OSA
Optical activity (OA) spectroscopy including CD and ORD, due to its high structure-sensitivity, has long served as a useful probe for studying structures of biomolecules and chiral compounds . Nevertheless, the extremely weak signal has made time-resolved optical activity measurement quite difficult. Over the past decades, only a few research groups with their own optical designs have successfully performed such transient CD/ORD experiments in the ultrafast time domain [2–13]. As an early attempt, quasi-null detection (QND) method was successfully used to enhance the chiral sensitivity and thereby enabled one to measure nanosecond electronic [4–7] and picosecond vibrational  CD/ORD signals. Later, a retarder (or analyzer) scanning method was also used to measure femtosecond CD/ORD change within a narrow range of frequency [9,10].
Recently, we showed that a femtosecond heterodyned IR OA measurement [14–19] is possible by detecting IR OA free-induction-decay (FID) field created by an impulsive excitation pulse (much like in pulsed NMR experiment). This time-domain approach has notable advantages over the conventional frequency-domain techniques based on differential absorption measurement with polarization modulation scheme. First, the IR OA FID is an ultrashort wave packet carrying the whole OA information, so the time-resolution is intrinsically ultrafast (fs to ps). Second, phase-sensitive detection of the coherent IR OA FID field by employing a Mach-Zehnder interferometric method allows simultaneous characterization of both imaginary (CD) and real (ORD) parts of the chiroptical susceptibility, . Finally, signal-to-noise (S/N) ratio can be greatly enhanced not only because the measurement is non-differential and background-free  but also because the whole spectrum can be obtained without frequency scan .
In principle, the above time-domain OA FID technique experimentally demonstrated in IR frequency domain can be generalized and applied to ultraviolet-visible (UV-vis) electronic CD/ORD measurements. However, such direct extension to the UV-vis frequency range poses a certain difficulty for reliable measurement. Since the method relies on an interferometric detection, it requires high phase stability between the two interfering fields traveling different optical paths. Although such phase problem could be negligible in the mid-IR range (λ~micrometers), it is not for UV-vis fields. Using diffractive optics [20–22] or active piezoelectric transducer control of the interferometer arm [23,24], one may achieve a good phase stability required in UV-vis interferometry, but this is not an easy task at all.
In this work, we for the first time demonstrate that broadband near UV-vis CD/ORD measurement with ultrashort supercontinuum light is feasible by using a self-heterodyned detection method, which is intrinsically free from the phase noise problem. The key idea is that the incident radiation itself is used as not only the excitation field but also the local oscillator for heterodyning, namely, self-heterodyned. At first sight, this approach may appear to be similar to the QND method in that both use the self-heterodyning effect. However, the fundamental difference lies in the fact that the present technique has a single-shot detection capability so that it does not require any polarization modulation technique at all. In the following sections, the working principles of the femtosecond self-heterodyned CD/ORD method and the relevant experimental details based on the single-shot measurement are discussed. To verify the method, we examined CD/ORD of small organometallic complex and DNA-templated helical J-aggregate dye systems.
2.1. Linear polarization chiroptical technique
The chiroptical susceptibility represents the differential optical response of a chiral medium for left- and right-circularly polarized (LCP and RCP) lights. Its real and imaginary parts describe differential phase retardation (ORD) and differential attenuation (CD) of the propagating left- and right-handed helical radiations. These effects essentially transform a linearly polarized beam, which consists of 50% LCP and 50% RCP, into an elliptical one whose major axis slightly rotates. In our previous studies, it has been demonstrated that such chiroptical response signal produced by the linearly polarized excitation field () can bemeasured by detecting the parallel () and perpendicular () electric field spectra (Fig. 1(a) ). We showed that their ratio is directly related to the complex chiroptical susceptibility as 
2.2. Self-heterodyned CD/ORD detection
To characterize and spectra, one might use Fourier-transform spectral interferometry (FTSI) [20–29] that has proven to be a useful method for measuring the phase and amplitude of unknown electric field. However, since the FTSI method based on a Mach-Zehnder-type interferometer utilizes an external local oscillator traveling different optical path from the signal beam path, the phase noise problem caused by the optical path fluctuations becomes a serious obstacle, as the light wavelength is getting shorter. We believed that a possible way to overcome such difficulty is to use self-heterodyned detection scheme, where the signal and local oscillator travel a common optical path and the phase of the local oscillator is fixed with respect to the excitation radiation. The incident radiation excites the chiral molecules to produce the OA FID signal field of which polarization direction is perpendicular to that of the excitation radiation, and simultaneously its orthogonal polarization component is used as the local oscillator that can be heterodyned with the signal field.
