Two-dimensional electronic spectroscopy

Last updated October 07, 2024

Two-dimensional electronic spectroscopy (2DES) is an ultrafast laser spectroscopy technique that allows the study of ultrafast phenomena inside systems in condensed phase.^[1] The term electronic refers to the fact that the optical frequencies in the visible spectral range are used to excite electronic energy states of the system; however, such a technique is also used in the IR optical range (excitation of vibrational states) and in this case the method is called two-dimensional infrared spectroscopy (2DIR).^[2] This technique records the signal which is emitted from a system after an interaction with a sequence of 3 laser pulses. Such pulses usually have a time duration of few hundred femtosecond (10⁻¹⁵ s) and this high time resolution allows capturing of dynamics inside the system that evolves with the same time scale. The main result of this technique is a two-dimensional absorption spectrum that shows the correlation between excitation and detection frequencies. The first 2DES spectra were recorded in 1998.^[3] 2DES has been combined with photoelectrochemical recordings (PEC2DES) to study charge separation in the photosynthetic complex photosystem I, which is the physiological output signal in contrast to fluorescence.^[4]

Basic concepts about 2DES

Pulse sequence

The pulse sequence in this experiment is the same as 2DIR in which the delay between the first and second pulse is called the coherence time and is usually labeled as $t_{1}$ . The delay between the second and the third pulse is called the population time and it is labeled as $t_{2}$ . The time after the third pulse corresponds to the detection time $t_{3}$ which is usually Fourier transformed by a spectrometer.^{[ clarification needed ]} The interaction with the pulses creates a third-order nonlinear response function $S(t_{1},t_{2},t_{3})$ of the system from which it is possible to extract two-dimensional spectra as a function of excitation and detection frequencies.^[5] Although third-order two-dimensional spectroscopy is historically first and most popular, high-order two-dimensional spectroscopy approaches have also been developed.^[6]^[7]^[8]

2D Signal

A possible way to recover an analytical expression of the response function is to consider the system as an ensemble and deal with the light-matter interaction process by using the density matrix approach.^[5] Such a result shows that the response function is proportional to the product of the three pulses' electric fields. Considering ${\vec {k_{1}}},{\vec {k_{2}}},{\vec {k_{3}}}$ the wave vectors of the three pulses, the nonlinear signal will emit in several directions ${\vec {k_{s}}}$ which are derived from a linear combination of the three wave vectors: ${\vec {k_{s}}}=\pm {\vec {k_{1}}}\pm {\vec {k_{2}}}\pm {\vec {k_{3}}}$ . For this technique, two different signals which propagate in different directions are usually taken into account. When ${\vec {k_{s}}}=-{\vec {k_{1}}}+{\vec {k_{2}}}+{\vec {k_{3}}}$ the signal is called rephasing and when ${\vec {k_{s}}}={\vec {k_{1}}}-{\vec {k_{2}}}+{\vec {k_{3}}}$ the signal is called non-rephasing. An interpretation of these signals is possible by considering the system to be composed of many electric dipoles. When the first pulse interacts with the system, the dipoles start to oscillate in phase. The signal generated from each dipole rapidly dephases due to the different interaction that each dipole experienced with the environment. The interaction with the third pulse, in the case of rephasing, generates a signal which has an opposite temporal evolution with respect to the previous one. The dephasing of the last signal during $t_{3}$ compensates the one during $t_{1}$ . When $t_{3}=t_{1}$ the oscillations are in-phase again and the new signal generated is called photon echo. In the other case, there is no creation of a photon echo and the signal is called non-rephasing.

From these signals is possible to extract the pure absorptive and dispersive spectra which are usually shown in literature. The real part of the sum of these two signals represents the absorption of the system and the imaginary part contains the dispersion contribution.^[9] In the absorptive 2D spectra, the sign of the peak implies different effects. If the transmitted signal is plotted, a positive peak can be associated to a bleaching signal with respect to the ground state or stimulated emission. If the sign is negative, that peak on the 2D spectra is associated with a photoinduced absorption.