Figure 1(b) and 1(c) schematically show the underlying optical processes of the present self-heterodyned method. The CD or ORD is selectively measured here by controlling the polarization state of the incident radiation as elliptical polarization (EP) or rotated-linear polarization (r-LP), respectively. Note that the major axis of the EP is aligned vertically and the r-LP is rotated with a small angle of δ from the vertical axis in a laboratory-fixed frame. The vertical component () of the incident radiation is used as an excitation field, whereas it is its horizontal component () that acts as the local oscillator () after passing through the sample. One may consider the reverse case (; excitation, ; local oscillator source), but its contribution can be safely ignored here because the incident radiation is controlled in such a way that in the present case.
With the chiral signal being heterodyned with , the resultant perpendicular () and parallel () signal components with respect to the vertical axis are spatially separated with a polarizing beam splitter (PBS). Then, a fast CCD detector is used to record those spatially-resolved signals simultaneously. The ratio of the signals detected is given asEq. (4) can be neglected. By using the relationship, derived from Eqs. (1) to (3), Eq. (4) can be rewritten asEq. (5), is selectively measured because is + π/2 or -π/2 (positive or negative sign indicates handedness of the EP used). For the ORD measurement, on the other hand, the incident radiation is controlled to be r-LP (). Consequently, the ORD contribution, i.e., , is then measured. In both cases, the phase difference between the two interfering fields (signal and local oscillator) is always constant and fixed so that there is no phase problem to be resolved.
In practice, due to the fact that the field intensity is very strong, a variable neutral density (ND) filter was used to attenuate the signal such that the attenuated signal intensity equals . In this case, the ratio is given asEq. (6) is quite smaller than unity. Thus, the logarithm of can be approximately written asEquation (7) shows that the CD/ORD signal is enhanced roughly by a factor of 1/θ. A similar enhancement effect was also discussed by Kliger and associates  and Helbing and associates  in their experiments with the QND scheme.
The experimental layout of our spectrometer is shown in Fig. 2 . For near UV-vis supercontinuum (SC) generation, about 0.1% of the fundamental output (centered at 800 nm) from a commercial regenerative amplifier was focused into water contained in a 1 cm-quartz cuvette cell. The injection energy and focal point of the pump pulse were carefully controlled to obtain a stable SC spectrum extended from 750 nm down to 380 nm. Neither pulse compression nor precise chirp determination of the generated SC was made here because the present equilibrium experiment does not need an optimized time resolution. The SC pulse width at the sample is estimated to be roughly a few picoseconds considering dispersions of some materials.
For the CD and ORD measurements, the polarization state of the incident radiation should be differently controlled, i.e. EP and r-LP, respectively. To make the incident radiation EP for CD, a Glan-Taylor polarizer (P) and a home-built strain plate (SP)  were used. The vertically polarized beam after the P transmits through the SP whose strain axis is aligned + 45° (or −45°) to the vertical axis. Due to birefringence of the SP, the SC beam becomes highly eccentric EP with its major axis being retained vertically. The ellipticity (θ) is controllable by varying the strain intensity and it was set to be ~1/10 radian for all the CD measurements – note that the ellipticity is set to be 1/10 radian at 425 nm for Ni-(tartrate)2 solution and at 460 nm for DNA-dye complex solution and that the ellipticity is inversely proportional to the wavelength so that it is about 0.75/10 at 600 nm for DNA-dye solution. On the other hand, r-LP for the ORD can be obtained simply by removing the SP and rotating the P by a small angle δ (≤ 5 deg) from the vertical axis. Since handedness (left or right) of the polarization used just influences the sign of the signal, it can easily be determined by using a reference sample whose signal phase is already known.
The detection scheme is identical for both measurements. After the sample (1 cm path length), the horizontal () and vertical () signals were spatially separated by a PBS (Glan-Thomson type) and then focused with being vertically aligned into the monochromator slit. The spacing between the focused spots at the slit was controlled to be about 1 mm so that the spectrally dispersed beams should separately illuminate up- and down-tracks of CCD (PIXIS 100B, Princeton Instruments) and be simultaneously detected. To avoid the detector saturation, a variable ND filter was used to attenuate the strong vertical signal down to . Each measurement for a single pulse was performed with fast data-acquisition (DAQ) of the CCD synchronized with the laser system. Typical regenerative amplifier runs at 1 kHz, but for realization of shot-by-shot DAQ, the repetition rate was reduced to 200 Hz, which is the maximum rate of our CCD.
For the parallel and perpendicular polarization signals, their spectral responses are different because of polarization dependence of optical components as well as of different detection sensitivity of the two CCD tracks. In addition, frequency dependence of the ellipticity θ(ω) should also be considered in the CD measurement because the phase delay in the SP determining the ellipticity varies with the wavelength. Such spectral dependences, however, can easily be corrected by comparing reference spectra measured in both CD and ORD setups without the sample.
To verify the experimental feasibility of our method, we first considered organometallic complexes, which are ( + ) and (―) forms of Ni-(tartrate)2. Figure 3(a) depicts the electronic CD spectra of the two optical isomers measured with our spectrometer. As expected, the two spectra are mirror-image of each other and the overall spectral features are in quantitative agreement with the results measured by means of commercial CD spectrometer (see the inset of Fig. 3(a)).
The ORD spectra measured at a fixed rotation angle δ = + 5 deg are also plotted in Fig. 3(b). The ORD intensity increases with the sample concentration and the mirror-imaged aspects of the two isomers are found as well. For a negative rotation angle, i.e. δ = −5 deg, the signs of all the ORD spectra are reversed (data are not shown), which proves the phase-sensitive detectability of our technique. Furthermore, our ORD signal also show a quantitative agreement with the results obtained from conventional angle scan method (square dot in Fig. 3(b)), which directly records rotation angles giving a minimum transmission as a function of wavelength by scanning the analyzer. This indicates that the present method is robust and reliable.
Since the current measurement is made on a shot-by-shot basis, each ORD spectrum measured with each SC pulse can be individually recorded and then accumulated for subsequent averaging. Figure 4 shows the ORD spectra obtained by averaging over 1000, 100, 10 and 1 shot measurements. It is interesting to note that such a broadband ORD measurement is achievable even at a single-shot level (see the bottom panel in Fig. 4) without analyzer angle scan or polarization switching. Although the S/N ratio in the single shot spectrum is a bit poor due to comparative weak power of each SC pulse, still it is sufficiently informative to identify the handedness of the sample. A stronger light source would provide greatly improved result.
In section 2, it was theoretically shown that the CD/ORD signal enhancement is determined by the factor, 1/θ. For example, when the rotation angle δ = 1 deg, the enhancement factor (1/θ = cosδ/sinδ) is about 60. Figure 5(a) shows such δ-dependence of the enhanced ORD signal measured at 400 nm with the second harmonic of the main oscillator. As the rotation angle δ decreases, the ORD signal (dots) increases inversely, indicating that the predicted enhancement (dashed lines) is real. In addition, the S/N ratio, obtained from 1000-shot- averaged data measured at 400 nm, is significantly improved and again it is inversely proportional to the rotation angle as well (Fig. 5(b)), which clearly shows that only the chiral signal is amplified without any undesired increase of noise.
Secondly, we studied the completely different chiral system, which is the cyanine dyes bound to an adenine-thymine-rich double helical DNA (see Fig. 6 for the DNA base pair sequence and for the structure of the cyanine dye molecule considered here). Note that each cyanine dye has no molecular chirality, but, due to its helical J-aggregate formation along the minor groove of the DNA acting like a template, it exhibits an induced chiroptical property in the visible frequency range . Figure 6 depicts the electronic CD and ORD spectra of the aqueous buffer solution of the DNA-dye complex, which were measured with the same setup mentioned above. A characteristic Davydov split CD spectral pattern is clearly observed at around 590 nm, which results from exciton couplings between cyanine molecules assembled along the minor groove of the DNA. The ORD spectrum shows a spectroscopic signature of dispersive spectrum, which should be related to the CD via Kramers-Kronig transformation.