Acquisition of the 2DES spectra

The first and the second pulses act as a pump and the third as a probe. The time-domain nonlinear response of the system interferes with another pulse called local oscillator (LO) which allows measurement of both amplitude and phase. Such a signal is usually acquired with a spectrometer which separates the contribution of each spectral components (detection frequencies $\nu _{3}$ ). The acquisition proceeds by scanning the delay $t_{1}$ for a fixed delay $t_{2}$ . Once the scan ends, the detector has acquired a signal as a function of coherence time per each detection frequency $S(t_{1},t_{2},\nu _{3})$ . The application of the Fourier transform along the $t_{1}$ axis allows for recovery of the excitation spectra for every $\nu _{3}$ . The result of this procedure is a 2D map that shows the correlation between excitation ( $\nu _{1}$ ) and detection frequency ( $\nu _{3}$ ) at a fixed population time $S(\nu _{1},t_{2},\nu _{3})$ . The time evolution of the system can be measured by repeating the procedure described before for different values of $t_{2}$ .

There are several methods to implement this technique, all of which are based on the different configurations of the pulses.^[10] Two examples of possible implementations are the "boxcar geometry" and the "partially collinear geometry". The boxcar geometry is a configuration where all the pulses arrive at the system from different directions ${\vec {k_{1}}}\neq {\vec {k_{2}}}\neq {\vec {k_{3}}}$ this property allows acquiring separately the rephasing and non-rephasing signal. The partially collinear geometry is another implementation of this technique where the first and the second pulse coming from the same direction ${\vec {k_{1}}}={\vec {k_{2}}}\neq {\vec {k_{3}}}$ . In this case, the rephasing and non-rephasing signal are emitted in the same direction and it is possible to directly recover the absorptive and dispersive spectra of the system.^[11]^[12]

Information acquired from 2DES

2D spectra contain a lot of information about the system; in particular amplitude, position and lineshape of the peaks are related to different effects that happened inside of the system.

Position of the peaks

Diagonal Peaks

The peaks that stay along the diagonal line in the 2D spectra are called diagonal peaks. These peaks appear when the system emits a signal that oscillates at the same frequency of the excitation signal. These points reflect the information of the linear absorption spectrum.^[9]

Cross Peaks

The peaks that stay out of the diagonal line are called cross peaks. These peaks appear when the system emits a signal that oscillates at a different frequency with respect to the signal used to excite. When a cross peak appears means that two electronic states of the system are coupled because when the pulses pump an electronic state, the system responds with emission from a different energy level. This coupling can be related to an energy transfer or charge transfer process between molecules.^[5]

Lineshape of the peaks

Short population times

Thanks to the high spectral resolution, this technique acquires information based on the two dimensional shape of the peaks. When $t_{2}$ is close to zero the diagonal peaks show an elliptical lineshape as is shown in the figure on the right.^[13] The width along the diagonal line represents the inhomogeneous broadening which contains information about interactions between the environment and the system. If the system is composed of a large amount of identical molecules, each of them interacts with the environment in a different way; this implies that the same electronic state of each molecule assumes different small variations. The value of the linewidth will be close to the one calculated in the linear absorption spectrum. On the other hand, the linewidth along the off-diagonal shows a smaller value with respect to the diagonal one. In this case the spectral broadening contains a contribution from a local interaction inside of the system; for this reason, the width reflects the homogeneous broadening.^[9]

Long population times

For $t_{2}\gg 0$ fs, the shape of the peaks becomes circular and the width along diagonal and off-diagonal line are similar. This phenomenon takes place because all the molecules of the system experienced different local environments and the entire system lose memory of the initial condition. This effect is called Spectral Diffusion.^[14]

Temporal lineshape evolution

The temporal evolution of the lineshape can be evaluated with several methods. One method evaluates the linewidth along diagonal and off-diagonal line separately.^[15] From the two values of the widths it is possible to calculate the flattening as $f={\frac {a-b}{a}}$ where $a$ is the linewidth along diagonal line and $b$ is the linewidth along off-diagonal line. The flattening curve as a function of $t_{2}$ assumes a value close to 1 at $t_{2}=0$ fs ( $a\gg b$ ) and then decreases to zero at $t_{2}\gg 0$ fs ( $a\simeq b$ ). Another method is called Central Line Slope (CLS).^[16]^[17] In this case the positions of the maximum values in the 2D spectra per each detection frequency are considered. These points are then interpolated with a linear function where is possible to extract the slope $\theta$ between this function and the detection axis (x axis). From a theoretical point of view, this value should be 45° when $t_{2}$ is close to zero because the peak is elongated along the diagonal line. When the peak assumes a circular lineshape, the value of the slope goes to zero. The same approach can also be used by considering the positions of the maximum values per each excitation frequency (y axis) and the slope will be 45° at $t_{2}=0$ fs and 90° when the shape becomes circular.^[18]

Related Research Articles

Infrared spectroscopy is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functional groups in solid, liquid, or gaseous forms. It can be used to characterize new materials or identify and verify known and unknown samples. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer which produces an infrared spectrum. An IR spectrum can be visualized in a graph of infrared light absorbance on the vertical axis vs. frequency, wavenumber or wavelength on the horizontal axis. Typical units of wavenumber used in IR spectra are reciprocal centimeters, with the symbol cm⁻¹. Units of IR wavelength are commonly given in micrometers, symbol μm, which are related to the wavenumber in a reciprocal way. A common laboratory instrument that uses this technique is a Fourier transform infrared (FTIR) spectrometer. Two-dimensional IR is also possible as discussed below.

Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum.

Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared spectroscopy, nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy.

<span class="mw-page-title-main">X-ray photoelectron spectroscopy</span> Spectroscopic technique

X-ray photoelectron spectroscopy (XPS) is a surface-sensitive quantitative spectroscopic technique that measures the very topmost 200 atoms, 0.01 um, 10 nm of any surface. It belongs to the family of photoemission spectroscopies in which electron population spectra are obtained by irradiating a material with a beam of X-rays. XPS is based on the photoelectric effect that can identify the elements that exist within a material or are covering its surface, as well as their chemical state, and the overall electronic structure and density of the electronic states in the material. XPS is a powerful measurement technique because it not only shows what elements are present, but also what other elements they are bonded to. The technique can be used in line profiling of the elemental composition across the surface, or in depth profiling when paired with ion-beam etching. It is often applied to study chemical processes in the materials in their as-received state or after cleavage, scraping, exposure to heat, reactive gasses or solutions, ultraviolet light, or during ion implantation.

In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces. Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning "measuring gauge" or "standard".

Tunable diode laser absorption spectroscopy is a technique for measuring the concentration of certain species such as methane, water vapor and many more, in a gaseous mixture using tunable diode lasers and laser absorption spectrometry. The advantage of TDLAS over other techniques for concentration measurement is its ability to achieve very low detection limits. Apart from concentration, it is also possible to determine the temperature, pressure, velocity and mass flux of the gas under observation. TDLAS is by far the most common laser based absorption technique for quantitative assessments of species in gas phase.

In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or chemical compounds by means of spectroscopic techniques. Most often, processes are studied after the illumination of a material occurs, but in principle, the technique can be applied to any process that leads to a change in properties of a material. With the help of pulsed lasers, it is possible to study processes that occur on time scales as short as 10⁻¹⁶ seconds. All time-resolved spectra are suitable to be analyzed using the two-dimensional correlation method for a correlation map between the peaks.

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The rotational spectrum of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy where rotational, vibrational and electronic energy changes occur simultaneously.

<span class="mw-page-title-main">Raman scattering</span> Inelastic scattering of photons by matter

In physics, Raman scattering or the Raman effect is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a molecule as incident photons from a visible laser are shifted to lower energy. This is called normal Stokes-Raman scattering.

Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes and organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, and was developed independently at the same time by Brebis Bleaney at the University of Oxford.

In atomic, molecular, and optical physics, the Einstein coefficients are quantities describing the probability of absorption or emission of a photon by an atom or molecule. The Einstein A coefficients are related to the rate of spontaneous emission of light, and the Einstein B coefficients are related to the absorption and stimulated emission of light. Throughout this article, "light" refers to any electromagnetic radiation, not necessarily in the visible spectrum.

Two-dimensional nuclear magnetic resonance spectroscopy is a set of nuclear magnetic resonance spectroscopy (NMR) methods which give data plotted in a space defined by two frequency axes rather than one. Types of 2D NMR include correlation spectroscopy (COSY), J-spectroscopy, exchange spectroscopy (EXSY), and nuclear Overhauser effect spectroscopy (NOESY). Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of a molecule, particularly for molecules that are too complicated to work with using one-dimensional NMR.