One of the distinct features of our method in comparison to previous works is that a single fixed polarization state radiation is used for measuring CD or ORD spectra, which is in stark contrast to the conventional differential technique requiring both left- and right-handed polarizations, e.g. left- and right-circular [2,8,11,12] (or elliptical [3,4,7,13]), or linear polarizations rotated by ± δ [5–7,13]. More specifically, two pulses (one is left, the other right) are needed in the conventional experiments, whereas a single pulse is enough to acquire the complete CD or ORD information in the present case. The two signal components (,) simultaneously detected at the CCD are produced by the same parent incident pulse so that their intensity fluctuations are highly correlated to each other. The OA signal given by their ratio is thus less susceptible to any possible instability of the SC source. An additional benefit from the fixed optical geometry is that there is no need to use any polarization-switching components such as Pockels cell and photoelastic modulator. Thus, one can avoid a stringent alignment procedure required to eliminate any artifacts from imperfect polarization-switching techniques, which makes fabrication of the optical setup far much simpler and easier.
Due to the so-called multiplex advantage, simultaneous detection of the entire spectral components, i.e. spectrum, makes the S/N ratio better. A pioneering work on such broadband transient CD/ORD measurement was carried out by Kliger’s group [3–7]. Using a flash lamp as the probe source and an optical multichannel analyzer, they were able to observe broadband nanosecond CD/ORD changes without frequency scan. Nevertheless, its time-resolution limited by the speed of electronics is relatively poor in comparison to the case of using a coherent optical pulse. Recently, femtosecond CD spectrometer utilizing the SC light similar to the present case was also demonstrated by Trifonov et al. , where perfect polarization control of the broad SC beam into LCP and RCP was found to be crucial for the success of CD measurement. However, our heterodyned method does not suffer from such difficulty because even depolarized SC beam can be transformed into r-LP or EP by the first polarizer P or its combination with the strain plate. Consequently, the broadband CD or ORD is easily obtained, owing to the fixed phase relationship applied to all the frequency components.
Although the present experiment has been limited to the equilibrium CD/ORD measurements so far, it could be easily extended to time-resolved experiments by employing a pump-probe method. According to our preliminary pump-probe experiments with the CCD, the noise level measured at a negative time delay is nominally less than 10−4 for ΔCD = ΔA pump-on-ΔA pump-off and 5 × 10−5 rad for ΔORD = Δφ pump-on-Δφ pump-off, which shows that a fairly small CD/ORD change can be accurately measured in our method. In some cases, however, the transient chiroptical signal is extremely weak so that its discrimination from the static signal could be quite challenging only with the CCD. Our non-switching technique should be of definite use in capturing such a minute pump-induced change because it can be used in combination with a pump-modulation technique [9,10] for further improving the S/N ratio. Note that the conventional difference measurement methods are, however, not easy to introduce such pump-modulation because the circular or elliptical polarization state of the probe radiation should be modulated alternately between left- and right-handed ones.
Nevertheless, time-resolved CD/ORD experiments would still be difficult because of the pump-induced artifacts such as linear birefringence (LB) and linear dichroism (LD), which originate from transient anisotropy of a chiral solution sample, i.e. photoselection problem. In fact, they will affect the CD and ORD, respectively. Furthermore, since the present method relies on a linear or a highly eccentric probe polarization, the measured chiroptical pump-probe signal would be significantly affected by the LB and LD artifacts. However, such contributions can often be eliminated or at least minimized by properly aligning the pump polarization direction to be either parallel or perpendicular to the major-axis of the probe polarization (EP or r-LP) or by making the pump perfectly depolarized.
Before we close this section, it should be mentioned that the relationship between the active- and self-heterodyned measurements of optical activity is quite analogous to that between spectral interferometric detection of two-dimensional (2D) photon echo signal and self-heterodyne-detected 2D pump-probe signal. In our previous studies, the FTSI method based on the heterodyned detection with the external local oscillator was used to characterize the IR OA FID [15–19]. This can be viewed as an active-heterodyned detection because phase difference between the signal and local oscillator was actively controlled. By means of phase-amplitude retrieval procedures, both imaginary (CD) and real (ORD) parts of were simultaneously obtained. In the present self-heterodyned detection, on the other hand, such phase relation is fixed for all frequency components so that either CD or ORD should be independently measured by controlling the polarization state of the incident radiation. It is very interesting to note that the relationship between these active- and self-heterodyned approaches to chiroptical measurement is analogous to that between the self-heterodyned pump-probe (PP)  and the active-heterodyned stimulated photon echo (PE) [20,21,28,33,34] methods used in 2D vibrational or electronic spectroscopy. The former provides information on the absorptive part of the complex 2D response spectrum, whereas the latter both its absorptive and dispersive parts.
The PE method has been widely and preferentially used despite of its phasing problem, because a better S/N ratio is often obtainable by controlling the intensity level of the external local oscillator separately, which is not the case in the 2D PP. In the present case, though it is based on the self-heterodyning technique much like the PP, such improvement of the S/N ratio is achievable by varying θ that is determined by the strain intensity of the SP or the rotation angle (δ). The enhancement factor (1/θ) was optimally set to be ~10 in the present experiments. This is because the detected photon level at a larger enhancement condition becomes too low due to consequent decrease of minor-axis signal intensity (). At such a low light level, the signal is significantly affected by thermal noise of the CCD instead, which deteriorates the S/N ratio. If a stronger SC radiation by tuning pump frequency for SC generation close to the target frequency window were used, fairly good CD/ORD spectra could be obtained even at a single-shot level.
This is the first experimental demonstration proving that the self-heterodyned near UV-vis CD/ORD measurement is achievable using broadband supercontinuum light pulse. Depending on specially controlled polarization state of the incident radiation, the imaginary (CD) or real (ORD) part of is selectively measured. The single-shot CD/ORD measurement is therefore realized through the simultaneous detection of both parallel and perpendicular signal components that are directly associated with . In addition to the quasi-null detection advantage, the self-referencing feature on shot-by-shot basis results in a significant enhancement of the chiral sensitivity. We anticipate that the present spectrometry will be an excellent tool for ultrafast electronic CD/ORD experiments.
This work was supported by a KBSI grant (T31401). MC is grateful for financial support by National Research Foundation (NRF) of Korea funded by the Ministry of Education, Science and Technology (2090078897).
References and links
1. N. Berova, K. Nakanishi, and R. W. Woody, Circular Dichroism: Principles and Applications, 2nd ed. (Wiley-VCH, 2000).
2. X. Xie and J. D. Simon, “Picosecond time-resolved circular dichroism study of protein relaxation in myoglobin following photodissociation of carbon monoxide,” J. Am. Chem. Soc. 112(21), 7802–7803 (1990). [CrossRef]
3. J. W. Lewis, R. A. Goldbeck, D. S. Kliger, X. Xie, R. C. Dunn, and J. D. Simon, “Time-resolved circular dichroism spectroscopy - experiment, theory, and applications to biological systems,” J. Phys. Chem. 96(13), 5243–5254 (1992). [CrossRef]
4. C. F. Zhang, J. W. Lewis, R. Cerpa, I. D. Kuntz, and D. S. Kliger, “Nanosecond circular dichroism spectral measurements - extension to the far-ultraviolet region,” J. Phys. Chem. 97(21), 5499–5505 (1993). [CrossRef]
5. D. B. Shapiro, R. A. Goldbeck, D. Che, R. M. Esquerra, S. J. Paquette, and D. S. Kliger, “Nanosecond optical rotatory dispersion spectroscopy: application to photolyzed hemoglobin-CO kinetics,” Biophys. J. 68(1), 326–334 (1995). [CrossRef]
6. E. Chen, Y. Wen, J. W. Lewis, R. A. Goldbeck, D. S. Kliger, and C. E. M. Strauss, “Nanosecond laser temperature-jump optical rotatory dispersion: application to early events in protein folding/unfolding,” Rev. Sci. Instrum. 76(8), 083120 (2005). [CrossRef]
8. T. Dartigalongue and F. Hache, “Observation of sub-100 ps conformational changes in photolyzed carbonmonoxy-myoglobin probed by time-resolved circular dichroism,” Chem. Phys. Lett. 415(4-6), 313–316 (2005). [CrossRef]
9. C. Niezborala and F. Hache, “Measuring the dynamics of circular dichroism in a pump-probe experiment with a Babinet-Soleil Compensator,” J. Opt. Soc. Am. B 23(11), 2418–2424 (2006). [CrossRef]