Ultrafast laser spectroscopy is a category of spectroscopic techniques using ultrashort pulse lasers for the study of dynamics on extremely short time scales. Different methods are used to examine the dynamics of charge carriers, atoms, and molecules. Many different procedures have been developed spanning different time scales and photon energy ranges; some common methods are listed below.

A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10¹³ Hz to approximately 10¹⁴ Hz, corresponding to wavenumbers of approximately 300 to 3000 cm⁻¹ and wavelengths of approximately 30 to 3 μm.

Two-dimensional infrared spectroscopy is a nonlinear infrared spectroscopy technique that has the ability to correlate vibrational modes in condensed-phase systems. This technique provides information beyond linear infrared spectra, by spreading the vibrational information along multiple axes, yielding a frequency correlation spectrum. A frequency correlation spectrum can offer structural information such as vibrational mode coupling, anharmonicities, along with chemical dynamics such as energy transfer rates and molecular dynamics with femtosecond time resolution. 2DIR experiments have only become possible with the development of ultrafast lasers and the ability to generate femtosecond infrared pulses.

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI). The original application of NMR to condensed matter physics is nowadays mostly devoted to strongly correlated electron systems. It reveals large many-body couplings by fast broadband detection and should not be confused with solid state NMR, which aims at removing the effect of the same couplings by Magic Angle Spinning techniques.

Two dimensional correlation analysis is a mathematical technique that is used to study changes in measured signals. As mostly spectroscopic signals are discussed, sometime also two dimensional correlation spectroscopy is used and refers to the same technique.

Laser linewidth is the spectral linewidth of a laser beam.

Spectral line shape or spectral line profile describes the form of an electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. Actual line shapes are determined principally by Doppler, collision and proximity broadening. For each system the half-width of the shape function varies with temperature, pressure and phase. A knowledge of shape function is needed for spectroscopic curve fitting and deconvolution.

The Elliott formula describes analytically, or with few adjustable parameters such as the dephasing constant, the light absorption or emission spectra of solids. It was originally derived by Roger James Elliott to describe linear absorption based on properties of a single electron–hole pair. The analysis can be extended to a many-body investigation with full predictive powers when all parameters are computed microscopically using, e.g., the semiconductor Bloch equations or the semiconductor luminescence equations.