10. C. Niezborala and F. Hache, “Conformational changes in photoexcited (R)-(+)-1,1′-bi-2-naphthol studied by time-resolved circular dichroism,” J. Am. Chem. Soc. 130(38), 12783–12786 (2008). [CrossRef]
11. A. Trifonov, I. Buchvarov, A. Lohr, F. Würthner, and T. Fiebig, “Broadband femtosecond circular dichroism spectrometer with white-light polarization control,” Rev. Sci. Instrum. 81(4), 043104 (2010). [CrossRef]
13. J. Helbing and M. Bonmarin, “Vibrational circular dichroism signal enhancement using self-heterodyning with elliptically polarized laser pulses,” J. Chem. Phys. 131(17), 174507 (2009). [CrossRef]
15. H. Rhee, Y.-G. June, J.-S. Lee, K.-K. Lee, J.-H. Ha, Z. H. Kim, S.-J. Jeon, and M. Cho, “Femtosecond characterization of vibrational optical activity of chiral molecules,” Nature 458(7236), 310–313 (2009). [CrossRef]
16. H. Rhee, Y.-G. June, Z. H. Kim, S.-J. Jeon, and M. Cho, “Phase sensitive detection of vibrational optical activity free-induction-decay: vibrational CD and ORD,” J. Opt. Soc. Am. B 26(5), 1008–1017 (2009). [CrossRef]
17. H. Rhee, S.-S. Kim, S.-J. Jeon, and M. Cho, “Femtosecond measurements of vibrational circular dichroism and optical rotatory dispersion spectra,” ChemPhysChem 10(13), 2209–2211 (2009). [CrossRef]
19. H. Rhee, S.-S. Kim, and M. Cho, “Multichannel array detection of vibrational optical activity free-induction-decay,” J. Anal. Sci. Technol. 1(2), 147–151 (2010). [CrossRef]
20. G. D. Goodno and R. J. D. Miller, “Femtosecond heterodyne-detected four-wave-mixing studies of deterministic protein motions. 1. theory and experimental technique of diffractive optics-based spectroscopy,” J. Phys. Chem. A 103(49), 10619–10629 (1999). [CrossRef]
21. T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, “Two-dimensional spectroscopy of electronic couplings in photosynthesis,” Nature 434(7033), 625–628 (2005). [CrossRef]
23. N. Belabas and M. Joffre, “Visible-infrared two-dimensional Fourier-transform spectroscopy,” Opt. Lett. 27(22), 2043–2045 (2002). [CrossRef]
24. T. Zhang, C. N. Borca, X. Li, and S. T. Cundiff, “Optical two-dimensional Fourier transform spectroscopy with active interferometric stabilization,” Opt. Express 13(19), 7432–7441 (2005). [CrossRef]
25. L. Lepetit, G. Cheriaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995). [CrossRef]
26. W. J. Walecki, D. N. Fittinghoff, A. L. Smirl, and R. Trebino, “Characterization of the polarization state of weak ultrashort coherent signals by dual-channel spectral interferometry,” Opt. Lett. 22(2), 81–83 (1997). [CrossRef]
27. S. M. Gallagher, A. W. Albrecht, T. D. Hybl, B. L. Landin, B. Rajaram, and D. M. Jonas, “Heterodyne detection of the complete electric field of femtosecond four-wave mixing signals,” J. Opt. Soc. Am. B 15(8), 2338–2345 (1998). [CrossRef]
28. M. T. Zanni, N. H. Ge, Y. S. Kim, and R. M. Hochstrasser, “Two-dimensional IR spectroscopy can be designed to eliminate the diagonal peaks and expose only the crosspeaks needed for structure determination,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11265–11270 (2001). [CrossRef]
29. S.-H. Lim, A. G. Caster, and S. R. Leone, “Fourier transform spectral interferometric coherent anti-Stokes Raman scattering (FTSI-CARS) spectroscopy,” Opt. Lett. 32(10), 1332–1334 (2007). [CrossRef]
30. R. M. Esquerra, J. W. Lewis, and D. S. Kliger, “An improved linear retarder for time-resolved circular dichroism studies,” Rev. Sci. Instrum. 68(3), 1372–1376 (1997). [CrossRef]
32. C. Kolano, J. Helbing, M. Kozinski, W. Sander, and P. Hamm, “Watching hydrogen-bond dynamics in a β-turn by transient two-dimensional infrared spectroscopy,” Nature 444(7118), 469–472 (2006). [CrossRef]
33. S. H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. U.S.A. 104(36), 14197–14202 (2007). [CrossRef]
34. S. T. Roberts, J. J. Loparo, K. Ramasesha, and A. Tokmakoff, “A Fast-scanning Fourier transform 2D IR interferometer,” Opt. Commun. 284(4), 1062–1066 (2011). [CrossRef]