References

↑ Cho, Minhaeng (2009). Two-dimensional Optical Spectroscopy. CRC Press.
↑ Hamm, Peter (2011). Concepts and methods of 2d infrared spectroscopy. Zanni, Martin T. Cambridge: Cambridge University Press. ISBN 9781139040884. OCLC 710992325.
↑ Hybl, J. D.; Albrecht, A. W.; Faeder, S. M. G.; Jonas, D. M. (1998). "Two-dimensional electronic spectroscopy". Chem. Phys. Lett. 297: 307–313.
↑ López-Ortiz, Manuel; Bolzonello, Luca; Bruschi, Matteo; Fresch, Elisa; Collini, Elisabetta; Hu, Chen; Croce, Roberta; van Hulst, Niek F.; Gorostiza, Pau (2024-08-21). "Photoelectrochemical Two-Dimensional Electronic Spectroscopy (PEC2DES) of Photosystem I: Charge Separation Dynamics Hidden in a Multichromophoric Landscape". ACS Applied Materials & Interfaces. 16 (33): 43451–43461. doi:10.1021/acsami.4c03652. ISSN 1944-8244. PMC 11345722 . PMID 39121384.
1 2 3 S. Mukamel (2000). "Multidimensional Femtosecond Correlation Spectroscopies of Electronic and Vibrational Excitations". Annual Review of Physical Chemistry. 51: 691–729. Bibcode:2000ARPC...51..691M. doi:10.1146/annurev.physchem.51.1.691. PMID 11031297.
↑ Turner, D. B.; Nelson, K. A. (2010). "Coherent measurements of high-order electronic correlations in quantum wells". Nature. 466 (7310): 1089–1092.
↑ Zhang, Z.; Wells, K. L.; Seidel, M. T.; Tan, H.-S. (2013). "Fifth-order three-dimensional electronic spectroscopy using a pump–probe configuration". J. Phys. Chem. B. 117 (49): 15369–15385.
↑ Kefer, Oskar; Kolesnichenko, Pavel V.; Buckup, Tiago (2024). "Two-dimensional coherent electronic spectrometer with switchable multi-color configurations". Rev. Sci. Instrum. 95: 023003.
1 2 3 Cho, Minhaeng; Brixner, Tobias; Stiopkin, Igor; Vaswani, Harsha; Fleming, Graham R. (Feb 2006). "Two Dimensional Electronic Spectroscopy of Molecular Complexes". Journal of the Chinese Chemical Society. 53 (1): 15–24. doi:10.1002/jccs.200600002. ISSN 0009-4536.
↑ Fuller, Franklin D.; Ogilvie, Jennifer P. (2015-04-01). "Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy". Annual Review of Physical Chemistry. 66 (1): 667–690. doi: 10.1146/annurev-physchem-040513-103623 . ISSN 0066-426X. PMID 25664841.
↑ Brańczyk, Agata M.; Turner, Daniel B.; Scholes, Gregory D. (2014). "Crossing disciplines – A view on two-dimensional optical spectroscopy". Annalen der Physik. 526 (1–2): 31–49. arXiv: 1307.5855 . doi:10.1002/andp.201300153. ISSN 1521-3889. S2CID 119061334.
↑ Réhault, Julien; Maiuri, Margherita; Oriana, Aurelio; Cerullo, Giulio (2014-12-01). "Two-dimensional electronic spectroscopy with birefringent wedges". Review of Scientific Instruments. 85 (12): 123107. doi:10.1063/1.4902938. hdl: 11311/874164 . ISSN 0034-6748. PMID 25554272. S2CID 10699168.
↑ Kwac, Kijeong; Cho, Minhaeng (2003). "Two-color pump-probe spectroscopies of two- and three-level systems: 2-Dimensional line shapes and solvation dynamics". J. Phys. Chem. A. 107: 5903.
↑ Roberts, Sean T.; Loparo, Joseph J.; Tokmakoff, Andrei (2006-08-22). "Characterization of spectral diffusion from two-dimensional line shapes". The Journal of Chemical Physics. 125 (8): 084502. doi:10.1063/1.2232271. ISSN 0021-9606. PMID 16965024.
↑ Kwac, Kijeong; Cho, Minhaeng (2003). "Two-color pump-probe spectroscopies of two- and three-level systems: 2-Dimensional line shapes and solvation dynamics". J. Phys. Chem. A. 107: 5903.
↑ Lazonder, Kees; Pshenichnikov, Maxim; Wiersma, Douwe (2006). "Easy interpretation of optical two-dimensional correlation spectra". Opt. Lett. 31 (22): 3354. doi:10.1364/OL.31.003354.
↑ Roberts, Sean; Loparo, Joseph; Tokmakoff, Andrei (2006). "Characterization of spectral diffusion from two-dimensional line shapes". J. Phys. Chem. 125 (8): 084502. doi:10.1063/1.2232271.
↑ Šanda, František; Perlík, Václav; Lincoln, Craig N.; Hauer, Jürgen (2015-11-05). "Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy". The Journal of Physical Chemistry A. 119 (44): 10893–10909. doi:10.1021/acs.jpca.5b08909. ISSN 1089-5639. PMC 4637928 . PMID 26463085.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Cho, Minhaeng (2009). Two-dimensional Optical Spectroscopy. CRC Press.

[2] Hamm, Peter (2011). Concepts and methods of 2d infrared spectroscopy. Zanni, Martin T. Cambridge: Cambridge University Press. ISBN 9781139040884. OCLC 710992325.

[3] Hybl, J. D.; Albrecht, A. W.; Faeder, S. M. G.; Jonas, D. M. (1998). "Two-dimensional electronic spectroscopy". Chem. Phys. Lett. 297: 307–313.

[4] López-Ortiz, Manuel; Bolzonello, Luca; Bruschi, Matteo; Fresch, Elisa; Collini, Elisabetta; Hu, Chen; Croce, Roberta; van Hulst, Niek F.; Gorostiza, Pau (2024-08-21). "Photoelectrochemical Two-Dimensional Electronic Spectroscopy (PEC2DES) of Photosystem I: Charge Separation Dynamics Hidden in a Multichromophoric Landscape". ACS Applied Materials & Interfaces. 16 (33): 43451–43461. doi:10.1021/acsami.4c03652. ISSN 1944-8244. PMC 11345722 . PMID 39121384.

[Mukamel-5] 1 2 3 S. Mukamel (2000). "Multidimensional Femtosecond Correlation Spectroscopies of Electronic and Vibrational Excitations". Annual Review of Physical Chemistry. 51: 691–729. Bibcode:2000ARPC...51..691M. doi:10.1146/annurev.physchem.51.1.691. PMID 11031297.

[6] Turner, D. B.; Nelson, K. A. (2010). "Coherent measurements of high-order electronic correlations in quantum wells". Nature. 466 (7310): 1089–1092.

[7] Zhang, Z.; Wells, K. L.; Seidel, M. T.; Tan, H.-S. (2013). "Fifth-order three-dimensional electronic spectroscopy using a pump–probe configuration". J. Phys. Chem. B. 117 (49): 15369–15385.

[8] Kefer, Oskar; Kolesnichenko, Pavel V.; Buckup, Tiago (2024). "Two-dimensional coherent electronic spectrometer with switchable multi-color configurations". Rev. Sci. Instrum. 95: 023003.

[Cho-9] 1 2 3 Cho, Minhaeng; Brixner, Tobias; Stiopkin, Igor; Vaswani, Harsha; Fleming, Graham R. (Feb 2006). "Two Dimensional Electronic Spectroscopy of Molecular Complexes". Journal of the Chinese Chemical Society. 53 (1): 15–24. doi:10.1002/jccs.200600002. ISSN 0009-4536.

[10] Fuller, Franklin D.; Ogilvie, Jennifer P. (2015-04-01). "Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy". Annual Review of Physical Chemistry. 66 (1): 667–690. doi: 10.1146/annurev-physchem-040513-103623 . ISSN 0066-426X. PMID 25664841.

[11] Brańczyk, Agata M.; Turner, Daniel B.; Scholes, Gregory D. (2014). "Crossing disciplines – A view on two-dimensional optical spectroscopy". Annalen der Physik. 526 (1–2): 31–49. arXiv: 1307.5855 . doi:10.1002/andp.201300153. ISSN 1521-3889. S2CID 119061334.

[12] Réhault, Julien; Maiuri, Margherita; Oriana, Aurelio; Cerullo, Giulio (2014-12-01). "Two-dimensional electronic spectroscopy with birefringent wedges". Review of Scientific Instruments. 85 (12): 123107. doi:10.1063/1.4902938. hdl: 11311/874164 . ISSN 0034-6748. PMID 25554272. S2CID 10699168.

[13] Kwac, Kijeong; Cho, Minhaeng (2003). "Two-color pump-probe spectroscopies of two- and three-level systems: 2-Dimensional line shapes and solvation dynamics". J. Phys. Chem. A. 107: 5903.

[14] Roberts, Sean T.; Loparo, Joseph J.; Tokmakoff, Andrei (2006-08-22). "Characterization of spectral diffusion from two-dimensional line shapes". The Journal of Chemical Physics. 125 (8): 084502. doi:10.1063/1.2232271. ISSN 0021-9606. PMID 16965024.

[15] Kwac, Kijeong; Cho, Minhaeng (2003). "Two-color pump-probe spectroscopies of two- and three-level systems: 2-Dimensional line shapes and solvation dynamics". J. Phys. Chem. A. 107: 5903.

[16] Lazonder, Kees; Pshenichnikov, Maxim; Wiersma, Douwe (2006). "Easy interpretation of optical two-dimensional correlation spectra". Opt. Lett. 31 (22): 3354. doi:10.1364/OL.31.003354.

[17] Roberts, Sean; Loparo, Joseph; Tokmakoff, Andrei (2006). "Characterization of spectral diffusion from two-dimensional line shapes". J. Phys. Chem. 125 (8): 084502. doi:10.1063/1.2232271.

[18] Šanda, František; Perlík, Václav; Lincoln, Craig N.; Hauer, Jürgen (2015-11-05). "Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy". The Journal of Physical Chemistry A. 119 (44): 10893–10909. doi:10.1021/acs.jpca.5b08909. ISSN 1089-5639. PMC 4637928 . PMID 26463085.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]